Foundation Tier - Year 10

Year 10 Paper 1: Number and Proportion

Covers number and calculation, fractions, decimals and percentages, indices, surds and standard form, ratio and proportion, and linear algebra.

13 questions - 40 marks - calculator allowed

Year 10 here means a typical teaching order, not a syllabus rule. No exam board defines what belongs to Year 10, and schools sequence the course differently. Check it against your own scheme of work before using it to decide what a class has covered.

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Questions

Question 1 [2 marks]

Indices, Surds and Standard Form

Evaluate 25^(1/2) + 8^(1/3).

Question 2 [2 marks]

Linear Equations and Inequalities

Solve x/4 - 3 = 9.

Question 3 [2 marks]

Indices, Surds and Standard Form

Simplify 5a^4 x 3a^6.

Question 4 [3 marks]

Number and Calculation

Write 4620 as a product of its prime factors.

Question 5 [3 marks]

Fractions, Decimals and Percentages

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

Question 6 [3 marks]

Ratio and Proportion

A fruit squash is made from concentrate and water in the ratio 1:6.

Yuki uses 150 ml of concentrate. Find the total volume of squash she makes, in millilitres.

Question 7 [3 marks]

Number and Calculation

Work out 6 + 4 x (9 - 5)^2 / 8.

Question 8 [4 marks]

Fractions, Decimals and Percentages

A gym membership costs 27.99 pounds per month.

The price increases by 12%.

Find the new monthly price, giving your answer to the nearest penny.

Question 9 [3 marks]

Indices, Surds and Standard Form

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

Give your answer using positive indices.

Question 10 [4 marks]

Number and Calculation

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

Question 11 [3 marks]

Indices, Surds and Standard Form

Simplify sqrt(8) x sqrt(18), giving your answer as an integer.

Question 12 [4 marks]

Number and Calculation

Find the HCF of 168 and 180 by expressing each number as a product of its prime factors.

Question 13 [4 marks]

Linear Equations and Inequalities

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

Model solutions

Mark scheme for Question 1 [2 marks]
Question 1[2 marks]
Answer or working	Marks
25^(1/2) = 5 and 8^(1/3) = 2	M1
7	A1

Mark scheme for Question 2 [2 marks]
Question 2[2 marks]
Answer or working	Marks
adding 3 to both sides to get x/4 = 12	M1
x = 48	A1

Mark scheme for Question 3 [2 marks]
Question 3[2 marks]
Answer or working	Marks
multiplying coefficients and adding powers of a	M1
15a^10	A1

Mark scheme for Question 4 [3 marks]
Question 4[3 marks]
Answer or working	Marks
a complete prime factor method, such as a factor tree or repeated division	M1
identifying all the prime factors 2, 2, 3, 5, 7 and 11	M1
2^2 x 3 x 5 x 7 x 11	A1

Mark scheme for Question 5 [3 marks]
Question 5[3 marks]
Answer or working	Marks
finding 42/56	M1
converting to a decimal, 0.75	M1
75%	A1

Mark scheme for Question 6 [3 marks]
Question 6[3 marks]
Answer or working	Marks
recognising 150 ml represents 1 part of the ratio	M1
total parts = 1 + 6 = 7	M1
1050 ml	A1

Mark scheme for Question 7 [3 marks]
Question 7[3 marks]
Answer or working	Marks
evaluating the bracket (9 - 5) = 4 and squaring to get 16	M1
multiplying by 4 and dividing by 8 to get 8	M1
14	A1

Mark scheme for Question 8 [4 marks]
Question 8[4 marks]
Answer or working	Marks
finding 12% of 27.99	M1
12% of 27.99 = 3.3588	M1
adding to the original price	M1
31.35 pounds (nearest penny)	A1
Final answer: 31.35 pounds

Mark scheme for Question 9 [3 marks]
Question 9[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 10 [4 marks]
Question 10[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 11 [3 marks]
Question 11[3 marks]
Answer or working	Marks
multiplying to get sqrt(8 x 18) = sqrt(144)	M1
evaluating 8 x 18 = 144	M1
12	A1

Mark scheme for Question 12 [4 marks]
Question 12[4 marks]
Answer or working	Marks
168 = 2^3 x 3 x 7	M1
180 = 2^2 x 3^2 x 5	M1
identifying the common prime factors 2^2 and 3	M1
HCF = 12	A1
Final answer: 12

Mark scheme for Question 13 [4 marks]
Question 13[4 marks]
Answer or working	Marks
multiplying both sides by 3 to get 2x + 5 = 3(x - 4)	M1
expanding to 2x + 5 = 3x - 12	M1
collecting terms to get 17 = x	M1
x = 17	A1