# GCSE Calculator Questions 2 (2013/Higher Tier)

This worksheet contains a sample of practice questions based on the 2013 GCSE Higher Level syllabus. Calculators may be used.

Key stage:  KS 4

Curriculum topic:  GCSE Practice Papers

Curriculum subtopic:  Selection of Topics for Calculator Practice

Difficulty level:

### QUESTION 1 of 10

Formula Sheet

Higher Tier

Area of trapezium = ½ (a + b) h

Volume of prism = area of cross-section x length

In any triangle ABC:

Area of triangle = ½ab sinC

Sine rule

 a = b = c sin A sin B sin C

Cosine rule

a2 = b2 + c2 - 2bc cos A

The solutions of ax2 + bx + c = 0, where a ≠ 0, are given by

Ben thinks of a number.

He multiplies it by 3.

He then squares the result.

What number did he first think of?

What is the smallest integer that satisfies this inequality:

5x - 7 > 12 - x

Fatima bakes a small round cake of diameter 11 cm.

She wishes to put a ribbon around the circumference of the cake.

Calculate the least length of ribbon that she can use.

(Just write the number to 3 sig. figs)

Write the following fraction as a decimal:

 9 40

The diagram shows a circle centre C.

Work out the value of angle a.

(Just write the number)

Calculate the value of the following to 3 decimal places:

 √7.36 - 5.14 3.98

The diagram below shows a  triangle PQR.

Use the sine rule to find ∠QPR to 1 dp.

(Just write the number)

3x2 = 19x - 2

x = 6.23

x = 0.407

x = 0.623

x = 0.107

After a 12% reduction in price, a bicycle costs £109.12 in the sale.

How much did it cost in pounds before the sale?

Simplify the following and select the correct answer:

 a + 4 - a - 3 4 8

 1 a + 11 2. 9a + 8 3. 2a + 18 8 32 12

1.

2.

3.

The diagram shows two fair spinners.

Both spinners are spun and the sum of the scores is found.

Calculate the probability that the sum of the scores is 10 or more.

ABCDEFGH is a cuboid.

Select the coordinates of the midpoint of FG.

(5, -1, 3)

(3, 5, -1)

(5½, -1, 3)

(5, 1, 3)

(3, 5, 1)

(-½, 3, 5)

ABCDEFGH is a cuboid.

Calculate the length BH to 3 sig. figs.

Here is a formula.

s = ut + ½at2

Calculate s when u = 6.2 x 102, t = 4.5 and a = 9.8

2.89 × 106

28.9 × 102

2.88 × 103

2.89 × 103

2889 × 103

Eight men can dig a trench in 3 hours.

How long will it take five men to dig a similar trench of the same size?

4 hours 8 mins

13 hours 20 mins

4 hours 48 mins

4 hours 80 mins

5 hours 20 mins

The pilot of a plane wishes to fly due North but there is an 80 mph Easterly wind (i.e. from the East.  The plane's airspeed is 200 mph.  At what bearing must the pilot fly the plane in order to head due North?

(Just write the three figure number)

Solve the equation:

(2x + 1)2 = (x + 5)2

x = -4, -2

x = -4, 2

x = 8, -1

x = 4, 2

x = 4, -2

A cyclist travels 25 kilometres at a speed of 20 km/h and then another 80 km at a speed of 25 km/h.

Calculate the cyclist's average speed for the whole journey in km/h to 1 decimal place.

(Just write the number)

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the interquartile range.

 Stem Leaf 0 7   9 1 1   4   4   7 2 0   3   3   3   9 3 0   4   4 4 4

The diagram shows a solid prism made from a metal with density of 5.8 grams per cm3.

(measurements in cm, but not drawn accurately)

Calculate the mass of the prism in kilograms.

(Just write the number)

Jack's mass increases from 45.6 kg to 52.4 kg.

Calculate the percentage increase in Jack's mass.

(Just write the number to 3 significant figures)

Calculate the side length x to 3 sig. figs.

(Diagram not drawn accurately)

Charlie is experimenting with seedlings and measures the height of his seedling plants after two weeks.  The results are recorded in this frequency table.

Work out the Frequency Density for the 25 ≤ h < 30 class interval.

(Just write the number)

In △ABC above,

c = 14 cm

a = 9.5 cm

∠ABC = 80.5º

Calculate its area in cm2 to 3 s.f.

(Just write the number)

Rearrange the following formula to make a the subject.

s = ut + ½at2

a = (s - ½at²)/t

a = 2(s - ut)/t²

a = sut²

a = ½s - ut²

• Question 1

Ben thinks of a number.

He multiplies it by 3.

He then squares the result.

What number did he first think of?

5.6
EDDIE SAYS
We work backwards, carrying out the inverse of each operation. √432.64 = 20.8
20.8 - 4 = 16.8
16.8 ÷ 3 = 5.6
• Question 2

What is the smallest integer that satisfies this inequality:

5x - 7 > 12 - x

4
EDDIE SAYS
5x - 7 > 12 - x
6x - 7 > 12
6x > 19
x > 19/6 = 3.166666...
Smallest integer greater than 3.16... is therefore 4
• Question 3

Fatima bakes a small round cake of diameter 11 cm.

She wishes to put a ribbon around the circumference of the cake.

Calculate the least length of ribbon that she can use.

(Just write the number to 3 sig. figs)

34.6
EDDIE SAYS
Diameter d = 11cm
Circumference = π × d = π × 11 = 34.5575 cm
• Question 4

Write the following fraction as a decimal:

 9 40

0.225
EDDIE SAYS
9 ÷ 40 = 0.225
• Question 5

The diagram shows a circle centre C.

Work out the value of angle a.

(Just write the number)

42
EDDIE SAYS
Triangle ABC is isosceles because AC and BC are both radii of the circle.
∠ACB = 180° - 2 × 48° = 84°
Angle at circumference is twice angle at centre.
Angle a = ½ of 84° = 42°
• Question 6

Calculate the value of the following to 3 decimal places:

 √7.36 - 5.14 3.98
-0.610
EDDIE SAYS
On the calculator, type:
(√7.36 - 5.14)÷ 3.98 =
-0.609816082 rounds to -0.610 to 3 decimal places.
• Question 7

The diagram below shows a  triangle PQR.

Use the sine rule to find ∠QPR to 1 dp.

(Just write the number)

26.2
EDDIE SAYS
 11 = 8 sin 111° sin ∠QRP

∠QPR = 180° - 111° - ∠QRP
• Question 8

3x2 = 19x - 2

x = 6.23
x = 0.107
EDDIE SAYS
Rearrange to read 3x² - 19x + 2 = 0
Use the quadratic formula, substituting a = 3, b = -19 and c = 2
• Question 9

After a 12% reduction in price, a bicycle costs £109.12 in the sale.

How much did it cost in pounds before the sale?

£124
£ 124
EDDIE SAYS
When we reduce something by 12%, we multiply it by 0.88
109.12 ÷ 0.88 = 124
• Question 10

Simplify the following and select the correct answer:

 a + 4 - a - 3 4 8

 1 a + 11 2. 9a + 8 3. 2a + 18 8 32 12

1.
EDDIE SAYS
Multiply top and bottom of first fraction by 2 to get (2a + 8)/8
Then combine the tops to get 2a + 8 - a + 3 = a + 11
• Question 11

The diagram shows two fair spinners.

Both spinners are spun and the sum of the scores is found.

Calculate the probability that the sum of the scores is 10 or more.

3/16
EDDIE SAYS
There are 4 × 8 = 32 outcomes.
Of these 2+8, 3+7, 3+8, 4+6, 4+7, 4+8 are the only six outcomes that give a sum of 10 or more.
Probability = 6/32 = 3/16.
• Question 12

ABCDEFGH is a cuboid.

Select the coordinates of the midpoint of FG.

(3, 5, -1)
EDDIE SAYS
F is at (3, 5, -2) and G is at (3, 5, 0)
• Question 13

ABCDEFGH is a cuboid.

Calculate the length BH to 3 sig. figs.

6.16
EDDIE SAYS
By Pythagoras' Theorem, BH² = 5² + 2² + 3² since the dimension of the cuboid are 5 by 2 by 3.
BH² = 25 + 4 + 9 = 38
BH = √38 = 6.16 (3 sf)
• Question 14

Here is a formula.

s = ut + ½at2

Calculate s when u = 6.2 x 102, t = 4.5 and a = 9.8

2.89 × 103
EDDIE SAYS
s = 6.2 × 102 × 4.5 + 0.5 × 9.8 × 4.52 = 2889.225
• Question 15

Eight men can dig a trench in 3 hours.

How long will it take five men to dig a similar trench of the same size?

4 hours 48 mins
EDDIE SAYS
8 men take 3 hours.
1 man would take 8 × 3 = 24 hours.
5 men would take 24 ÷ 5 = 4.8 hours = 4 hours 48 mins.
Remember that 0.8 hour = 0.8 × 60 = 48 mins.
• Question 16

The pilot of a plane wishes to fly due North but there is an 80 mph Easterly wind (i.e. from the East.  The plane's airspeed is 200 mph.  At what bearing must the pilot fly the plane in order to head due North?

(Just write the three figure number)

024
EDDIE SAYS
sin θ° = 80/200 = 0.4
θ° = sin-10.4 = 23.6
Bearing has three digits
• Question 17

Solve the equation:

(2x + 1)2 = (x + 5)2

x = 4, -2
EDDIE SAYS
(2x + 1)(2x + 1) = (x + 5)(x + 5)
4x² + 4x + 1 = x² + 10x + 25
3x² -6x - 24 = 0
x² -2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4, -2
• Question 18

A cyclist travels 25 kilometres at a speed of 20 km/h and then another 80 km at a speed of 25 km/h.

Calculate the cyclist's average speed for the whole journey in km/h to 1 decimal place.

(Just write the number)

23.6
EDDIE SAYS
Total time taken = 25/20 + 80/25 = 4.45 hours.
Total distance cycled = 25 + 80 = 105 km.
Average speed = 105/4.45 =23.6 km/h
• Question 19

The marks of 15 children in a maths test are represented on a Stem and Leaf Diagram as shown below.

Work out the interquartile range.

 Stem Leaf 0 7   9 1 1   4   4   7 2 0   3   3   3   9 3 0   4   4 4 4

6
EDDIE SAYS
The lower quartile is the median of the lowest 7 numbers, which is 14.
The upper quartile is the median of the highest 7 numbers, which is 30.
The interquartile range is 30 - 14 = 6.
• Question 20

The diagram shows a solid prism made from a metal with density of 5.8 grams per cm3.

(measurements in cm, but not drawn accurately)

Calculate the mass of the prism in kilograms.

(Just write the number)

1.4094
EDDIE SAYS
Volume of prism = (3 × 5 + 6 × 2) × 9 = 27 × 9 = 243 cm³
Mass = 243 × 5.8 = 1409.4 g = 1.4094 kg
• Question 21

Jack's mass increases from 45.6 kg to 52.4 kg.

Calculate the percentage increase in Jack's mass.

(Just write the number to 3 significant figures)

14.9
EDDIE SAYS
Actual increase = 52.4 - 45.6 = 6.8
Percentage increase = 6.8/45.6 × 100 = 14.9%
• Question 22

Calculate the side length x to 3 sig. figs.

(Diagram not drawn accurately)

8.90
EDDIE SAYS
x = 6 ÷ tan34°
• Question 23

Charlie is experimenting with seedlings and measures the height of his seedling plants after two weeks.  The results are recorded in this frequency table.

Work out the Frequency Density for the 25 ≤ h < 30 class interval.

(Just write the number)

2.2
EDDIE SAYS
Class width = 30 - 25 = 5
Frequency density = Frequency ÷ Class Width = 11 ÷ 5 = 2.2
• Question 24

In △ABC above,

c = 14 cm

a = 9.5 cm

∠ABC = 80.5º

Calculate its area in cm2 to 3 s.f.

(Just write the number)

65.6
EDDIE SAYS
Area = ½ × 9.5 × 14 × sin80.5° = 65.58799...cm²
• Question 25

Rearrange the following formula to make a the subject.

s = ut + ½at2