Exam prep
BNU1501
FACILITATOR:
PATRICIA HERSELMAN
BNU1501 Exam prep
© Patricia Herselman
,Table of Contents
Chapter 1 – Numbers and working with numbers ....................................................................... 1
Natural numbers ..........................................................................................................................1
Counting numbers .......................................................................................................................1
Negative integers ........................................................................................................................1
Example ........................................................................................................................................2
Priorities ....................................................................................................................................... 3
Priorities and brackets .................................................................................................................3
Laws of operations ...................................................................................................................... 3
Commutative law of addition ...................................................................................................3
Associative law of addition ........................................................................................................3
Example ........................................................................................................................................4
Commutative law of multiplication ..........................................................................................5
Associative law of multiplication ...............................................................................................5
Example ........................................................................................................................................6
Distributive law of multiplication over addition .......................................................................7
Comprehensive example...........................................................................................................8
Decimals ..................................................................................................................................... 9
Using a calculator......................................................................................................................10
Rounding numbers ................................................................................................................... 11
Example ......................................................................................................................................11
Factors ....................................................................................................................................... 12
What is a factor? .......................................................................................................................12
Example ......................................................................................................................................12
The lowest common multiple (LCM) .......................................................................................13
Example ......................................................................................................................................15
Fractions .................................................................................................................................... 16
What is a Fraction? ....................................................................................................................16
Types of fractions .......................................................................................................................16
Example ......................................................................................................................................16
Simplification of fractions .........................................................................................................17
Example ......................................................................................................................................17
The addition and subtraction of fractions .............................................................................18
Example ......................................................................................................................................18
Multiplication of fractions .........................................................................................................19
Example ......................................................................................................................................19
Division of fractions ....................................................................................................................20
Example ......................................................................................................................................20
Variables ................................................................................................................................... 21
Example ......................................................................................................................................22
Addition and subtraction .........................................................................................................25
Example ......................................................................................................................................25
Multiplication and division ........................................................................................................26
Comprehensive example.........................................................................................................27
BNU1501 Exam prep
© Patricia Herselman
, Powers and roots ...................................................................................................................... 28
Powers .........................................................................................................................................28
Exponents ...................................................................................................................................29
Calculator steps .........................................................................................................................30
Laws of exponents .................................................................................................................... 31
Example ......................................................................................................................................32
Roots .......................................................................................................................................... 33
Calculator steps .........................................................................................................................34
Example ......................................................................................................................................35
Ratios, proportions and percentages ..................................................................................... 36
Ratios ...........................................................................................................................................36
Example ......................................................................................................................................36
Example ......................................................................................................................................36
Proportion .................................................................................................................................. 37
Percent ...................................................................................................................................... 37
Example ......................................................................................................................................38
Chapter 2 – Units and measures ................................................................................................. 39
The international system .......................................................................................................... 39
Length .........................................................................................................................................40
Example ......................................................................................................................................41
Perimeter ................................................................................................................................... 42
Rectangles..................................................................................................................................42
Squares........................................................................................................................................43
Triangles ......................................................................................................................................43
Circles ..........................................................................................................................................44
Irregular figures...........................................................................................................................45
Composite figures......................................................................................................................45
Example ......................................................................................................................................46
Area .............................................................................................................................................47
Rectangles..................................................................................................................................47
Squares........................................................................................................................................48
Triangles ......................................................................................................................................49
Circles ..........................................................................................................................................49
Example ......................................................................................................................................50
Volume ........................................................................................................................................53
Cubes ..........................................................................................................................................53
Prisms ...........................................................................................................................................54
Cylinders .....................................................................................................................................54
Conversions and litres ...............................................................................................................55
Example ......................................................................................................................................57
Chapter 3 – Functions and representations of functions ........................................................... 59
Expressions, equations and formulas ...................................................................................... 59
What is a function? ................................................................................................................... 59
Manipulation and solving of equations..................................................................................60
BNU1501 Exam prep
© Patricia Herselman
, Example ......................................................................................................................................61
Changing the subject of a formula ........................................................................................62
Example ......................................................................................................................................62
Linear functions (Straight lines) ................................................................................................ 63
Axes .............................................................................................................................................63
The straight line expression .......................................................................................................65
Drawing straight lines on a graph and Intercepts ................................................................65
Example ......................................................................................................................................66
Slope/gradient ...........................................................................................................................67
Representing a function on a set of axes ..............................................................................67
Example ......................................................................................................................................68
Chapter 4 – Mathematics of finance .......................................................................................... 70
Simple interest ........................................................................................................................... 70
Time value of money ................................................................................................................70
Example ......................................................................................................................................70
Compound interest................................................................................................................... 72
Example ......................................................................................................................................72
Using a financial calculator .....................................................................................................73
Present value ..............................................................................................................................74
Example ......................................................................................................................................74
Annuities .................................................................................................................................... 75
Ordinary annuity ........................................................................................................................75
Ordinary annuity ........................................................................................................................75
The future value of an ordinary annuity .................................................................................75
Using a financial calculator: ....................................................................................................76
Present value of an ordinary annuity......................................................................................77
Example ......................................................................................................................................77
Annuity due ................................................................................................................................78
The future value of an annuity due ........................................................................................78
Present value of an annuity due .............................................................................................78
Perpetuities ................................................................................................................................ 79
Amortisation .............................................................................................................................. 80
Calculator steps .........................................................................................................................81
BNU1501 Exam prep
© Patricia Herselman
BNU1501
FACILITATOR:
PATRICIA HERSELMAN
BNU1501 Exam prep
© Patricia Herselman
,Table of Contents
Chapter 1 – Numbers and working with numbers ....................................................................... 1
Natural numbers ..........................................................................................................................1
Counting numbers .......................................................................................................................1
Negative integers ........................................................................................................................1
Example ........................................................................................................................................2
Priorities ....................................................................................................................................... 3
Priorities and brackets .................................................................................................................3
Laws of operations ...................................................................................................................... 3
Commutative law of addition ...................................................................................................3
Associative law of addition ........................................................................................................3
Example ........................................................................................................................................4
Commutative law of multiplication ..........................................................................................5
Associative law of multiplication ...............................................................................................5
Example ........................................................................................................................................6
Distributive law of multiplication over addition .......................................................................7
Comprehensive example...........................................................................................................8
Decimals ..................................................................................................................................... 9
Using a calculator......................................................................................................................10
Rounding numbers ................................................................................................................... 11
Example ......................................................................................................................................11
Factors ....................................................................................................................................... 12
What is a factor? .......................................................................................................................12
Example ......................................................................................................................................12
The lowest common multiple (LCM) .......................................................................................13
Example ......................................................................................................................................15
Fractions .................................................................................................................................... 16
What is a Fraction? ....................................................................................................................16
Types of fractions .......................................................................................................................16
Example ......................................................................................................................................16
Simplification of fractions .........................................................................................................17
Example ......................................................................................................................................17
The addition and subtraction of fractions .............................................................................18
Example ......................................................................................................................................18
Multiplication of fractions .........................................................................................................19
Example ......................................................................................................................................19
Division of fractions ....................................................................................................................20
Example ......................................................................................................................................20
Variables ................................................................................................................................... 21
Example ......................................................................................................................................22
Addition and subtraction .........................................................................................................25
Example ......................................................................................................................................25
Multiplication and division ........................................................................................................26
Comprehensive example.........................................................................................................27
BNU1501 Exam prep
© Patricia Herselman
, Powers and roots ...................................................................................................................... 28
Powers .........................................................................................................................................28
Exponents ...................................................................................................................................29
Calculator steps .........................................................................................................................30
Laws of exponents .................................................................................................................... 31
Example ......................................................................................................................................32
Roots .......................................................................................................................................... 33
Calculator steps .........................................................................................................................34
Example ......................................................................................................................................35
Ratios, proportions and percentages ..................................................................................... 36
Ratios ...........................................................................................................................................36
Example ......................................................................................................................................36
Example ......................................................................................................................................36
Proportion .................................................................................................................................. 37
Percent ...................................................................................................................................... 37
Example ......................................................................................................................................38
Chapter 2 – Units and measures ................................................................................................. 39
The international system .......................................................................................................... 39
Length .........................................................................................................................................40
Example ......................................................................................................................................41
Perimeter ................................................................................................................................... 42
Rectangles..................................................................................................................................42
Squares........................................................................................................................................43
Triangles ......................................................................................................................................43
Circles ..........................................................................................................................................44
Irregular figures...........................................................................................................................45
Composite figures......................................................................................................................45
Example ......................................................................................................................................46
Area .............................................................................................................................................47
Rectangles..................................................................................................................................47
Squares........................................................................................................................................48
Triangles ......................................................................................................................................49
Circles ..........................................................................................................................................49
Example ......................................................................................................................................50
Volume ........................................................................................................................................53
Cubes ..........................................................................................................................................53
Prisms ...........................................................................................................................................54
Cylinders .....................................................................................................................................54
Conversions and litres ...............................................................................................................55
Example ......................................................................................................................................57
Chapter 3 – Functions and representations of functions ........................................................... 59
Expressions, equations and formulas ...................................................................................... 59
What is a function? ................................................................................................................... 59
Manipulation and solving of equations..................................................................................60
BNU1501 Exam prep
© Patricia Herselman
, Example ......................................................................................................................................61
Changing the subject of a formula ........................................................................................62
Example ......................................................................................................................................62
Linear functions (Straight lines) ................................................................................................ 63
Axes .............................................................................................................................................63
The straight line expression .......................................................................................................65
Drawing straight lines on a graph and Intercepts ................................................................65
Example ......................................................................................................................................66
Slope/gradient ...........................................................................................................................67
Representing a function on a set of axes ..............................................................................67
Example ......................................................................................................................................68
Chapter 4 – Mathematics of finance .......................................................................................... 70
Simple interest ........................................................................................................................... 70
Time value of money ................................................................................................................70
Example ......................................................................................................................................70
Compound interest................................................................................................................... 72
Example ......................................................................................................................................72
Using a financial calculator .....................................................................................................73
Present value ..............................................................................................................................74
Example ......................................................................................................................................74
Annuities .................................................................................................................................... 75
Ordinary annuity ........................................................................................................................75
Ordinary annuity ........................................................................................................................75
The future value of an ordinary annuity .................................................................................75
Using a financial calculator: ....................................................................................................76
Present value of an ordinary annuity......................................................................................77
Example ......................................................................................................................................77
Annuity due ................................................................................................................................78
The future value of an annuity due ........................................................................................78
Present value of an annuity due .............................................................................................78
Perpetuities ................................................................................................................................ 79
Amortisation .............................................................................................................................. 80
Calculator steps .........................................................................................................................81
BNU1501 Exam prep
© Patricia Herselman
