Questions from Notes

Question 1

Solving an equation with an x on both sides.
4 - 8x = -27 - 4x

Answer 1

4 - 8x = -27 - 4x
-8x + 4x = -27 - 4
-4x = -31
-4 x 7.75 = -31
x = 7.75

Question 2

Fully Factorise
24 + 32x

Answer 2

Fully Factorise
24 + 32x
=4 ( 6 + 8x)

Question 3

Fully Factorise
10st^2 - 5s^2

Answer 3

Fully Factorise
10st^2 - 5s^2
=5s (2t^2 - s)

Question 4

Fully Factorise
2r^2 + 25rs^2

Answer 4

Fully Factorise
2r^2 + 25rs^2
=rs (2r + 25s)

Question 5

Fully factorise
Method to use if equation starts with x^2

x^2 + 4x - 12

Answer 5

*Method
find 2 numbers that multiply to -12 and add to 4.
1, -12
-1, 12
2, -6
*-2, 6
3, -4
-3, 4
start with (x ) (x ) then fill in blanks

x^2 + 4x - 12
(x - 2) (x +6)

Question 6

3^-2

Answer 6

3^-2
=1/3^2
=1/9.

Question 7

What is 5^-1 equal to?

Answer 7

5^-1 is equal to ⅕

Question 8

What is x^-4 equal to?

Answer 8

1/(x^4)

Question 9

What is (2x+3y)^-2 equal to?

Answer 9

1/((2x+3y)^2)

Question 10

What is 2^-4?

Answer 10

2^-4
=1/(2^4) = 1/16

Question 11

What is 16^5/4?

Answer 11

16^5/4
=(16^1/4)^5
=(2)^5
32

Question 12

9^3/2

Answer 12

9^3/2
=(9^1/2)^3
=(3) ^3
=27

Question 13

^3√64^2

Question 14

^4√81^2

Answer 14

^4√81^2
=81^3/4
=(81^1/4)^3
=(3)^3
=27

Question 15

Solve 5x - 2 > 3x +11

Answer 15

5x - 2 > 3x +11
=5x - 3x > 11 + 2
=2x > 13
so, x >13/2
x > 6.5

Question 16

The nth term of a sequence is 2n+1. The nth term of a different sequence is 3n-1. Work out the three numbers that are in both sequences and between 20 and 40.

Answer 16

2n+1: 21, *23, 25, 27, *29, 31, 33, *35, 37, 39

3n-1: 20, *23, 26, *29, 32, *35, 38

Answer: 23, 29, 35

Question 17

Solve 2/3 x 1/5

Answer 17

2/3 x 1/5
=(2x1)/(3x5)
=2/15

Question 18

Solve 2/3 ÷ 1/5

Answer 18

2/3 ÷ 1/5
=2/3 x 5/1
=10/3
=3 1/3

Question 19

Fraction to Percentage.
Find the percentage for 3/8.

Answer 19

3/8
= 0.375 x 100
=37.5%

Question 20

Decimal to Fraction.
Find the fraction for 0.125.

Answer 20

0.125
=125/1000
=1/8

Question 21

Write this ratio in the form n:1

10:4

Answer 21

10:4
n:1 (÷4)
2.5:1

To turn the 4 into a 1, divide by 4. Now divide the 10 by 4 to find n.

Question 22

Write this ratio in the form 1:n

5:12

Answer 22

5:12
1:n (÷5)
1:2.4

Question 23

Write this ratio in the form 1:n

0.5:2

Answer 23

0.5:2
1:n (x 2)
1:4

(to get to this answer you could multiply by 2 or divide by 0.5)

Question 24

What does 1cm to 100m mean as a ratio on a map?

Answer 24

1 : 10 000

Every 1cm on the map equals 10,000cm (or 100m) on the ground.

Question 25

What does 1cm to 1km mean as a ratio on a map?

Answer 25

1 : 100 000

Every 1cm on the map equals 100,000 cm (or 1km) on the ground.

Question 26

What does 1cm to 3km mean as a ratio on a map?

Answer 26

1 : 300 000

Every 1 cm on the map equals 300,000cm (or 3km) on the ground.

Question 27

The number of robins in a woodland area is counted over two different months. In December 15 robins were counted. In January 23 robins were counted. What is the percentage increase of robins in the woodland?

Answer 27

a) the difference between the two numbers is 8
b) 8 ÷ 15 × 100 = 53.3
c) the percentage increase of robins found in the woodland is: 53.3%

Question 28

The number of robins in a woodland in February and March is counted. In February 22 robins were counted. In March 12 robins were counted. What is the percentage decrease of robins in the woodland?

Answer 28

a) the difference between the two numbers is 10
b) 10 ÷ 22 × 100 = 45.4
c) the percentage decrease of robins found in the woodland is: 45.4%

Question 29

Using a multiplier, increase £270 by 20%.

Answer 29

An increase of 20% means I have 120% of the original amount.

120% as a multiplier is 1.2

£270 x 1.2 = £324

Question 30

Using a multiplier, decrease £135 by 7%.

Answer 30

A decrease of 7% means I have 93% of the original amount.

93% as a multiplier is 0.93

£135 x 0.93 = £125.55

Question 31

Reverse Percentage

45% of a number is 36. Find the original number.

Answer 31

Reverse percentage means working backwards to find the original amount, given a percentage of that amount.

45% = 36
÷45 ÷45
1% = 0.8
x100 x100
100% = 80

Question 32

125 ÷ 100 =

Answer 32

125 ÷ 100 = 1.25

Question 33

95 ÷ 100 =

Answer 33

0.95

Question 34

Increase £230 by 30%

Answer 34

230 x 1.3 = 299

Question 35

Decrease £65 by 45%

Answer 35

65 x 0.55 = 34.65

Question 36

What is 10% of 365

Answer 36

365 ÷ 10 = 36.5

Question 37

What is 5% of 240?

Answer 37

240 ÷ 10 = 24
24 ÷ 2 = 12

(find 10% then divide by 2)

Question 38

What is 1% of 546?

Answer 38

546 ÷ 100 = 5.46

To find 1% of something (1/100 of something), divide by 100. Remember how to divide by 100 mentally: Just move the decimal point two places to the left. )

Question 39

What is 2% of 75?

Answer 39

75 ÷ 100 x 2 = 1.5

(Find 1% and multiply by 2)

Question 40

What is 20% of 1345?

Answer 40

1345 ÷ 10 x 2
=134.5 x 2
=269

(Find 10% then multiply by 2)

Question 41

What is 25% of 12550?

Answer 41

12550 ÷ 4 = 3,137.5

Question 42

What is 75% of 650?

Answer 42

650 ÷ 4 x 3
=162.5 x 3
=487.5

(find 25% and multiply by 3)

Question 43

What is 43% of 2100?

Answer 43

10% of 2100 = 210.
so 40% = 840
1% = 2100 ÷ 100 = 21
4% is 21 x 3 = 63
84 + 840 = 903

Question 44

FOIL Method

(x = 4) (x + 8)

Answer 44

(x = 4) (x + 8)
=x^2 + 8x + 4x + 32
=x^2 +12x +32

The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product.

Question 45

Factorising Quadratics

x^2 - 25

Answer 45

(√x^2 - √25) (√x^2 + 25)
(x - 5) (x + 5)

Question 46

Factorise:

4x^2 - 121

Answer 46

(√4x^2 - √121) (√x^2 + √25)
(2x - 11) (2x + 11)