Year 10 Paper 1: Number and Algebra
Covers number and calculation, fractions, decimals and percentages, ratio and proportion, indices and standard form, and linear algebra.
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.
Questions
Question 1 [3 marks]
Number and Calculation
Here are the bank balances, in pounds, of five friends: Jamal +85 Priya -40 Callum -120 Erin +15 Oliwia -65
Write down these balances in order, starting with the most overdrawn (the lowest).
Work out the total of all five balances.
Question 2 [3 marks]
Fractions, Decimals and Percentages
A drama club has 36 members. 21 of them are in the acting group and the rest are in the backstage crew.
Write down the fraction of drama club members who are in the backstage crew.
Write your answer to part (a) in its simplest form.
Write down the fraction of drama club members who are in the acting group, in its simplest form.
Question 3 [4 marks]
Indices and Standard Form
Work out the value of each square root.
sqrt(36)
sqrt(64)
sqrt(1)
sqrt(121)
Question 4 [5 marks]
Ratio and Proportion
Aisha is baking a cake. Her recipe uses flour, sugar and butter with masses 300 g flour, 150 g sugar and 100 g butter.
Write the ratio flour : sugar : butter in its simplest form.
Aisha decides to make a bigger cake using 900 g of flour, keeping the same ratio. Work out the mass of sugar and the mass of butter she needs.
Question 5 [1 marks]
Linear Algebra
Make h the subject of the formula V = l × w × h.
Question 6 [1 marks]
Linear Algebra
Solve (1/3)p = 4.
Question 7 [1 marks]
Number and Calculation
Priya pours 250 ml of squash equally into 4 cups. Work out the volume in each cup in millilitres.
Question 8 [1 marks]
Linear Algebra
Solve x + 3.5 = 7.2.
Question 9 [2 marks]
Linear Algebra
Make m the subject of the formula: k = 3m + 2n
Question 10 [2 marks]
Number and Calculation
Use your calculator to work out (2.5 x 10^6) x (4 x 10^3). Give your answer in standard form.
Question 11 [3 marks]
Linear Algebra
Priya is designing a rectangular garden. It has length x metres and width 6 metres. The perimeter of the garden must be at least 30 metres. Form an inequality in x and solve it to find the possible values of x.
Question 12 [3 marks]
Number and Calculation
A school orders 24 tables at £39.50 each. There is a one-off delivery charge of £27.50. Work out the total cost.
Question 13 [8 marks]
Linear Algebra
A playground has a rule: children may play only if their height h in metres satisfies 1.2 < h <= 1.6. a) Which of these children are allowed to play? Alice is 1.2 m, Jamal is 1.45 m, Priya is 1.6 m, Yusuf is 1.61 m. (2 marks) b) Write the inequality that shows the allowed heights. (2 marks) c) Find the smallest possible whole number of centimetres greater than 1.2 m that a child's height could be to be allowed to play. (4 marks)
Which of these children are allowed to play? Alice 1.2 m, Jamal 1.45 m, Priya 1.6 m, Yusuf 1.61 m.
Write the inequality for allowed heights h.
Find the smallest whole number of centimetres greater than 1.2 m that is allowed. Give your answer in centimetres.
Question 14 [3 marks]
Number and Calculation
Work out 4,206 - 3,789.
Model solutions
| Question 1[3 marks] | |
|---|---|
| Answer or working | Marks |
| -120, -65, -40, 15, 85 | B1cao |
| attempts to add all five balances with correct signs | M1oe |
| -125 (pounds) | A1cao |
| Final answer: a) -120, -65, -40, +15, +85 b) -GBP125 | |
| Question 2[3 marks] | |
|---|---|
| Answer or working | Marks |
| 15/36 | B1oe |
| 5/12 ft | B1cao |
| 7/12 | B1cao |
| Final answer: 15/36 | 5/12 | 7/12 | |
| Question 3[4 marks] | |
|---|---|
| Answer or working | Marks |
| 6 | B1cao |
| 8 | B1cao |
| 1 | B1cao |
| 11 | B1cao |
| Final answer: 6 | 8 | 1 | 11 | |
| Question 4[5 marks] | |
|---|---|
| Answer or working | Marks |
| divide all three masses by a common factor (e.g. 50) | M1oe |
| 6:3:2 | A1cao |
| find the scale factor, 900 / 300 = 3 | M1oe |
| multiply the sugar and butter masses by 3 (or use ratio part = 150 g) | M1 |
| sugar = 450 g and butter = 300 g | A1cao |
| Final answer: a) 6:3:2 b) sugar = 450 g, butter = 300 g | |
| Question 5[1 mark] | |
|---|---|
| Answer or working | Marks |
| h = V/(l × w) | B1cao |
| Question 6[1 mark] | |
|---|---|
| Answer or working | Marks |
| p = 12 | B1cao |
| Final answer: 12 | |
| Question 7[1 mark] | |
|---|---|
| Answer or working | Marks |
| 62.5 ml | B1cao |
| Final answer: 62.5 ml. Working check: 250 ÷ 4 = 62.5. | |
| Question 8[1 mark] | |
|---|---|
| Answer or working | Marks |
| x = 3.7 | B1cao |
| Final answer: 3.7 | |
| Question 9[2 marks] | |
|---|---|
| Answer or working | Marks |
| subtracts 2n from both sides, e.g. k - 2n = 3m | M1 |
| m = (k - 2n)/3 oe | A1cao |
| Final answer: m = (k - 2n)/3 | |
| Question 10[2 marks] | |
|---|---|
| Answer or working | Marks |
| correct unrounded value 10000000000 seen (or equivalent working) | M1 |
| 1 x 10^10 cao (correct standard form) | A1 |
| Final answer: 1 x 10^10 | |
| Question 11[3 marks] | |
|---|---|
| Answer or working | Marks |
| 2(x + 6) >= 30 oe, correct inequality formed for the perimeter | M1 |
| x + 6 >= 15 oe, dependent on a correct inequality being formed | M1 |
| x >= 9 oe | A1cao |
| Final answer: x >= 9 | |
| Question 12[3 marks] | |
|---|---|
| Answer or working | Marks |
| multiplies 24 × 39.50 | M1 |
| adds delivery charge to the product | M1 |
| £975.50 | A1cao |
| Final answer: £975.50. Working check: 39.50 × 24 = 948.00; 948.00 + 27.50 = 975.50. | |
| Question 13[8 marks] | |
|---|---|
| Answer or working | Marks |
| Jamal and Priya identified as allowed | B1 |
| Alice and Yusuf identified as not allowed (Alice is exactly 1.2, Yusuf > 1.6) | B1 |
| use correct inequality with strict lower bound and inclusive upper bound | M1 |
| 1.2 < h <= 1.6 | A1cao |
| convert 1.2 m to 120 cm and consider strictly greater, so next whole cm is 121 cm | M1 |
| check 121 cm = 1.21 m <= 1.6 m | M1 |
| 121 cm | A1cao |
| explicit statement smallest whole number of cm is 121 | B1 |
| Final answer: Jamal and Priya are allowed; Alice and Yusuf are not. | 1.2 < h <= 1.6 | 121 cm | |
| Question 14[3 marks] | |
|---|---|
| Answer or working | Marks |
| correct column subtraction set up | M1 |
| borrowing/decomposition shown for at least one column | M1 |
| 417 | A1cao |