# GCSE Calculator Questions 1 (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

Write the following fraction as a decimal:

 10 32

Write the following recurring decimal as a fraction in its lowest terms.

Calculate the value of the following to 3 decimal places:

 5.962 - 2.145 1.986

Express 350 as a product of prime factors.

2×52 ×73

2×42 ×72

2×52 ×74

2×52 ×7

A triangle has a height of 7x and a base length of 3x.

The area of the triangle is 147 cm2.

Select the equation which shows this information.

3x + 7x = 147

10x² = 147

21x² = 147

21x² = 294

Charlie invests £3200 for 3 years in a savings account that gives 5% interest per year.

How much more interest will Charlie earn if he invests the money at compound interest rather than at simple interest?

Look at the diagram below which shows the sector of a circle of radius 4 cm.

Calculate the arc length AB in cm to 3 sig. figs.

(Just write the number)

Solve the quadratic equation by selecting all the correct solutions below.

8x2 + 2x - 3 = 0

x = ¾

x = -¾

x = -½

x = ½

x = -2

Sam measures the angle of elevation of a point at the top of the Tower of Pisa to be 28°.

Use the information shown in the diagram below to calculate the height of the Tower of Pisa to the nearest metre.

(Just write the number)

In  triangle PQR, which is not drawn to scale,

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

Use the cosine rule to find ∠PQR to the nearest degree.

(Just write the number)

In  triangle PQR, which is not drawn to scale,

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

Calculate ∠PQR to the nearest degree.

(Just write the number)

Here is a formula invented by Einstein.

E = mc2

Calculate E when m = 6.2 x 10-5 and c = 3 x 108.

5.58 × 103

5.58 × 10-12

5.58 × 1012

1.86 × 104

1.86 × 1012

150 cm of copper wire has a mass of 10.4 grams.

Calculate the mass of 270 cm of the copper wire in grams to 2 dps.

Calculate the length of the line segment shown in the diagram below to the nearest tenth of a unit.

Ben is a keen photographer.

He goes on holiday for 14 days and takes roughly 350 photographs per day.  Each photograph uses 12.5 MB of disk space and his camera has a new 64 GB card at the start of his holiday.

What percentage of disk space remains on the card at the end of his holiday?

(1GB = 1000 MB)

4.3%

95.7%

4.2%

95.8%

There are 405 people in a school.

The ratio of children to adults is 25:2.

How many children are at the school?

Find the length of the cuboid's diagonal BH of this 4 cm x 5 cm x 12 cm cuboid in cm to 3 sig. figs.

(Just write the number)

One solution to the following equation lies between x = 4 and x = 5.

2x3 + 2x2 + x = 200

Using trial and improvement, find this solution to 1 d.p.

(Just write the number)

Solve the following equation for a:

 7a - 10 = 8a - 5 5 7

(Just write the value of a)

There are 16 boys and 10 girls in a class.

The teacher choses two children at random.

What is the probability of choosing a boy and a girl?

In the diagram below, C is the centre of the circle and TU is a tangent.

Calculate the size of angle CRS.

(Just write the number)

A sequence begins:

12, 19, 26, 33, 40 ...

Write down the nth term of the sequence.

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

Estimate the mean height of the seedlings in mm to the nearest whole number.

(Just write the number)

Calculate the area of the triangle PQR in cm2 to 1 decimal place.

All lengths are shown in cm.

The diagram shows a solid cylinder, made from metal with a density of 7.4 grams per cm3.

Calculate the mass of the cylinder in grams to 3 significant figures.

(Just write the number)

• Question 1

Write the following fraction as a decimal:

 10 32

0.3125
EDDIE SAYS
10 ÷ 32 = 0.3125
• Question 2

Write the following recurring decimal as a fraction in its lowest terms.

5/11
EDDIE SAYS
45/99 reduces to 5/11
• Question 3

Calculate the value of the following to 3 decimal places:

 5.962 - 2.145 1.986
16.806
EDDIE SAYS
On the calculator, type:
5.96 x² - 2.145 = ÷ 1.986 =
• Question 4

Express 350 as a product of prime factors.

2×52 ×7
EDDIE SAYS
350 = 10 × 35
350 = 2 × 5 × 5 × 7
• Question 5

A triangle has a height of 7x and a base length of 3x.

The area of the triangle is 147 cm2.

Select the equation which shows this information.

21x² = 294
EDDIE SAYS
Area of triangle = Base × Height ÷ 2
147 = 3x × 7x ÷ 2
147 × 2 = 3x × 7x
294 = 21x²
• Question 6

Charlie invests £3200 for 3 years in a savings account that gives 5% interest per year.

How much more interest will Charlie earn if he invests the money at compound interest rather than at simple interest?

£24.40
£ 24.40
EDDIE SAYS
Simple interest will earn him 0.05 × 3200 × 3 = £480
Compound interest will earn him 1.05³ × 3200 - 3200 = £504.40
£504.40 - £480 = £24.40
• Question 7

Look at the diagram below which shows the sector of a circle of radius 4 cm.

Calculate the arc length AB in cm to 3 sig. figs.

(Just write the number)

2.09
EDDIE SAYS
Circumference = 8π
Arc Length = 30/360 × 8π = 2.094395.....
• Question 8

Solve the quadratic equation by selecting all the correct solutions below.

8x2 + 2x - 3 = 0

x = -¾
x = ½
EDDIE SAYS
This factorises to give the equation (2x-1)(4x+3)= 0
• Question 9

Sam measures the angle of elevation of a point at the top of the Tower of Pisa to be 28°.

Use the information shown in the diagram below to calculate the height of the Tower of Pisa to the nearest metre.

(Just write the number)

57
EDDIE SAYS
Let height above Sam's eye be h.
Using trig, h = 104 tan 28° = 55.3 m
Height of tower from ground = 55.3 + 1.6 = 56.9 ≅ 57 m
• Question 10

In  triangle PQR, which is not drawn to scale,

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

Use the cosine rule to find ∠PQR to the nearest degree.

(Just write the number)

22
EDDIE SAYS
12² = 10² + 4.5² - 2 × 10 × 4.5 × cosθ°
• Question 11

In  triangle PQR, which is not drawn to scale,

PQ = 4.5 cm, QR = 10 cm, and PR = 12 cm.

Calculate ∠PQR to the nearest degree.

(Just write the number)

22
EDDIE SAYS
12² = 10² + 4.5² - 2 × 10 × 4.5 × cosθ°
• Question 12

Here is a formula invented by Einstein.

E = mc2

Calculate E when m = 6.2 x 10-5 and c = 3 x 108.

5.58 × 1012
EDDIE SAYS
E = 6.2 × 10-5 × 3 × 108 × 3 × 108
• Question 13

150 cm of copper wire has a mass of 10.4 grams.

Calculate the mass of 270 cm of the copper wire in grams to 2 dps.

18.72
EDDIE SAYS
10.4 ÷ 150 × 270 = 18.72
• Question 14

Calculate the length of the line segment shown in the diagram below to the nearest tenth of a unit.

9.2
EDDIE SAYS
Build a right-angled triangle using the end-points of the line segment.
The triangle has side lengths of 7 and 6.
Use Pythagoras' Theorem to calculate the length as
√(6² + 7²) = √85
• Question 15

Ben is a keen photographer.

He goes on holiday for 14 days and takes roughly 350 photographs per day.  Each photograph uses 12.5 MB of disk space and his camera has a new 64 GB card at the start of his holiday.

What percentage of disk space remains on the card at the end of his holiday?

(1GB = 1000 MB)

4.3%
EDDIE SAYS
Disk space used = 14 × 350 × 12.5 = 61250 MB
Percentage remaining = (64000 - 61250) ÷ 64000 × 100 = 4.2968... %
• Question 16

There are 405 people in a school.

The ratio of children to adults is 25:2.

How many children are at the school?

375
EDDIE SAYS
Number of children = 25 ÷ (25 + 2) × 405 = 375
• Question 17

Find the length of the cuboid's diagonal BH of this 4 cm x 5 cm x 12 cm cuboid in cm to 3 sig. figs.

(Just write the number)

13.6
EDDIE SAYS
Use Pythagoras' Theorem to get:
BH² = 4² + 5² + 12² = 16 + 25 + 144 = 185
• Question 18

One solution to the following equation lies between x = 4 and x = 5.

2x3 + 2x2 + x = 200

Using trial and improvement, find this solution to 1 d.p.

(Just write the number)

4.3
EDDIE SAYS
2 × 4.25³ + 2 × 4.25² + 4.25 = 193.90625 (just too small)
2 × 4.3³ + 2 × 4.3² + 4.3 = 200.294 (just too big)
• Question 19

Solve the following equation for a:

 7a - 10 = 8a - 5 5 7

(Just write the value of a)

5
EDDIE SAYS
Multiply both sides by 35 to get:
7(7a - 10) = 5(8a - 5)
• Question 20

There are 16 boys and 10 girls in a class.

The teacher choses two children at random.

What is the probability of choosing a boy and a girl?

32/65
EDDIE SAYS
16/26 × 10/25 + 10/26 × 16/25
• Question 21

In the diagram below, C is the centre of the circle and TU is a tangent.

Calculate the size of angle CRS.

(Just write the number)

45
EDDIE SAYS
∠CTP = 90 - 65 = 25°
∠TSR = ½ of 140 = 70°
reflex ∠TCR = 360 - 140 = 220°
∠CRS = 360 - 220 - 70 - 25 = 45°
• Question 22

A sequence begins:

12, 19, 26, 33, 40 ...

Write down the nth term of the sequence.

7n+5
EDDIE SAYS
The terms increase by 7, so the nth term is related to 7n.
Compare the sequence to 7, 14, 21, 28, 35 and we realise that we must add 5 to get the given sequence.
• 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.

Estimate the mean height of the seedlings in mm to the nearest whole number.

(Just write the number)

16
EDDIE SAYS
We use the midpoint of each class, i.e. 2.5mm, 7.5mm, 12.5 mm etc.. to work out the total of all the seedling heights as:
4 × 2.5 + 12 × 7.5 + 22 × 12.5 + 29 × 17.5 + 15 × 22.5 + 11 × 27.5 = 1522.5
There are 93 seedlings if we add up the numbers in the frequency column.
Mean = 1522.5 ÷ 93 = 16.37...
• Question 24

Calculate the area of the triangle PQR in cm2 to 1 decimal place.

All lengths are shown in cm.

27.4
EDDIE SAYS
Area = ½ × 5 × 11 × sin95° = 27.395...cm²
• Question 25

The diagram shows a solid cylinder, made from metal with a density of 7.4 grams per cm3.

Calculate the mass of the cylinder in grams to 3 significant figures.

(Just write the number)