### Maths Scope and Sequence

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**Please note:** There is additional information on the Math PACE's in the Ordering: Notes by Subject (Math) page in the Member's Area. It provides a helpful list for ordering of the PACE's in each Level and their relevant Score Keys. There are also links to informative videos explaining some of the subjects as well as if there are any additional items to purchase.

### Primary and secondary pre-credit level PACEs

### Secondary credit level PACEs

##### Maths 1001-1012

**Maths 1001-1012**

**1001 **Counting 1-5: groups of how many; Numbers 1-5: write how many

**1002 **Counting 1-9: groups of how many; Numbers 6-9: identify how many objects in a group

**1003 **Addition 1 - 5: Add 1, 2, 3 and 4 more; Vertical Addition; Word Problems; Colour

**1004 **Addition 6-9: Add 1, 2, 3 and 4 more; Vertical addition, Word problems

**1005 **Subtraction: Take away, Facts; Add and subtract 1, 2, 3 and 4; Vertical subtraction, Word problems

**1006 **Subtraction 6-9: Take away, Facts; Add and subtract 1, 2, 3 and 4; Vertical subtraction, Word problems

**1007 **Write 0: Addition of zero; Commutative aspect of addition; Addition and Subtraction facts – 1-9; Maze, Group of ten, names for ten; Numbers 1-20: Count, Write

**1008 **Group of ten: names for ten, tens and ones; Addition: sums from 10-18; Numbers 1 -30: count, write, Dot-to-dot; Pairs of numbers, Addition facts 5-18; Subtraction facts 0-9, the calendar

**1009 **Number 1-100: count, write; Dot-to-dot, 2 digit addition; Addition facts 2-18, Subtraction: differences 1-9 from 2 digit numbers

**1010A **To add 5 cent pieces, 10 cent pieces and, 20 cent pieces; to learn shorter and longer; to tell time; to obey people who rule over me

**1011A **To learn number words; to learn about cups and litres; to know a circle and a square; to know a triangle and a rectangle; to learn to make new friends

**1012 **Numerical similarities and differences; More or less; Before, after, between; Quantities, more and less; Number line addition and subtraction, 0-9, money

##### Maths 1013-1024

**Maths 1013-1024**

**1013 **Numbers 1-100: count, write; Count by 10s; Circle, square, triangle, rectangle, cones; Count by 2s and 10s; Dot-to-dot; Number order, before and after; Vertical and horizontal operations; Add and subtract 2 numbers; Word problems; Recognise circle, square, rectangle, triangle and cone; Writing number words; recognise symbols +, - & =

**1014 **Addition and subtraction; Circle, square, triangle, rectangle, cones; Review number order – before, after, between; Add 3 digit numbers vertically and horizontally; Review counting, 1s, 2s, 10s; Count by 5s; Add one number to a multiple of 10; Word problems; Complete patterns of geometric shapes; Before, after or between

**1015 **Review adding 3 numbers; Add and subtract multiples of 10; Review before, between after, counting by 2s, 5s, 10s; Even and odd numbers; Review adding 1 digit to multiples of 10; Add 3 digits and subtract 2 and 1 digit numbers; Ones and tens; Count and write 101 to 200; Word problems; Before, after & between

**1016 **Review even and odd numbers; Place value – ones and tens; Add and subtract 2 digit numbers; Write and count from 201 to 300; Add and subtract fast; Dot-to-dot; Maths facts timed; Even and odd numbers; See circle, square, triangle, rectangle, cone as everyday objects; Ordinal numbers from first to tenth; Word problems

**1017 **Review: even and odd numbers, place value ones and tens, add and subtract; Place value hundreds; Add and subtract multiples of 100; Add and subtract 3 digit numbers; Write and count from 301 to 400; Dot-to-dot; Match which one (first tenth); Number chart; Even and odd numbers; Review ordinal numbers; Greater than and less than; Word problems

**1018 **Review: ordinal numbers; Counting by 2s, 5s, 10s, even and odd numbers, greater than and less than, addition and subtraction; Count and write from 401 to 500; Know + is plus, - is minus, = is equals; How to “carry” when adding; Work problems; Patterns and geometric shapes; Write which one (first tenth); Place value

**1019 **Addition and subtraction; Dot-to-dot; Count by 2s, 5s & 10s; Comparison between addition and subtraction, with variations; Answering questions from a pictograph; Place value; Add and “carry”; Using graphs to solve problems; Review even and odd, numbers and number words; Word problems; Geometric shapes; Greater than, less than; Number words; Before, after, between; Writing even and odd numbers

**1020 **Add and carry; Write even and odd numbers; Add and subtract very fast; Dot-to-dot; 3 digit addends; Count by 2s, 5s & 10s; Add and carry; Geometric shapes; Write missing numbers In addition and subtraction problems; Learn to “borrow’ and subtract; Word problems; Number words; Before, after and between

**1021 **Review numbers and number words. To add and carry, “borrow” and subtract. Count and write by 2s, 3s, 5s & 10s. Review ordinal numbers; Word problems; Coding; Number to word and word to number

**1022 **To review place value; ones, tens, and hundreds; To add numbers very fast; To add four numbers; To add and carry; To work word problems with carry; To count on a number line; To write numbers that come after, before, and between

**1023 **Tell the time; Dividing time; Dividing a clock face; “Borrow” and subtract; Begin to learn about multiplication, relating it to addition 2x1 digits; Points and lines; Geometric shapes; Word problems

**1024A **To measure how long things are; to compare cups, litres, 2 litre and other containers; to learn about 1’s, 10’s and 100’s

##### Maths 1025-1036

**Maths 1025-1036**

**1025 **Review: counting, addition and subtraction, and arithmetic facts (oral); Subtract multiples of 10; Add and “carry”, “borrow” and subtraction; Relating addition to multiplication; Even and odd numbers; Geometric shapes; Word problems; Telling the time in hour, half-hour, quarter –hour and five minute increments; Before, after and between; Place value 1s, 10s & 100s

**1026 **Count from 501 to 600; Add and “carry”; “Borrow” and subtract development; Dot-to-dot; Count and write by 1s, 2s, 3s,4s, 5s, 10s and 100s; Data table, statistical problems; Multiply 2 by 1-9; Timed multiplication drill; Time; Even / odd numbers; Sequences; Word problems

**1027 **Count and write from 601-700; Count and write by 1s, 2s, 3s, 4s, 5s, 10s, 100s and 1,000s; Place value up to 1,000s; Add and subtract 1s, 10s, 100s, 1,000s; Add and “carry”; “Borrow” and subtract; Count by 2s and 10s forward and backward; Adding developed; Review multiplying by 0s, 1s and 2s; Timed multiplication drill; Ordinal numbers; Number sentences

**1028 **Subtract large numbers; “Borrow’ and subtract; Count and write from 701 to 800; Dot-to-dot; Count and write by 1s, 2s, 3s, 4s, 5s, 10s, 100s and 1,000s; Development of add and “carry” and borrowing in subtraction; Multiplying by 3s; Review multiplying by 0s, 1s, and 2s; Maze

**1029 **Add and subtract; Count and write from 801 to 900; Add and “carry”; “Borrow” and subtraction; Multiplying by 4s; Review multiplying by 0s, 1s, 2s and 3s; Word problems; Multiplication drill; Sets and division; Maze; Colour

**1030 **“Borrow” and subtraction; Number sentences and word sentence matching; Count and write from 901 to 1,000; Dot-to-dot; Add 4 numbers; Copy problems in columns and add; Review counting and multiplication of 0s, 1s, 2,s 3s, 4s and 5s; Multiplication drill; Sets and division; Colour; Number words to the thousands; Word problems

**1031 **Add and “carry’ two times; Roman numerals; Review counting and multiplying by 0s, 1s, 2s,3s, 4s, 5s and 6s; Graphs and charts; “Borrow” and subtract two times; Word problems; Mathematical symbols; Number sequencing; Roman numerals

**1032 **Shapes; Review ordinal numbers; Sets; Compare numbers greater than, less than; Review counting and multiplying by 1s, 2s, 3s, 4s, 5s, 6s and 7s; Sets; Greater than less than; Open and closed shapes; Inside and outside of shapes; Finding geometric shapes in everyday shapes; Writing ordinals (first-tenth)

**1033 **Multiply by 8s; Review counting and multiplying by 1s, 2s, 3s, 4s, 5s, 6s, and 7s; Divide by 2; Forming groups of 2; Even and odd numbers; Add and “carry”; Addition and subtraction charts; Checking subtraction by addition

**1034 **Add two columns of 4 numbers; Add and “carry” two or three columns of 4 numbers; Review multiplying by 1s, 2s, 3s, 4s, 5s, 6s, 7s, and 8s; Multiply by 9s; The Commutative property; Divide by 3; Word problems; Sets

**1035 **Addition and subtraction using a number line; Add and “carry”; “Borrow” and subtract; Fractions – ½; Dividing objects and sets of objects by ½ ;Telling the time; Review counting and multiplying by 1s, 2s, 3s, 4s, 5s, 6s, 7s, 8s and 9s; Adding and subtracting and dividing using a number line; Word problems; Writing odd and even numbers

**1036A **To count coins; to add and subtract cents; to work word problems about money; to love and respect people who help me to do right

##### Maths 1037-1048

**Maths 1037-1049**

**1037 **Review adding 3 numbers; review addition; to add and carry; to borrow and subtract; to review checking subtraction by addition; to review multiplication; to learn to multiply by 10’s; to work word problems

**1038 **To add and carry; to borrow and subtract; to review subtraction; to write numbers in words; to write numbers in expanded form; to review multiplication; to learn to multiply by 11’s; to divide by 1 and 2; to work word problems

**1039 **To add 4 numbers; to add and carry; to borrow and subtract; to review multiplying 0’s through to 11’s; to round a number to the nearest 10; to review dividing by 1 and 2; to check division by multiplication; to divide by 3; to work word problems

**1040 **To add or subtract; to add and carry; to borrow and subtract; to review multiplying 0’s through to 11’s; to multiply and carry; to round a number to the nearest 5 or 10; to review dividing by 1, 2, and 3; to divide by 4; to work word problems

**1041 **To write Roman numerals to 50; to add and carry; to borrow and subtract; to review multiplication; to multiply and carry; to divide by 1 to 5; to check division by multiplication; to work word problems

**1042 **To add and subtract; to add and carry; to borrow and subtract; to multiply; to multiply and carry; to divide by 1 to 6; to check division by multiplication; to work word problems

**1043 **To add and subtract; to add and carry; to borrow and subtract; to check addition by subtraction; tocheck subtraction by addition; to multiply; to multiply and carry; to divide by 1 to 7; to check division by multiplication; to divide with remainders; to work word problems

**1044 **To add and subtract; to add and carry; to borrow and subtract; to multiply; to multiply and carry; to divide by 1 to 8; to check division by multiplication; to divide with remainders; to work word problems

**1045 T**o add and carry; to borrow and subtract; to multiply; to multiply and carry; to divide by 1 to 9; to check division by multiplication; to divide with remainders; to work word problems

**1046 **To add and subtract; to add and carry; to borrow and subtract; to check addition by subtraction; to check subtraction by addition; to multiply; to multiply and carry; to learn about fractions; to divide; check division by multiplication; to divide with remainders; to work word problems

**1047 **To do time problems; to multiply and carry; to add and carry and check by subtraction; to borrow and subtract and check by addition; to learn about decimals; to add and subtract decimals; to review numbers that tell which one; to divide; to add and subtract like fractions; to work word problems

**1048A **To tell time; To count dollars and cents; to multiply cents; to count change; to work word problems; to measure length, weight and volume

##### Maths 1049-1060

**Maths 1049-1060**

**1049 **To review adding two- three- and four-digit numbers; To review subtracting two-, three- and four-digit numbers; To write in place value and expanded form to thousands; To write number words to thousands; to review counting by ones through to thousands; to review basic addition, subtraction, multiplication and division facts; to review checking of addition, subtraction and division; To review the basic concept of fractions; To use division to find an equal part of a group; To solve word problems

**1050 **To use place value through to hundred thousands’ place; to write number words to ten thousands; to borrow with zeros; to review adding and subtracting five-digit numbers; to review multiplication; to review how to use division to find a part of a group; to review long division and division with remainders; to learn more about numerators and denominators;; to write ordinal numbers in two ways; to learn about equivalent fractions; to solve word problems – especially learning more about solving multiplication and division problems

**1051 **To review equivalent fractions; to determine the larger of two fractions with the same numerator or the same denominator; to review using division to find a part of a group; to list the factors of a number from the least to the greatest; to learn about prime numbers; to use the commutative property of multiplication; to determine the Greatest Common Factor (GCF); to learn more about multiplying two-digit numbers; to reduce fractions to the lowest terms; to review place value to hundred thousands’ place; to write number words to hundred thousands’; to check long division with remainders; to learn about mixed numbers; to work long division and show the remainders as fractions; to solve word problems

**1052 **To review place value to hundred thousands’ place; to learn to estimate by rounding to the nearest ten; to learn about multiples; to multiply 2- and 3-digit numbers; to divide 3- and 4- digit numbers by 1-digit numbers; to review dividing with remainders and checking; to review dividing with remainders as fractions; to use long division to find a part of a group; to learn to figure probability; to determine if a fraction is in the lowest terms; to learn rules for finding factors; to reduce fractions by using some helpful guidelines for finding the Greatest Common Factor (GCF); to add and subtract like fractions and reduce answers to the lowest terms; to solve word problems by using three easy steps

**1053 **To learn about decimals to tenths’ place; to add and subtract decimals to tenths’ place; to compare large numbers, decimals and fractions, and number sentences using >, <, or =; to review place value through to the hundred thousands’ place; to multiply with 10 and 100 and multiples of 10 and 100; to find the perimeter of a figure or an object; to multiply 3-digit numbers with 3-digit numbers; to review estimating by rounding to the nearest ten; to learn the factoring rule for 9; to reduce fractions by doing the steps mentally; to review adding and subtracting like fractions and reducing answers tothe lowest terms; to divide 3- and 4-digit numbers by 1-digit numbers with remainders as fractions in lowest terms; to review probability; to solve word problems with hidden facts

**1054 **To review comparison of large numbers, decimal fractions, and number sentences using >, <, or =; to learn about decimals to hundredths’ place; to add and subtract decimals to hundredths’ place; to review multiplying 3-digit numbers with 3-digit numbers; to review multiplying with 10 and 100 and multiples of 10 and 100; to estimate by rounding to the nearest hundred; to add and subtract mixed numbers with like fractions and reduce answers to lowest terms; to learn about fractions equal to one; to learn about proper and improper fractions; to change improper fractions to whole or mixed numbers and reduce answers to lowest terms; to solve two-part word problems

**1055 **To review adding and subtracting mixed numbers with like fractions and reducing answers to lowest terms; to change mixed numbers with improper fractions to whole or mixed numbers; to subtract fractions from the whole number 1; to multiply fractions; to begin learning to divide with 2-digit divisors; to review rounding to the nearest 10 and 100; to read and answer questions using line graphs; to review Roman numerals 1-20; to multiply 3-digits with 3-digits with a 0 in the ones’ place; to learn about equivalent decimals; to add and subtract decimals; to learn about percents; to find the area of a figure; to solve word problems

**1056 **To learn about decimals and decimal equivalents to thousandths’ place; to add and subtract decimals to thousandths’ place; to learn Roman numerals to 399; to learn more about dividing with 2-digit divisors; to divide by 10 and 100; to multiply by 3-digit numbers with a 0 in tens’ place; to review changing mixed numbers with improper fractions to whole or mixed numbers; to use borrowing to subtract fractions from whole or mixed numbers; to multiply fractions using cancellation; to find equivalent fractions using multiplication; to learn about points, lines, angles, and polygons; to learn about congruent sides and figures; To solve word problems

**1057 **To use division to check multiplication; to find the average; to read and answer questions about charts; to learn about ratio; to learn that probability is a ratio; to add and subtract fractions and mixed numbers with unlike denominators; to learn more about multiplying fractions using cancellation; to multiply fractions and whole numbers; to review lines, angles and polygons; to learn about lines of symmetry; to define geometric shapes as plane figures or solid figures; to learn about solid figures; to learn about similar figures and compare them with congruent figures; to solve word problems

**1058 **To review addition and subtraction up to 6 digits; to solve addition and subtraction problems whilst being timed; to review finding averages; to review multiplication, including 3 digits times 3 digits, and 2 digits times 4 digits; to solve multiplication problems whilst being timed; to learn more about dividing by 2-digit divisors; to learn to multiply decimals; to complete activities using bar graphs; to learn about parallelograms; to review geometric shapes, lines of symmetry, and congruent figures; to begin learning about volume; to find the Least Common Denominator (LCD); to add and subtract fractions using the LCD; to review multiplication of fractions; to solve word problems

**1059 **To review number comparison by using place value; to review rounding to the nearest 10 and 100; to solve problems whilst being timed; to use subtraction to find the missing addend; to learn more about dividing with 2-digit divisors; to use division to find the missing factor; to change mixed numbers to improper fractions; to multiply mixed numbers with whole numbers, mixed numbers, or fractions; to review addition and subtraction of fractions using the LCD; to review geometric figures and terms; to use place value to compare decimals; to review addition, subtraction, and multiplication of decimals; to round decimals to the nearest whole number; to learn about a.m. and p.m.; to solve word problems

**1060A **To learn to count dollars and cents; to learn the metric system of measurements of length, weight and liquid volume; to learn to be thankful to God and others

##### Maths 1061-1072

**Maths 1061-1072**

**1061 **Place value to hundred millions; Add, subtract 3, 4, 5 digit numbers.; Use number sentences to show commutative and associative properties of addition; Introduce inverse operations; Multiply 2 & 3 digit numbers; Divide by 1 digit divisors & by multiples of 10; Rules for finding factors; Identify prime & composite numbers; Basic concept of fractions, equivalent fractions, and fractions with like denominators; Solve word problems

**1062 **Write number words to hundred millions; Change the value of large numbers by increasing or decreasing one of the digits by a multiple of 10; Multiply 4 digit numbers by 3 digit numbers; Round numbers to the nearest multiple of 1,000; Divide by 2 digit divisors; Learn about commutative and associative properties of addition and multiplication; Learn identity properties of addition and multiplication; Find common factors and determine the GCF; Identify proper, improper, and equivalent fractions; Change improper fractions to whole or mixed numbers; Add/subtract mixed numbers with like fractions and write answers in simplest form; Make and interpret bar graphs; Solve word problems

**1063 **Write numbers in expanded notation by multiplying each digit times its place value; Write numbers in standard notation from expanded notation; Multiply with multiples 10, 100, and 1,000 mentally; Review commutative, associative and identity properties; Divide by 2 digit divisors with larger dividends and quotients; Introduce dividing by 3 digit divisors; Find the average; Learn about equations and equalities; Borrow and subtract fractions from whole or mixed numbers (like fractions); Find equivalent fractions; Use cross products in determining equivalent fractions; Find the Least Common Denominator; Add/subtract mixed numbers with unlike fractions; Use borrowing to subtract mixed numbers with unlike fractions; Learn about decimals through the thousandths’ place; Learn about equivalent decimals; Compare decimals by place value through the thousandths’ place; Add/subtract decimals through the thousandths’ place; Solve word problems

**1064 **Define and work with exponents; Write powers of 10 as exponents; Learn more about rounding to the nearest 10, 100, and 1,000; Estimate products by rounding the factors; Learn more about dividing with 3 digit factors; Find the Least Common Multiple; Add/subtract mixed numbers with unlike fractions; Apply the commutative, associative, and identity properties of addition to fractions; Learn more about ratios; Multiply fractions with fractions and fractions with whole numbers using cancellation; Multiply fractions with mixed numbers using cancellation; Write decimals as fractions in simplest form; Learn about decimals through the ten thousandths’ place; Add/subtract decimals through the ten thousandths’ place; Solve word problems

**1065 **Review exponents; Multiply numbers times powers of 10 using exponents; Write expanded notation using exponents; Compare large numbers by place value; Round large numbers; Estimate sums and differences by rounding large numbers; Determines the function rule by patterns in function tables; Use multiplication to check division; Learn about “mean”; Find the Least Common Multiple of three numbers; Find the Least Common Denominator of three fractions and add; Multiplying fractions; Multiply mixed numbers with whole numbers and mixed numbers with mixed numbers; Learn about ratio and probability*; Compare decimals by place value through the ten thousandths’ place; Multiply decimals through the ten thousandths’ place; Find the area, using decimals as the length and width; Study and compare line graphs and bar graphs; Solve word problems

**1066 **Use the order of operations in evaluating expressions; Substitute numbers for variables in evaluating expressions; Use formula to determine the area of a rectangle; Work long division problems with zero in the quotient; Round whole numbers to the place of greatest value; Learn to use divisibility rules; Use the GCF to solve problems; Review multiplying fractions; Divide whole numbers by fractions and fractions by fractions; Add and subtract whole numbers and fractions; Review multiplying decimals; Round decimals to the nearest whole number; Round decimals to the nearest tenth, hundredth, and thousandth; Define and learn about percents; Solve word problems

**1067 **Study the pattern of a sequence in order to determine the next term of the sequence; Study the pattern for all pairs of numbers of a function table in order to write the function rule as an equation; Use inverse operations to solve for missing number in addition and subtraction equations; Compare unlike fractions by the Least Common Denominator (LCD); Review dividing fractions by fractions and whole numbers by fractions; Divide fractions by whole numbers or mixed numbers; Divide decimals by whole numbers; Multiply and divide decimals by powers of 10 by moving the decimals point; Learn about circle graphs; Solve word problems

**1068 **Know place value through the hundred billions’ place; Read and write numbers through hundred billions’ place; Write in expanded notation through hundred billions by using exponents; Use inverse operations to solve for the missing numbers in multiplication and division equations; Determine if two ratios are equivalent by using cross products; Define proportions; Compare unlike fractions by using cross products; Divide mixed numbers; Divide by decimal divisors; Divide and express remainders as decimals; Solve word problems

**1069 **Review place value and expanded notation through the hundred billions’ place; Review order of operations; Review solving for the missing number using inverse operations; Learn about positive and negative numbers using the number line and the thermometer; Adding, subtracting, multiplying and dividing fractions; Multiply three fractions using cancellation; Learn more about taking a fraction of a whole number; Solve for the missing number in a proportion; Review dividing a decimal; Divide whole numbers when the divisor is greater than the dividend; Change a fraction to a decimal by dividing the numerator by the denominator; Review the relationship between fractions, decimals, and percents; Change a fraction to a percent and a percent to a fraction; Solve word problems

**1070 **Review positive and negative numbers; Write positive and negative numbers in order from least to greatest; Round numbers and find the closest estimate; Find the best equation to use to mentally estimate an answer; Review adding, subtracting, multiplying and dividing decimals; Learn about terminating and repeating decimals; Change fractions to terminating or repeating decimals; Find decimal equivalents for mixed numbers and mixed number equivalents for decimals; Compare decimals, fractions and percents; Use decimal equivalents to find the percent of a number; Use proportions to write ratios as percents; Find what percent one number is of another, Solve word problems

**1071 **Learn more about points, lines, line segments, and rays; Name perpendicular lines and line segments using the symbol ┴; Name parallel lines and line segments using the symbol ║; Name angles in three ways using the symbol <; Identify and compare kinds of angles; Use a protractor to construct angles; Use a protractor to construct angles to a given measure; Name congruent line segments and angles using the symbol = (with ~ above); Classify polygons by the number of sides or angles; Recognise regular polygons; Compare congruent and similar polygons; Learn about lines of symmetry; Identify and compare quadrilaterals; Recognise kinds of angles in quadrilaterals; Plot points for ordered pairs on a grid; Connect the points of ordered pairs to form polygons

**1072 **Find the perimeter of a polygon; Find the length of each side of a regular polygon; Use a formula to find the area of a rectangle; Use a formula to find the area of a parallelogram; Classify triangles by kinds of angles and by the number of degrees in each angle; Use inverse operations to solve for the missing angle measure of a triangle; Describe and identify the parts of a circle; Learn about the relationship between the parts of a circle; Describe and identify solid figures; Compare plane figures and solid figures; Learn about volume and cubic units; Use formula to find the volume of a rectangular prism; Determine whether a given situation is calling for perimeter, area or volume; Solve word problems

##### Maths 1073-1084

**Maths 1073-1084**

**1073 **To practice reading writing whole numbers through to hundred trillions; To review writing powers of ten in standard notation; To review writing numbers in expanded notation using exponents; Review the commutative, associative and identity properties for addition and multiplication; To learn the distributive property ; To review the basic operations of addition, subtraction, multiplication and division; To review comparing and ordering fractions and mixed numbers; To review addition and subtraction of fractions from whole and mixed numbers; To review exponents; To learn to identify and solve for perfect squares and square roots; To review basic number theory and concepts of fractions; To find the prime factors of a number; To solve word problems by estimating answers

**1074 **To review basic concepts of fractions; To review addition and subtraction of mixed numbers; To review changing mixed numbers to improper fractions; To review multiplying and dividing fractions and mixed numbers; To review solving word problems using fractions and mixed numbers; To review the properties of addition and multiplication for fractions; To review naming, comparing and ordering decimals; To review changing decimals to fractions and fractions to decimals; To review adding, subtracting, multiplying and dividing decimals; To review multiplying and dividing decimals by powers of ten; To review identifying terminating and repeating decimals; To review rounding decimals to the nearest tenth, hundredth, and thousandth; to solve word problems by estimating mixed numbers and decimals

**1075 **To rank a list of data; To determine the mean, mode, median and range from a list of data; To identify outliers; To draw frequency tables; To review and expand drawing graphs representing a specific list of data (bar, line, circle and pictographs); To graphically represent and interpret data from various displays including histograms, stem and leaf plots, and box and whisker plots; To collect, analyse and present data about a problem situation involving two data sets; To review and expand learning about probability; To express probability as ratios, decimals, and percents; To construct sample spaces using lists, tree diagrams, and the counting principle; To identify the complement; To find the probability for compound events, both dependent and independent; To distinguish between permutations and combinations and use factorial notation to solve for each; To solve word problems using probability; permutations, and combinations

**1076 **To review and expand using the order of operations for evaluating numeric expressions, whole numbers, fractions and decimals; To review order of operations and expand to include variables; To review variables; To translate word phrases and word problems into numeric expressions for all operations; To translate word phrases and word problems into algebraic expressions; To review and expand evaluating algebraic expressions given the value of its variable; To review learning about equations (open sentences and solutions); To write equations for word sentences; To review and expand solving one-step equations; To solve two-step equations; To review and expand using equations to solve written problems; To review and expand writing a function rule (as an equation) for a function table; To learn about inequalities; to use symbols for less than or equal to( ≤) and greater than or equal to ( ≥); To solve and graph inequalities on a number line

**1077 **To learn about integers; To compare and order integers; To use a number line to model addition and subtraction of integers; To add and subtract positive and negative integers; To multiply and divide positive and negative integers; To read and write equations with integers; To solve equations with integers; To plot and identify plotted points on a coordinate plain; To review negative exponents; To define a set; To learn proper set notation; To draw Venn diagrams

**1078 **To write numbers in scientific notation; To change numbers from scientific notation back to standard form; To describe and recognize rational and irrational numbers; To review ratios and proportions; To describe and solve for equivalent ratios; To solve proportions using tables and cross products; To solve application problems using proportions; To solve word problems using proportions in similar triangles, map scales, unit cost, and unit price; To use the distance formula to solve for distance, rate, and time; To convert between English and metric measures

**1079 **To review changing fractions, decimals, and mixed numbers to equivalent percents; To review changing percents to equivalent fractions and decimals; To review the percent equivalents of commonly used fractions; To memorize the percent equivalents of commonly used fractions; to change fractional percents to fractions and decimals; To learn about percents greater than 100%; To compare, order, and determine equivalent relationships among fractions, decimals and percents; To review and expand finding the percent of a number; To review and expand finding what percent one number is of another; To find a number when a percent of it is known; To solve word problems using percents

**1080 **To review basic geometry concepts: points, line segments, lines and rays; To review angles and kinds of angles: acute, obtuse, right and straight; To review and expand using a protractor to measure angles; To identify the kinds of angles formed by a transversal; To learn to use a compass and straightedge to make geometric constructions; To learn to construct congruent line segments; To learn to construct a perpendicular bisector of a line; To learn to construct and bisect angles; To learn to construct parallel lines; To review classifying triangles by angles and expand to classifying triangles by sides; To learn about the corresponding parts of congruent triangles; To learn to construct congruent triangles; To review and expand learning about polygons up to ten sides; To review classifying quadrilaterals; To learn about the diagonals of quadrilaterals; To determine the measure of the interior angles of a quadrilateral

**1081 **To review and expand learning about congruent and similar polygons; To review plotting the points of the vertices of a polygon on a coordinate plane; To locate the ordered pair of the other vertex on a coordinate plane given the coordinates of three vertices of a square or rectangle; To review calculating the perimeter of polygons; To use formulas to find the perimeters of rectangles and squares; To use the perimeter of a quadrilateral to find a missing dimension; To use a formula to find the area of a rectangle, square, and parallelogram; To calculate the area of irregular shapes; To review the parts of a circle and expand to include arcs and central angles; To use formulas to find the circumference of a circle; To use a formula to find the area of a circle; To review and expand learning about solids (polyhedrons); To compare and contrast the number of faces, vertices, and edgesof three-dimensional figures; To learn how to find the surface area of rectangular, cubic and triangular prisms

**1082 **To review using a formula to find the volume of a rectangular prism; To determine whether a given situation is calling for surface area or volume; To describe the relationship between the edge lengths and the volume of similar prisms; To learn some Biblical principles of finance; To learn to prepare a budget; To learn the value of savings; To learn about the services provided by banks; To examine some Biblical principles to guide investing; To learn about investing money

**1083 **To learn to make change; To use circle graphs with budgets to show decimal and percent relationships; To learn how interest is earned; To learn how interest is charged; To calculate simple and compound interest; To solve problems involving tips, discounts, and sales tax; To calculate profit and loss of sales; To calculate rate of profit and loss; To calculate commission and net proceeds; To calculate rate of commission; To calculate discounts and net prices

**1084A **To use the metric units of length, mass, and volume; To learn the standard units and the derived units; To convert units; To work practical applications using the units; To use the standard metric unit of temperature

##### Maths Overview 1085-1096

**Maths Overview 1085-1096**

**1085** Properties of Numbers To review and expand reading and writing whole numbers through the hundred trillions’ place; To round and estimate with whole numbers; To reinforce the basic operations of addition, subtraction, multiplication, and division ; To solve word problems for the basic operations of addition, subtraction, multiplication, and division ; To review and expand the properties of numbers: commutative, associative, identify, and distributive ; To reinforce basic number theory and fractions; To add, subtract, multiply, and divide fractions and mixed numbers; To name, compare, and order decimals; To review and expand terminating and repeating decimals; To change fractions to decimals and decimals to fractions; To add, subtract, multiply, and divide decimals; To round decimals to specified place values

**1086** Scientific Notation & Exponents To review integers and the absolute value of integers; To use a number line to compare and order integers; To add, subtract, multiply, and divide integers; To write numbers in standard form and in scientific notation; To learn to multiply and divide powers with the same base; To learn to multiply numbers in scientific notation; To use negative and zero exponents; To learn to raise a power to a power; To learn to raise a product to a power; To understand the base of a number system; To convert from the binary and octal systems to the decimal system; To expand the use of perfect squares roots; To use a calculator to find the squares and square roots of numbers; To learn to simplify radicals; To estimate the value of a number that is not a perfect square.

**1087** Algebraic Expressions To translate word phrases and word problems into algebraic expressions; To review and expand using the order of operations for evaluating algebraic expressions; To write equations for word sentences; To solve one-step equations; To solve two-step equations; To learn to add, subtract, multiply, and divide monomials; To solve equations using fractions; To solve problems using formulas as equations; To learn to solve formulas for any variable within the formula; To learn to solve equations using exponents

**1088** Multistep Equations To solve multistep equations; To solve equations containing squares and radicals; To solve inequalities by adding, subtracting, multiplying, and dividing; To review and expand by adding, subtracting, multiplying, and dividing monomials; To learn to add, subtract, multiply, and divide binomials and polynomials; To solve two-step inequalities; To solve word problems using equations; To solve word problems that contain two unknowns.

**1089** Ratios, Rates, Pythagoras & Trigonometry To review the meaning of ratios and proportions; To determine the equality of ratios; To solve proportions using cross products; To calculate rates and unit rates; To solve application problems using proportions in similarity, scaling, unit costs, and related measurement units; To solve word problems using proportions in similarity, scaling, unit costs, and related measurement units; To find the scale factor of a dilation; To use the Pythagorean Theorem to find length of the hypotenuse and legs of right triangles; To use the tangent, sine, and cosine ratios to find the length of the hypotenuse and legs of right triangles.

**1090** Statistics & Probability To learn to use measures of central tendency to analyze a set of data; To make and evaluate frequency tables and line plots; To read graphs correctly; To make and interpret data from various graphs including histograms, bar, line, and circle graphs; stem and leaf plots, and box and whisker plots; To analyze and present data about a problem situation involving two data sets; To review and expand learning about probability; To express probability as ratios, decimals, and percents ; To construct sample spaces using tree diagrams and the counting principle; To review and expand finding the number of permutations and combinations using factorial notation to solve for each; To find combinations using Pascal’s Triangle

**1091** Angles, Polygons & Circles To review and expand basic geometry concepts; To review and expand using a protractor to measure and construct angles; To identify intersecting lines and the angles formed by them; To identify the angles formed when a parallel lines are cut by a transversal; To calculate the measure of an unknown angle based on the relationship between the angles formed when parallel lines are cut by a transversal; To use a compass and straightedge to make geometric constructions; To learn to classify triangles and identify congruent triangles; To review and expand classifying quadrilaterals and polygons by sides and angles; To find the sum of the measure of the interior angles of a polygon; To use formulas to find the area of polygons; To use formulas to find the area of irregular-shaped polygons; To use formulas to find the area and circumference of circles

**1092** To learn to identify three-dimensional figures; To calculate the surface areas of rectangular, cubic, and triangular prisms; To learn the formulas for calculating the surface area of cylinders, pyramids, cones, and sphere; To learn the formulas for calculating the volume of prisms, cylinders, pyramids, cones, and spheres; To calculate the volume of prisms, cylinders, pyramids, cones, and spheres

**1093** Linear Equations To review and expand graphing points on a coordinate plane; To graph ordered pairs on a coordinate plane; To identify the domain and range of a relation; To determine if a relation is a function; To learn to use functional notation; To graph linear equations with two variables on a coordinate plane; To graph vertical and horizontal lines; To find the slope of a line; To learn to identify and write an equation in slope-intercept form; To solve a system of two simultaneous equations by graphing; To graph and describe translations; To graph reflections and identify lines of symmetry; To graph rotations and identify rotational symmetry.

**1094** The Metric System To solve problems in length, weight, and volume using the metric system of measurement; To learn the relationships between the English and metric systems of measurement; To convert the English system to the metric system; To convert the metric system to the English system; To convert Celsius degrees to Fahrenheit degrees; To convert Fahrenheit degrees to Celsius degrees; To convert Celsius degrees to Kelvin

**1095** Percentage and Interest To write fractions and decimals as percents; To write percents as fractions and decimals; To find percents greater than 100%; To find a part of a number when the percent and whole are known; To find a percent of a number when the part and whole are known; To find a number when the percent and part are known; To find percent of increase and decrease; To calculate profit and loss on sales; To calculate markup, amount of discount, sales price, and regular price; To calculate simple and compound interest and find the value of an investment.

**1096** Interest, Insurance and Tax To determine interest payments on loans; To determine sales tax on sales at varying percentages; To determine the basis of property taxes; To calculate property taxes; To define different types of life insurance; To determine basic life insurance rates and policies; To discuss types of automobile insurance

##### Algebra I 1097-1108

**Algebra I 1097-1108**

**1097** Algebraic operations, expressions, coefficients; exponential notation; radicals; simplifying algebraic expressions; positive and negative numbers, polynomials.

**1098** Solving and proving algebraic equations; equations with one unknown; axioms for solving algebraic equations; transposing terms in algebraic equations; simplifying equations by multiplying or dividing; equations with parentheses; solving word problems.

**1099** Review of monomials in addition, subtraction, multiplication, and division; polynomials in proper order in addition, subtraction, multiplication and division; review of basic maths and algebra.

**1100** Using parentheses, brackets, and braces in algebra; multiplying polynomials horizontally; recognising and factoring the difference of two squares; recognizing and factoring a perfect square trinomial; factoring polynomials.

**1101** Fractions: reducing simple fractions, factoring polynomials before canceling, multiplication, factoring polynomials before multiplying, division; addition and subtraction of algebraic fractions; Fractional expressions: complex fractions, evaluating fractional expressions, solving fractional equations, cross multiplying; solving word problems.

**1102** Graphing: number lines, cartesian coordinate system, degree of a polynomial, linear equations of one and two variables; Systems of equations: simultaneous equations, consistent, inconsistent and dependent equations; Solving simultaneous equations algebraically: substitution method, addition method; Solving word problems using systems of simultaneous equations.

**1103** Set theory: set notation, members of a set, finite, infinite and empty sets, subsets, intersection and union, Venn diagrams; Inequalities: symbols of inequality, solving inequalities, graphing solutions sets of inequalities, conjunctions and disjunctions, linear inequalities; systems of inequalities.

**1104** Review of exponents: multiplication, division, cancellation, evaluating exponential terms; Exponents and radicals: exponential terms raised to another power, zero exponents, negative exponents, square roots, fractional exponents, simplifying and combining radical expressions, rationalizing the denominator; Pythagorean theorem.

**1105** Radicals and Incomplete quadratic equations: radical equations, complete and incomplete quadratic equations, solving incomplete quadratic equations, simplifying radical solutions; Factoring and completing the square: solving quadratic equations by factoring, perfect square trinomials, solving quadratic equations by completing the square; the Quadratic formula and word problems.

**1106** True-to-life problems: averages, percents, interest; Geometry and bodies in motion; Numbers and Quantities: algebraic expressions, two-digit numerals, monetary-value problems and two-number problems.

**1107** Ratios and proportions: simplifying ratios, solving proportions, word problems involving proportions; More about formulas: evaluating formulas, direct and indirect variations; More about word problems: work problems, value problems, mixture problems.

**1108** Review of PACE 1097-1107

##### Geometry 1109-1120

**Geometry 1109-1120**

**1109** Types of angles and triangles; Construct triangles; SSS, SAS, ASA and AAS

**1110 **Deductive reasoning; formal proofs. Prove triangle congruence using SSS, SAS, ASA, and AAS Postulates. LL, LA, HA, and HL Theorems in proofs. Recognize auxiliary lines. Prove overlapping triangles congruent.

**1111** Using indirect proofs to prove theorems. Theorems dealing with parallel lines, perpendicular lines, and triangles. Angles formed when a transversal intersects parallel lines. Converse of a theorem. Sum of the angles of a triangle and the resulting corollaries. Construction of angles perpendicular lines and parallel lines.

**1112** Classifications of polygons. Quadrilaterals. Theorems related to parallel lines, transversals, and midpoints.

**1113 **Draw and describe a locus of points and the intersection of loci. Circle Geometry.

**1114** More Circle Geometry.

**1115** Inequalities; Proofs using the Hinge Theorem and its converse; Theorems concerning circles.

**1116 **Review ratios and proportions from Algebra. Properties of proportions. AA Similarity Theorem, Right Triangle Similarity Corollary; Segment proportionalities. Relationship between triangles and parallel lines. SAS and SSS Similarity Theorems.

**1117 **Geometric mean of proportions. Simplifying radicals. The significance of altitude in right angles. Constructing a geometric mean. Pythagorean Theorem. Using the 30-60 Right Triangle Theorem and the Isosceles Right Triangle Theorem. Trigonometric ratios.

**1118** Perimeter of a polygon. Area of a rectangle, parallelogram, triangle, rhombus, and trapezoid. Polyhedrons. Lateral area and total area of a prism, pyramid, cylinder, cone, and sphere. Volume of a prism, pyramid, cylinder, cone, and sphere.

**1119** The coordinate plane. Distance and midpoint formulas with straight lines. The slope-intercept form to graph equations. Parallel or perpendicular lines. Graphing circles. The coordinate system in geometric proofs.

**1120** Transformations; reflecting figures over lines and across points. Properties of isometries. Translation, rotation, and glide reflection. Line, rotational, and point symmetry. Dilations.

##### Algebra II 1121-1132

**Algebra II 1121-1132**

**1121** Set Theory; Developing the Real Number System; Application of Real Number Axioms.

**1122 **Arithmetic Sequences and Series; Geometric Sequences and Series; Open Sentences in One Variable

**1123 **Linear Equations; Graphs and Linear Equations; Systems of Linear Equations

**1124** Reviewing Polynomials; Factoring; Solving Algebraic Expressions

**1125 **Fractions and Operations; Fractions and Equations; Rational Numbers as Decimals

**1126** First-Degree Functions; Second-Degree Functions

**1127** Radicals; Operating with Radicals; More on Radicals and Exponents; Complex Numbers

**1128 **Quadratic Equations; Quadratic Solutions; Polynomial Functions

**1129** Quadratic Relations; The Parabola, Ellipse, and Hyperbola; Quadratic Systems

**1130 **Exponential Functions; Logarithms; Computations and Logarithms

**1131** Permutations; Combinations and Binomial Expansions; Probability

**1132** Matrices; Axioms of Matrices; Determinants and Systems of Equations

##### Trigonometry 1133-1138

**Trigonometry 1133-1138**

**1133 **Review properties of angles and triangles; Learn definitions of the six trigonometric functions for acute angles.; Find the values of the trigonometric functions using a graphing calculator; Establish and use basic trigonometric identities; Show that the values of the trigonometric functions depend only on the angle; Solve problems involving right triangles; Begin a study notebook for trigonometry

**1134 **Review properties of the Cartesian coordinate plane; Measure angles in both degrees and radians; Define the six trigonometric functions for any angle; Understand the trig functions are well-defined; Find reference angles and know how to use them; Use the unit circle to find values of the trig functions; Use identities and quadrants to find missing trig values

**1135 **Convert among speeds associated with a tire; Express intervals of real numbers in interval notation; Graph the sine and cosine functions by plotting points; Graph all six trig functions using a graphing calculator; Find the doman, range and period of a trig function; Determine the amplitude of a sine or cosine function; Identify special points on a graph using a graphing calculator

**1136 **Convert data to a more convenient form; Create a scatter plot for a set of bivariate data; Use sinusoidal regression to model data; Verify trigonometric identities; Learn several more important sets of identities; Define the inverse functions for sine, cosine and tangent; Find angle measures for the length of the sides of a triangle

**1137 **Solve trig equations graphically; Solve trig equations algebraically using the unit circle; Solve trig equations algebraically using the inverse trig functions; To find missing lengths and angle measures using the Law of Sines; To find missing lengths and angle measures using the Law of Cosines; Distinguish among AAS, ASA, SAS, SSS, and the Ambiguous Case; Find the areas of triangles using trigonometry

**1138 **Conclude our study of triangles; Model simple harmonic motion; Learn the polar coordinate system and graph equations in the polar plane; Convert equations and points between rectangular and polar coordinates; Review complex numbers and complex number arithmetic; Graph complex numbers as points in a plane; Multiply complex numbers in polar form and find powers and roots of complex numbers

##### SAT Maths Preparation (Multistrand Option 1)

**SAT Maths Preparation **

**1109** Types of angles and triangles; Construct triangles; SSS, SAS, ASA and AAS

**1110 **Deductive reasoning; formal proofs. Prove triangle congruence using SSS, SAS, ASA, and AAS Postulates. LL, LA, HA, and HL Theorems in proofs. Recognize auxiliary lines. Prove overlapping triangles congruent.

**1113 **Draw and describe a locus of points and the intersection of loci. Circle Geometry.

**1114** More Circle Geometry.

**1116 **Review ratios and proportions from Algebra. Properties of proportions. AA Similarity Theorem, Right Triangle Similarity Corollary; Segment proportionalities. Relationship between triangles and parallel lines. SAS and SSS Similarity Theorems.

**1117 **Geometric mean of proportions. Simplifying radicals. The significance of altitude in right angles. Constructing a geometric mean. Pythagorean Theorem. Using the 30-60 Right Triangle Theorem and the Isosceles Right Triangle Theorem. Trigonometric ratios.

**1120** Transformations; reflecting figures over lines and across points. Properties of isometries. Translation, rotation, and glide reflection. Line, rotational, and point symmetry. Dilations.

**1122 **Arithmetic Sequences and Series; Geometric Sequences and Series; Open Sentences in One Variable

**1123 **Linear Equations; Graphs and Linear Equations; Systems of Linear Equations

**1125 **Fractions and Operations; Fractions and Equations; Rational Numbers as Decimals

**1128 **Quadratic Equations; Quadratic Solutions; Polynomial Functions

**1130 **Exponential Functions; Logarithms; Computations and Logarithms

##### Senior Maths Preparation (Multistrand Option 2)

**Senior Maths Preparation **

**1109** Types of angles and triangles; Construct triangles; SSS, SAS, ASA and AAS

**1110 **Deductive reasoning; formal proofs. Prove triangle congruence using SSS, SAS, ASA, and AAS Postulates. LL, LA, HA, and HL Theorems in proofs. Recognize auxiliary lines. Prove overlapping triangles congruent.

**1111** Using indirect proofs to prove theorems. Theorems dealing with parallel lines, perpendicular lines, and triangles. Angles formed when a transversal intersects parallel lines. Converse of a theorem. Sum of the angles of a triangle and the resulting corollaries. Construction of angles perpendicular lines and parallel lines.

**1112** Classifications of polygons. Quadrilaterals. Theorems related to parallel lines, transversals, and midpoints.

**1113 **Draw and describe a locus of points and the intersection of loci. Circle Geometry.

**1114** More Circle Geometry.

**1117 **Geometric mean of proportions. Simplifying radicals. The significance of altitude in right angles. Constructing a geometric mean. Pythagorean Theorem. Using the 30-60 Right Triangle Theorem and the Isosceles Right Triangle Theorem. Trigonometric ratios.

**1118** Perimeter of a polygon. Area of a rectangle, parallelogram, triangle, rhombus, and trapezoid. Polyhedrons. Lateral area and total area of a prism, pyramid, cylinder, cone, and sphere. Volume of a prism, pyramid, cylinder, cone, and sphere.

**1119** The coordinate plane. Distance and midpoint formulas with straight lines. The slope-intercept form to graph equations. Parallel or perpendicular lines. Graphing circles. The coordinate system in geometric proofs.

**1126** First-Degree Functions; Second-Degree Functions

**1129** Quadratic Relations; The Parabola, Ellipse, and Hyperbola; Quadratic Systems

**1130 **Exponential Functions; Logarithms; Computations and Logarithms

##### Senior Maths 1

**Senior Mathematics 1**

**1 **The **Graphic Calculator:** This unit instructs students in the use of the graphic calculator. The model prescribed for this course is a Texas Instrument graphics calculator number TI83. *Simulated graphic calculators are available also on the Internet as downloadable programs or web-based calculators.*

**2 Variation: **Ratios, rates and rearrangement of formulae; Direct Variation; Joint Variation; Partial Variation; Graphing Variation

**3 Applications of Trigonometric Ratios: **Pythagoras' Theorem; Trigonometry; Angles and Bearings; Contour Maps; the Sine Rule; the Cosine Rule; Areas of Triangles

**4 Arithmetic and Geometric Progressions: **Arithmetic Sequences; arithmetic means; arithmetic series; sum to n terms; Geometric Sequences; geometric means; geometric series; sum to n terms; recurring decimals; difference equations

**5 Univariate Data: **Types of Data; Displaying Data - Charts, tables, stemplots, histograms; Statistical Measures

**6 Indices and Logarithmic Functions: **Index Laws; Solving Equations Involving Indices; Exponential Functions; Logarithmic Functions; Logarithmic Laws; Logarithmic Functions and their Graphs; Logarithms and Modelling; Exponential and Natural Logarithm Functions

**7 Growth and Decay of Money: **Compound Interest; Investments; Depreciation; Annuities; Future Value; Amortisation

**8 Data Descriptors: **Measures of Central Tendency; Measures of Dispersion; Populations and Samples

**9 Relations and Functions: **Relations and Mapping; Functions- testing, notation, domain and range, continuity, sum, difference, quotient and product, absolute value; Periodic Functions; Odd and Even Functions; Composite Functions; Reflections, Dilations, Translations

**10 Periodic Functions: **Radian measure; Tangent Function; Period, Cycle, Amplitude and Frequency; Sine and Cosine Functions; Reciprocal Ratios

**11 Introduction to Differentiation: **Continuity and Limits; Rates of Change; Derivatives of Polynomial Functions; General Rules for Differentiation; Higher Order Derivatives

##### Senior Maths 2

**Senior Maths 2**

**12 Sketching Graphs: **Linear Functions; Modelling Linear Functions; Polynomial Functions; Higher Order Simultaneous Equations; Cubic Functions; Quartic Functions; Rational Functions; Inverse Functions; Graphs of Inverse Functions

**13 Trigonometric Graphs: **Trigonometric Functions in different Quadrants and with Negative Angles; Graphing Trigonometric Functions; Unit Circle and the Tangent; Changing the Parameters; Sketching Trigonometric Functions; Applications

**14 Applications of Derivatives: **Particle Motion in a Straight Line; Applications of Differentiation; Applications of Rates of Change; the Equation of the Tangent and Normal; the Angle Between Two Curves; Increasing and Decreasing Functions; Nature of Stationary Values; Applications of the Derivative

**15 Differentiation Rules: **The Concept of a Limit; the Limit of a Function; the Derivative of a Function; Rules for Differentiation; Piecewise-Defined Functions; the Chain Rule; the Product Rule; the Quotient Rule

**16 Antidifferentiation: **Indefinite Integrals; Integrating the Sum or Difference of Functions; Definite Integrals; Areas Bounded by a Curve; the Calculation of Area

**17 Probability: **Set Notation and Probability Theory; Developing Sample Spaces; Complementary events and Mutually Exclusive Events; the Addition law of Probability; Independent Events; the Multiplication Law of Probability; Conditional Probability

**18 Discrete Probability Distributions: **Random Variables; Probability Distribution of Discrete Random Variables; Graphing Probability Distributions; Expected Values; Expected Value Theorems; the Binomial Probability Distribution; Parameters and their Effects; Expected Values and Standard Deviation

**19 Trigonometric, Exponential and Logarithmic Functions: **Trigonometric Functions; Trigonometric Derivatives; Derivatives of Exponential Functions; the Exponentail Function; Indices and Logarithms; Derivatives of Logarithmic Functions; the Integration of Trigonometric Functions; the Integration of exponential Functions; the Integration of 1/x

**20 Applications of the Integral: **Areas Between Two Curves; Volumes of Revolution; Rates of Change; Differential Equations; Growth and Decay; Applications of Exponential Derivatives

**21 The Normal Distribution: **Continuous Probability Distributions; the Normal Distribution; Probabilities less than 0.5; Solving the Impossible; Confidence Limits

**22 Hypothesis Testing: **Identifying a Hypothesis; Statistical Hypothesis; Testing the Null Hypothesis; the Sign Test; Testing a Hypothesis; Levels of Significance; Hypothesis Testing and the Binomial Distribution; Confidence Intervals

##### Business Math

**Business Math 1-12**

**1** Addition of whole numbers; short cuts for speed in addition; methods for checking addition; horizontal and vertical addition; addition of common fractions; addition of decimal fractions.

**2** Subtraction of whole numbers; methods of checking subtraction; horizontal subtraction; subtraction of common fractions; subtraction of decimal fractions; practical uses of subtraction (account reconciliation, making change).

**3** Multiplication of whole numbers; checking multiplication; multiplication of decimal fractions; multiplication by powers of ten; multiplication of common fractions; application of multiplication to extensions.

**4** Division of whole numbers; checking division; division of decimals; short cuts in division; computing averages; division of fractions and finding unit price.

**5** Working with percent: meaning, changing to equivalent forms and back; rounding numbers; applying the percentage formula.

**6** Hourly wage system; piecework wage system; commission; salary, contract or fee system; deductions; net pay.

**7** Checking (cheque) account; savings account; budget; auto ownership; home ownership.

**8** Property tax; sales tax (US); income tax; FICA tax (US); other taxes (excise, import).

**9** Life insurance: terms, types, premiums, net cost/net gain, mortality tables; home insurance: annual premium, refund on premiums, insurance collection; health insurance; automobile insurance: basic collision and comprehensive, liability, refunds.

**10** Trade discounts: discount rates, series, formula, cash discounts; bank discounts: interest- and noninterest-bearing notes, term of note, discounting notes; retail discounts and selling price: finding the sale price, rate of discount and regular price.

**11** Purchasing merchandise: buying, shipping; profit: gross, net and percent; pricing goods: sales-price and cost-price bases.

**12** Wholesaler: sales invoice, self-balancing account form; promissory note, bankruptcy, commission merchant; manufacturer: cost of manufacturing, distributing factory expense, depreciation, gross and net profit, finding selling price, manufacturer's list price, additional trade discounts.

##### College Basic Math

**College Basic Math**

*Resource book: “Man’s Mathematical Models”, Bill Williams and Gwen Crotts*

**An introduction to various mathematical concepts. This course covers such topics as sets, logic, functions, and mathematical systems.**

**1 Sets I:** A study of sets, symbols, roster and setbuilder notation in defining sets, with emphasis on identifying sets.

**2 Sets II:** A further study of sets: power sets, disjoint sets, intersection and union, relative complements of a set, and unary and binary operations.

**3 Sets III and Logic I:** A completion of sets: (infinite sets) and an introduction to logic, defining statements, and quantifiers.

**4 Logic II:** Defining the truth as a statement, using a Venn diagram, identifying logically true statements, and logically false statements.

**5 Logic III:** Another study of logical reasoning: conditional statements, biconditionals, variations on the conditional, and tautologies.

**6 Deductive Reasoning: **An introduction to deductive reasoning: the validity of arguments, theorems, indirect proofs, and invalid arguments.

**7 Relations and Functions: **A study in relations and functions, with ways of representing functions, inverses, and special functions.

**8 Compositions of Functions and Binary Operations: **A study of the composition of functions and binary operations.

**9 Groups: **A study of groups: definitions, proving theorems about groups, subgroups, and group generators.

**10 From Groups to Fields: **A further study of the isomorphisms of groups, rings and subrings, and integral domains and fields.

##### College Math: Pre-Calculus

**College Maths Pre-Calculus**

**11** To distinguish a function from a relation and state its range and domain; write and use function notation; Combine functions with arithmetic operations including compositions of functions; To find the inverse of a function if it has one

**12 **To identify and graph polynomial functions of degree one and two; To identify and graph the exponential function and its inverse; the logarithmic function; To graph combinations of the functions in objectives one and two

**13** To define and use the six trigonometric functions; To correctly use the trigonometric tables; To reduce angles to a first quadrant angle; To evaluate special function values of 30 – , 45 – , and 60 – degree angles; To evaluate the quadrantal function values

**14** To define the radian unit of measure; To convert radian measure to angle measure, and conversely angle measure to radian measure; To graph the six trigonometric functions

**15** To identify the amplitude of a trigonometric function and graph the functions with various amplitudes; To identify the period of a trigonometric function and graph the functions with various periods; To identify the phase shift of a trigonometric function and graph the functions with various phase shifts; To simplify various trigonometric expressions

**16 **To develop and apply the sum and difference formulas; To develop and apply the double – angle formulas; To develop and apply the half – angle formulas and to develop and apply all multiple angle formulas in identities and equations

**17** To define trigonometric functions with reference to the right triangle; To use the right triangle, trigonometric functions, and parallelogram of forces in applied problems to determine horizontal and vertical components and the resultant; To solve applied problems by using the Laws of Cosines and Sines; To solve navigation problems using the trigonometric functions and Law of Cosines and Sines

**18** To define the inverse trigonometric functions; To graph the inverse functions; To apply the inverse functions to problem situations

**19 **To convert Cartesian coordinates to polar coordinates; To convert polar coordinates to Cartesian coordinates; To graph polar coordinates; To convert equations from Cartesian form to polar form and conversely and to graph polar coordinates; To graph functions that are combinations of other functions; To identify the sine and cos series and compute the values of these functions from the series; To solve equations of higher degree involving the trigonometric functions

**20 **A study of algebraic and trigonometric functions, logarithmic, and exponential functions, trigonometric series and equations, and special applications

##### College Math: Calculus

**College Math Calculus**

**11.01 **Limits; Differentiation; Higher derivatives

**11.02 **Tangents and Normals to Curves; Stationary Points; Practical Applications

**11.03 **Anti-Differentiation; Application of the Anti-Derivative to Motion in a Straight Line

**11.04 **Area Under a Straight Line; Area Under a Curve; The Fundamental Theorem of Calculus; Negative Integral Values; Numerical Integration

**12.01 **Continuity and Limits; Gradients; Chords, Secants and Tangents; The Gradient Function; Derivatives; Functions; Polynomials; Rules for Differentiation: Product Rule; Quotient Rule

**12.02 **Composite Functions and their Derivatives; Inverse Relations and their Derivatives; Implicit Relations and their Derivatives; Reverse Differentiation

**12.03 **The Derivative of *e ^{x }*; Logarithmic Functions; Integration of Exponential Functions; The Derivative of sin

*x*and cos

*x;*Integration of sin

*x*and cos

*x*

**12.04 **Plotting nth Degree Polynomials, n≥3; Plotting Rational Functions

**12.05 **Integration of Special Quotients; Partial Fractions; Integration by Substitution; Integration by Parts; Recursive Form; Areas and Solids of Revolution

**12.06 **The Differential; Differential Equations of the form y' = k.y; Differential Equations of the form y' = a.y + c