Foundation Tier - Grades 1-5

IGCSE Maths Foundation Paper 2

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

16 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]

Fractions, Decimals and Percentages

A laptop costs 480 pounds before a 15% discount is applied.

Find the sale price of the laptop in pounds.

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]

Statistics and Probability

The numbers of goals scored by a football team in six matches are 2, 0, 3, 1, 4 and 2.

Find the mean and the range of the number of goals.

Question 5 [4 marks]

Linear Equations and Inequalities

Solve 4(x - 3) = 2(x + 5).

Question 6 [4 marks]

Pythagoras and Trigonometry

In a right-angled triangle, the side opposite angle y is 9 cm and the side adjacent to angle y is 6.5 cm.

Find y to 1 decimal place.

Question 7 [4 marks]

Sequences and Graphs

The first four terms of a sequence are 5, 9, 13, 17.

Find an expression for the nth term, then use it to determine whether 205 is a term of the sequence.

Question 8 [4 marks]

Quadratics and Simultaneous Equations

A number x satisfies x(x + 2) = 24. Find the two possible values of x.

Question 9 [3 marks]

Angles, Polygons and Circle Theorems

A regular polygon has each exterior angle equal to 15 degrees.

Find the number of sides of the polygon.

Question 10 [3 marks]

Indices, Surds and Standard Form

Simplify (x^7 y^3)/(x^3 y^-2).

Give your answer using positive indices.

Question 11 [4 marks]

Ratio and Proportion

In a school, the ratio of Year 10 students to Year 11 students is 5:4.

The ratio of Year 11 students to Year 12 students is 2:3.

Find the ratio of Year 10 to Year 11 to Year 12 students, in its simplest form.

Question 12 [4 marks]

Number and Calculation

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

Question 13 [4 marks]

Fractions, Decimals and Percentages

Ryan mixes 3.6 litres of orange squash.

He pours 40% of it into a jug for a party, then shares 1/4 of what remains between two bottles.

How many millilitres of squash are left in the original container?

Question 14 [5 marks]

Functions and Rates of Change

The function h is defined by h(x) = 3/(x - 2) for x is not equal to 2.

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

Question 15 [5 marks]

Number and Calculation

Three warning lights flash every 18 seconds, 24 seconds and 30 seconds respectively.

All three lights flash together at 9:00 am. Find the next time, in seconds after 9:00 am, that all three lights flash together at the same moment.

Question 16 [5 marks]

Linear Equations and Inequalities

n is an integer.

-3 < 2n - 5 <= 7.

Find all possible values of n.

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
the multiplier 0.85	M1
480 x 0.85	M1
408 pounds	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
summing the six values to get 12	M1
mean = 2	A1
range = 4	A1
Final answer: mean 2, range 4

Mark scheme for Question 5 [4 marks]
Question 5[4 marks]
Answer or working	Marks
expanding to 4x - 12 = 2x + 10	M1
collecting x terms, such as 4x - 2x = 10 + 12	M1
2x = 22	M1
x = 11	A1

Mark scheme for Question 6 [4 marks]
Question 6[4 marks]
Answer or working	Marks
using tan y = opposite/adjacent	M1
tan y = 9/6.5	M1
y = tan^-1(9/6.5)	M1
54.2 degrees	A1

Mark scheme for Question 7 [4 marks]
Question 7[4 marks]
Answer or working	Marks
identifying the common difference 4	M1
comparing with 4n to find the adjustment +1, giving 4n + 1	M1
solving 4n + 1 = 205	M1
n = 51, so 205 is a term of the sequence	A1
Final answer: 4n + 1; yes, 205 is the 51st term

Mark scheme for Question 8 [4 marks]
Question 8[4 marks]
Answer or working	Marks
rearranging to x^2 + 2x - 24 = 0	M1
factorising to (x + 6)(x - 4) = 0	M1
setting each bracket equal to zero	M1
x = -6 or x = 4	A1

Mark scheme for Question 9 [3 marks]
Question 9[3 marks]
Answer or working	Marks
exterior angles of a polygon sum to 360 degrees	M1
360 divided by 15	M1
24 sides	A1

Mark scheme for Question 10 [3 marks]
Question 10[3 marks]
Answer or working	Marks
subtracting powers of x to get x^4	M1
subtracting powers of y to get y^5	M1
x^4 y^5	A1

Mark scheme for Question 11 [4 marks]
Question 11[4 marks]
Answer or working	Marks
scaling the second ratio so the Year 11 parts match: 2:3 becomes 4:6	M1
combining to get Year 10 : Year 11 : Year 12 = 5 : 4 : 6	M1
checking the ratio cannot be simplified further	M1
5:4:6	A1

Mark scheme for Question 12 [4 marks]
Question 12[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 13 [4 marks]
Question 13[4 marks]
Answer or working	Marks
60% of 3.6 = 2.16 litres remaining after the jug is filled	M1
finding 1/4 of 2.16	M1
subtracting to leave 3/4 of 2.16	M1
1620 ml	A1

Mark scheme for Question 14 [5 marks]
Question 14[5 marks]
Answer or working	Marks
writing x = 3/(y - 2), swapping x and y	M1
multiplying both sides by (y - 2) to get x(y - 2) = 3	M1
expanding and rearranging to make y the subject	M1
h^-1(x) = (3 + 2x)/x	A1
h^-1(1) = 5	A1
Final answer: h^-1(x) = (3 + 2x)/x; h^-1(1) = 5

Mark scheme for Question 15 [5 marks]
Question 15[5 marks]
Answer or working	Marks
expressing each number as a product of primes	M1
18 = 2 x 3^2, 24 = 2^3 x 3, 30 = 2 x 3 x 5	M1
identifying the highest power of each prime: 2^3, 3^2 and 5	M1
multiplying to get 8 x 9 x 5	M1
360 seconds	A1

Mark scheme for Question 16 [5 marks]
Question 16[5 marks]
Answer or working	Marks
adding 5 to all three parts of the inequality	M1
-3 + 5 < 2n <= 7 + 5, giving 2 < 2n <= 12	M1
dividing all three parts by 2	M1
1 < n <= 6	A1
n = 2, 3, 4, 5 or 6	A1