Foundation Tier - Grades 1-5

IGCSE Maths Foundation Paper 3

Covers Number and Calculation, Fractions, Decimals and Percentages, Indices, Surds and Standard Form and 9 more.

17 questions - 60 marks - calculator allowed

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Questions

Question 1 [2 marks]

Number and Calculation

A stationery shop orders 34 boxes of pens. Each box contains 48 pens.

The shop already has 156 pens in stock. Work out the total number of pens now in the shop.

Question 2 [3 marks]

Angles, Polygons and Circle Theorems

Two angles on a straight line are labelled 4x degrees and 5x degrees.

Find the size of the larger angle.

Question 3 [3 marks]

Mensuration and Vectors

A rectangular garden has length 14 m and width 9 m.

Find its perimeter.

Question 4 [3 marks]

Pythagoras and Trigonometry

A right-angled triangle has shorter sides 9 cm and 12 cm.

Find the length of the hypotenuse.

Question 5 [3 marks]

Statistics and Probability

The table shows the number of pets owned by 20 students.

Number of pets: 0, frequency 5; 1, frequency 8; 2, frequency 4; 3, frequency 3.

Find the mean number of pets.

Question 6 [3 marks]

Linear Equations and Inequalities

Expand and simplify 3(2x - 5) + 4(x + 6).

Question 7 [3 marks]

Indices, Surds and Standard Form

A red blood cell has diameter 0.0000075 m. Write this number in standard form.

Question 8 [3 marks]

Fractions, Decimals and Percentages

In a test, Freya scored 42 out of 56. Express her score as a percentage.

Question 9 [3 marks]

Ratio and Proportion

A fruit drink is made from mango juice and orange juice in the ratio 3:4.

Freya makes 490 ml of the drink.

How many millilitres of orange juice does she need?

Question 10 [4 marks]

Sequences and Graphs

The straight line L has equation y = 3x + 2.

Find the equation of the line perpendicular to L that passes through (6, 1).

Question 11 [4 marks]

Quadratics and Simultaneous Equations

Factorise completely 2x^3 - 8x.

Question 12 [4 marks]

Angles, Polygons and Circle Theorems

In a triangle, the angles are 2x degrees, 3x degrees and 55 degrees.

Find the value of x.

Question 13 [4 marks]

Number and Calculation

Determine whether 259 is a prime number. Show your working.

Question 14 [4 marks]

Sequences and Graphs

Find the distance between the points (-1, 2) and (5, -4), giving your answer as a simplified surd.

Question 15 [4 marks]

Statistics and Probability

A bag contains counters that are red, blue, yellow or green.

P(red) = 0.15, P(blue) = 0.4 and P(green) = 0.2.

Find P(yellow), and find P(red or green).

Question 16 [5 marks]

Functions and Rates of Change

The function h is defined by h(x) = (2x + 9)/5 for all values of x.

Find h^-1(x), and hence find h^-1(3).

Question 17 [5 marks]

Mensuration and Vectors

A cylinder has base radius 4 cm and height 15 cm.

Find its volume and its total surface area, both to 3 significant figures.

Model solutions

Mark scheme for Question 1 [2 marks]
Question 1[2 marks]
Answer or working	Marks
34 x 48 = 1632	M1
1788 pens	A1

Mark scheme for Question 2 [3 marks]
Question 2[3 marks]
Answer or working	Marks
4x + 5x = 180	M1
x = 20	M1
100 degrees	A1

Mark scheme for Question 3 [3 marks]
Question 3[3 marks]
Answer or working	Marks
adding two lengths and two widths, or using 2(l + w)	M1
2(14 + 9)	M1
46 m	A1

Mark scheme for Question 4 [3 marks]
Question 4[3 marks]
Answer or working	Marks
using a^2 + b^2 = c^2	M1
9^2 + 12^2 = 225	M1
15 cm	A1

Mark scheme for Question 5 [3 marks]
Question 5[3 marks]
Answer or working	Marks
multiplying each number of pets by its frequency and summing to get 25	M1
dividing by the total frequency 20	M1
1.25 pets	A1

Mark scheme for Question 6 [3 marks]
Question 6[3 marks]
Answer or working	Marks
expanding to 6x - 15 + 4x + 24	M1
collecting like x terms and constants	M1
10x + 9	A1

Mark scheme for Question 7 [3 marks]
Question 7[3 marks]
Answer or working	Marks
identifying the first significant figures as 7.5	M1
counting the place value shift to give power -6	M1
7.5 x 10^-6	A1
Final answer: 7.5 x 10^-6 m

Mark scheme for Question 8 [3 marks]
Question 8[3 marks]
Answer or working	Marks
finding 42/56	M1
converting to a decimal, 0.75	M1
75%	A1

Mark scheme for Question 9 [3 marks]
Question 9[3 marks]
Answer or working	Marks
one ratio part = 490 / 7 = 70	M1
multiplying by 4	M1
280 ml	A1

Mark scheme for Question 10 [4 marks]
Question 10[4 marks]
Answer or working	Marks
identifying gradient 3 from line L	M1
using the perpendicular gradient -1/3	M1
substituting (6, 1) into y = -1/3 x + c	M1
y = -1/3 x + 3	A1

Mark scheme for Question 11 [4 marks]
Question 11[4 marks]
Answer or working	Marks
taking out the common factor 2x: 2x(x^2 - 4)	M1
recognising x^2 - 4 as a difference of two squares	M1
sqrt(x^2) = x and sqrt(4) = 2	M1
2x(x - 2)(x + 2)	A1

Mark scheme for Question 12 [4 marks]
Question 12[4 marks]
Answer or working	Marks
using angles in a triangle sum to 180 degrees	M1
2x + 3x + 55 = 180	M1
5x = 125	M1
x = 25	A1
Final answer: 25

Mark scheme for Question 13 [4 marks]
Question 13[4 marks]
Answer or working	Marks
testing division by small primes such as 2, 3 and 5	M1
testing division by 7	M1
259 = 7 x 37	A1
stating 259 is not a prime number, since it has factors other than 1 and itself	A1
Final answer: Not prime, since 259 = 7 x 37

Mark scheme for Question 14 [4 marks]
Question 14[4 marks]
Answer or working	Marks
finding the horizontal difference 5 - (-1) = 6	M1
finding the vertical difference -4 - 2 = -6	M1
using distance = sqrt(6^2 + 6^2) = sqrt(72)	M1
6 sqrt(2)	A1

Mark scheme for Question 15 [4 marks]
Question 15[4 marks]
Answer or working	Marks
probabilities summing to 1	M1
1 - 0.15 - 0.4 - 0.2	M1
P(yellow) = 0.25	A1
P(red or green) = 0.35	A1
Final answer: P(yellow) = 0.25, P(red or green) = 0.35

Mark scheme for Question 16 [5 marks]
Question 16[5 marks]
Answer or working	Marks
writing x = (2y + 9)/5, swapping x and y	M1
multiplying both sides by 5 to get 5x = 2y + 9	M1
rearranging to make y the subject, y = (5x - 9)/2	M1
h^-1(x) = (5x - 9)/2	A1
h^-1(3) = 3	A1
Final answer: h^-1(x) = (5x - 9)/2, h^-1(3) = 3

Mark scheme for Question 17 [5 marks]
Question 17[5 marks]
Answer or working	Marks
using volume = pi r^2 h	M1
pi x 4^2 x 15 = 240 pi	M1
volume = 754 cm^3 (3 s.f.)	A1
using total surface area = 2 pi r h + 2 pi r^2	M1
surface area = 478 cm^2 (3 s.f.)	A1
Final answer: volume = 754 cm^3, surface area = 478 cm^2