### Maths Scope and Sequence

*Click on the PACE range title to open the scope and sequence text. Click the title again to close the text.*

### 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 2×1 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

##### 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

##### 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

##### 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