GCSE Higher Tier revision

Question 1

Round 135 to 1sf

Answer 1

100

The 1 column is the first significant figure, so round that as normal

Question 2

How do you find the area of a triangle?

Answer 2

base times height divided by 2

Question 3

If boys and girls are in the ration 3:7, what fraction of them are boys?

Answer 3

3

10

Question 4

Which is better value, 9 pens for £1.75, 20 pens for £3.95 or 50 pens for £9.75?

Answer 4

9 pens.

9 pens - each pen is £0.194

20 pens - each pen is £0.1975

50 pens - each pen is £0.195

Question 5

If a sequence is:

3, 7, 11, 15

Which of the following numbers are in the sequence?

(hint - find the nth term)

29 41 31

Answer 5

31.

The nth terms is 4n - 1

If 4n - 1 = 31, n = 8 so the 8th number in the sequence is 31

For 29 and 41, n is a decimal.

Question 6

Which of these will give you a “U” shaped graph?

y = 3x + 1

y = x³ - 5

y = x² + 2x

Answer 6

y = x² + 2x

This is a quadratic graph. y = 3x + 1 is a straight line and y = x³ - 5 is a cubic (“S” shape)

Question 7

Which is further, 17 miles or 27km?

Answer 7

17 miles.

Convert both to the same unit, use 1 mile = 1.6 km

17 x 1.6 = 27.2km

or

27 divided by 1.6 = 16.85 miles

Question 8

A sequence begins with 4, 7, 10, 13, …

Is 500 in the sequence?

Answer 8

No

Find the nth term (3n + 1)

Put 500 = 3n + 1 then solve.

3n + 1 = 500

3n = 499

n = 166.6… so as n is not a whole number, it isn’t in the sequence.

Question 9

In a 4 sided shape, the angles add up to what?

Answer 9

360

Question 10

What do angles around a point add up to?

Answer 10

360

Question 11

If you get 31 out of 40 on a test, what is your percetage score?

Answer 11

72.5%

Get the denominator to 100. (or do 31/40 *100 on a calculator)

Because

31 = 155 = 72.5

40 = 200 = 100

Question 12

3a⁴b⁵ x 5a³b^-1 simplifies to:

Answer 12

15a⁷b⁴

Remember, mulitply numbers, add powers.

Question 13

If a circle has radius ot 5cm, what is its circumference?

Answer 13

31.4cm.

Circumference = pi x diameter.

As the radius = 5cm, the diameter = 10cm

So circumference = pi x 10 = 31.4 cm

Question 14

Which is quicker - 14 metres per second or 30 miles per hour?

You must show WHY!

Answer 14

14 metres per second

14 metres per second

= 840 metres per minute (x 60)

= 50400 metres per hour (x 60 again)

= 50.4 km per hour (divide by 1000)

= 31.5 mph (divide by 1.6)

You could also do these in the oppostie order to 30 instead! (x1.6, x1000, divde by 60, divide by 60)

Question 15

If a polygon is regular, what does this mean?

Answer 15

All the sides and angle are equal

Question 16

How do you find an exterior angle?

Answer 16

Extend a side of the shape, from the extension, draw the angle to the next side. This is the exterior angle.

Question 17

What do the exterior angles of a polygon add up to?

Answer 17

360⁰

Question 18

If the interior angle of a regular polygon is 108⁰, what is the exterior angle?

Answer 18

72

Interior + exterior angle = 180

Question 19

If a regular shape has 20 sides, calculate the size of one exterior angle.

Answer 19

18⁰

360 divided by 20 = 18

Question 20

Solve:

3(2x + 5) = 4(3x - 1)

Answer 20

x = 9.5

4(3x - 1) = 5(2x + 3)

12x - 4 = 10x + 15

2x - 4 = 15

2x = 19

x = 9.5

Question 21

What is 3.75 x 10⁶ as a normal number

Answer 21

3750000

Question 22

What is 6.713 x 10^-4

Answer 22

0.0006713

Question 23

What is (2 x 10⁵)x (8.1 x 10⁶). Give your answer in standard form.

Answer 23

1.62 x 10¹²

Multiply the numbers: 2 x 8.1 = 16.2

Add the powers: 10¹¹

16. 2 x 10¹¹ (as 16.2 is not between 1 and 10, this is not in standard form)
17. 62 x 10¹²

Question 24

Change 3180000 to standard form.

Answer 24

3.18 x 10⁶

Question 25

Convert 0.00014 to standard form

Answer 25

1.4 x 10^-4

Question 26

A t-shirt costs £15 in a 10% off sale. How much was it before the sale?

Answer 26

£16.67

If you said £16.50 you’re thinking of the wrong way.

If it is now reduced by 10%, it is 90% of it’s original price.

To find the find the original: 15 divided by 0.9 (90% as a decimal)

This gives £16.67

Question 27

AThe navy has 23000 people in 2015. This is a increase of 8% from 3 years ago. How many people were in the navy in 2012?

Answer 27

21296

8% increase means it is now 108% (1.08 as a decimal)

23000 divided by 1.08 = 21296

Question 28

Factorising the following expression:

x² - 36

Answer 28

(x + 6)(x - 6)

This is known as a difference of two squares as both x² and 36 are square numbers.

Question 29

Factorise the following expression:

4x² - 49y²

Answer 29

(2x - 7y)(2x + 7y)

Both 4x² and 49y² are both square numbers so you can use the difference of two squares.

Question 30

Make h the subject of

3y - ph = 2h + py

Answer 30

h = 3y- py

2 + p

Because (you might need to scrool down)

3y - ph = 2h + py

(move ph)

3y = 2h + py +ph

(move py)

3y - py = 2h + ph

Factorise the right

3y - py = h(2 + p)

Divide by 2 + p