Expressions & Formulae

Question 1

How do you simplify algebraic expressions by combining like terms?

Answer 1

Combine coefficients of like terms

Example: 3xy + 4z - 2xy + z = xy + 5z

Question 2

What is the rule for multiplying indices?

Answer 2

a^m × a^n = a^(m+n)

This rule applies when the bases are the same.

Question 3

What is the rule for dividing indices?

Answer 3

a^m ÷ a^n = a^(m-n)

This rule applies when the bases are the same.

Question 4

What does a^0 equal?

Answer 4

1

This is true for any non-zero base.

Question 5

How do you use the distributive law to simplify an expression?

Answer 5

Distribute each term in the parentheses

Example: 6(3x - 2y) + 2(x - y) becomes 18x - 12y + 2x - 2y = 20x - 14y

Question 6

How do you factorise the expression 3ax + 4ay?

Answer 6

a(3x + 4y)

Factor out the common term ‘a’.

Question 7

What is the result of simplifying 7x + 2x?

Answer 7

9x

Combine like terms.

Question 8

What is the result of simplifying x^3 + 3x^3?

Answer 8

4x^3

Combine like terms.

Question 9

What is the result of simplifying a - b - 2b?

Answer 9

a - 3b

Combine like terms.

Question 10

What is the result of simplifying 36^3 - 26 + b^3 - 46?

Answer 10

36^3 + b^3 - 72

Combine constant terms.

Question 11

What is the result of expanding 4(2x - 3)?

Answer 11

8x - 12

Apply the distributive law.

Question 12

What is the result of expanding 6(2x + 7y)?

Answer 12

12x + 42y

Apply the distributive law.

Question 13

What is the result of expanding 3x(2 - 4y)?

Answer 13

6x - 12xy

Apply the distributive law.

Question 14

What is the result of expanding 6x - (3 - 4x)?

Answer 14

10x - 3

Apply the distributive law and combine like terms.

Question 15

What is the result of expanding 3x(1 + 2y)?

Answer 15

3x + 6xy

Apply the distributive law.

Question 16

What is the result of expanding -2y(1 - 2x)?

Answer 16

-2y + 4xy

Apply the distributive law.

Question 17

What is the result of expanding 4y(1 - y) + 3y(2 - y)?

Answer 17

4y - 4y^2 + 6y - 3y^2

Combine like terms after expansion.

Question 18

How do you factorise the expression 20x + 15y?

Answer 18

5(4x + 3y)

Factor out the greatest common factor.

Question 19

How do you factorise the expression 3x - x^2?

Answer 19

x(3 - x)

Factor out the common term ‘x’.

Question 20

How do you factorise the expression 4xy - x?

Answer 20

x(4y - 1)

Factor out the common term ‘x’.

Question 21

How do you factorise the expression 6x + 72?

Answer 21

6(x + 12)

Factor out the greatest common factor.

Question 22

What is the result of expanding (x + 7)(x - 3)?

Answer 22

x^2 + 4x - 21

Apply the distributive law (FOIL method).

Question 23

What is the result of adding a common term in the expression 4 + 3?

Answer 23

7

Simply add the constants.

Question 24

What is the result of simplifying using A = 3.1?

Answer 24

3.1

Substitute A with its value.

Question 25

What is the result of simplifying using m = 3.1?

Answer 25

3.1 ## Footnote Substitute m with its value.

Question 26

nd y = 4

Question 27

4 and f = 3

Question 28

0 and w = 0.1

Question 29

- 2b

Question 30

2b + bở - 4b

Question 31

0.2

Question 32

e brackets and

Question 33

- 3)

Question 34

+ Ty)

Question 35

- 4y)

Question 36

- 4x)

Question 37

+ 2y)

Question 38

1 - 2x)

Question 39

- У)

Question 40

2 - У)

Question 41

- 15У

Question 42

- x°

Question 43

72

Question 44

5

Question 45

6

Question 46

7

Question 47

8

Question 48

9

Question 49

How to form equations to solve problems.

Question 50

For example:

Question 51

In four years' time James will be five times as old as he is now.

Question 52

What is his present age?

Question 53

Let his present age be x years.

Question 54

In four years' time his age will be x + 4

Question 55

Five times as old as his present age is 5x

Question 56

SO

Question 57

x + 4 = 5x

Question 58

- x]

Question 59

4 = 4x

Question 60

÷ 4]

Question 61

1 = x

Question 62

James is 1 year old now.

Question 63

How to change the subject of a formula.

Question 64

For example:

Question 65

Make x the subject of y = m Vx + c

Question 66

y = mVx + c

Question 67

- c

Question 68

y - c = mVx

Question 69

÷ m]

Question 70

Y - C = Vx

Question 71

square

Question 72

x =

Question 73

How to expand the product of two linear expressions and simplify

Question 74

the resulting quadratic expression.

Question 75

For example:

Question 76

Expand and simplify (x + 7)(x - 2)

Question 77

(x + 7)(x - 2)

Question 78

= x + 7x - 2x - 14

Question 79

- x2 + 5x - 14

Question 80

How to add and subtract simple algebraic fractions by finding

Question 81

a common denominator.

Question 82

For example:

Question 83

d

Question 84

3

Question 85

dy + 6

Question 86

+

Question 87

- = .

Question 88

4

Question 89

2y

Question 90

4y

Question 91

How to substitute numbers into an expression or formula and find

Question 92

the result following the rules of BIDMAS.

Question 93

For example:

Question 94

Using A = x* - Try

Answer 94

find A when x = 5 and y = 2.4.

Question 95

Using r = 3.142

Question 96

= 3.142 × 52 - 3.142 × 2.42

Question 97

= 3.142 X 25 - 3.142 × 5.76

Question 98

= 78.55 - 18.09792

Question 99

= 60.45208

Question 100

2 Expressions and formulae

Question 101

5

Question 102

The width of a rectangle

Question 103

is w cm. Its length is 4 cm

Question 104

more than its width. If

Question 105

the perimeter of the

Question 106

rectangle is 28 cm

Answer 106

find

Question 107

its length and width.

Question 108

6

Question 109

Make x the subject of

Question 110

these equations:

Question 111

a

Question 112

y = mx + c

Question 113

b

Question 114

y = x + 2

Question 115

x + c

Question 116

y =

Question 117

P - c

Question 118

7

Question 119

8

Question 120

9

Question 121

Expand and simplify:

Question 122

a

Question 123

(x + 5)(x + 1)

Question 124

(x - 3)(x + 4)

Question 125

d

Question 126

(x + 2)(x - 6)

Question 127

(x - 3)(x - 8)

Question 128

(x + 5)2

Question 129

Write as a single

Question 130

fraction:

Question 131

+

Question 132

2e

Question 133

5

Question 134

1

Question 135

2x

Question 136

b

Question 137

3

Question 138

d

Question 139

4

Question 140

d

Question 141

+

Question 142

8p

Question 143

Using the formula

Question 144

s = ut +

Question 145

Zat

Answer 145

find s

Question 146

when u = 20

Answer 146

a = 2.5

Question 147

and t = 15.

Question 148

37