Year 10 Paper 3: Number, Graphs and Data
Covers number and calculation, fractions, decimals and percentages, indices, surds and standard form, sequences and graphs, geometry, and statistics and probability.
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 [2 marks]
Statistics and Probability
A fair six-sided dice is rolled once. Find the probability of rolling a number greater than 4.
Question 2 [2 marks]
Number and Calculation
A youth club needs to transport 138 students to a trip.
Each coach seats 24 students. Find the minimum number of coaches needed.
Question 3 [3 marks]
Indices, Surds and Standard Form
Work out (2.5 x 10^4) x (6 x 10^-6).
Give your answer in standard form.
Question 4 [3 marks]
Fractions, Decimals and Percentages
In a test, Freya scored 42 out of 56. Express her score as a percentage.
Question 5 [3 marks]
Number and Calculation
Write 4620 as a product of its prime factors.
Question 6 [3 marks]
Fractions, Decimals and Percentages
A charity shop receives a delivery of 150 books. 2/5 of the books are fiction.
The rest of the books are non-fiction. How many of the books are non-fiction?
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]
Angles, Polygons and Circle Theorems
Three angles meet at a point. One angle is 130 degrees, another is 3x degrees and the third is 2x degrees.
Find the value of x, then state the size of the smallest of the three angles at the point.
Question 9 [4 marks]
Fractions, Decimals and Percentages
A tank holds 480 litres of water when full.
1/6 of the water is used for cleaning, and then 30 litres more is used for the garden.
How many litres of water remain in the tank?
Question 10 [4 marks]
Statistics and Probability
The prices, in pounds, of 6 items in a shop are 12, 15, 9, 18, 14 and 16.
Find the mean price. A seventh item priced at 30 pounds is then added to the list.
Find the new mean price of all 7 items.
Question 11 [4 marks]
Angles, Polygons and Circle Theorems
In parallelogram WXYZ, angle W = (4x + 10) degrees and angle X = (2x + 26) degrees, where W and X are adjacent vertices.
Find the value of x, then find angle W.
Question 12 [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 13 [4 marks]
Indices, Surds and Standard Form
Work out the value of 3^-2 + 2^0, giving your answer as a single fraction.
Question 14 [4 marks]
Number and Calculation
Find the HCF of 168 and 180 by expressing each number as a product of its prime factors.
Question 15 [5 marks]
Fractions, Decimals and Percentages
Container A holds 5/6 of its capacity in juice.
Sam pours 2/5 of the juice in container A into container B, which was empty.
What fraction of container A's capacity is now in container B, and what fraction remains in container A?
Question 16 [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 17 [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 18 [5 marks]
Number and Calculation
A submarine starts at a depth of 340 m below sea level.
It rises 155 m, then descends 210 m, then rises a further 98 m.
Find its final depth relative to sea level.
Question 19 [4 marks]
Indices, Surds and Standard Form
Work out the value of 4^0 + 5^-2.
Give your answer as a single fraction.
Question 20 [5 marks]
Fractions, Decimals and Percentages
A roll of ribbon is 5.4 m long.
Priya cuts off 1/3 of the ribbon for a project, then cuts 2/5 of what remains for a second project.
How many centimetres of ribbon are left?
Question 21 [5 marks]
Sequences and Graphs
A geometric sequence has first term 40 and common ratio 1/2.
Find the 5th term of the sequence, and find the sum to infinity of the sequence.
Model solutions
| Question 1[2 marks] | |
|---|---|
| Answer or working | Marks |
| identifying 2 favourable outcomes (5 and 6) out of 6 | M1 |
| 1/3 | A1 |
| Question 2[2 marks] | |
|---|---|
| Answer or working | Marks |
| dividing 138 by 24 to get 5.75 | M1 |
| 6 coaches (rounding up) | A1 |
| Final answer: 6 coaches | |
| Question 3[3 marks] | |
|---|---|
| Answer or working | Marks |
| 2.5 x 6 = 15 | M1 |
| 10^4 x 10^-6 = 10^-2, then adjusting 15 x 10^-2 | M1 |
| 1.5 x 10^-1 | A1 |
| Question 4[3 marks] | |
|---|---|
| Answer or working | Marks |
| finding 42/56 | M1 |
| converting to a decimal, 0.75 | M1 |
| 75% | A1 |
| Question 5[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 |
| Question 6[3 marks] | |
|---|---|
| Answer or working | Marks |
| finding 1/5 of 150 = 30 | M1 |
| finding 3/5 of 150, or 150 - 60 | M1 |
| 90 books | A1 |
| 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 | |
| Question 8[4 marks] | |
|---|---|
| Answer or working | Marks |
| using angles around a point sum to 360 degrees | M1 |
| 130 + 3x + 2x = 360 | M1 |
| solving to x = 46 | M1 |
| the smallest angle = 2 x 46 = 92 degrees | A1 |
| Final answer: x = 46; smallest angle = 92 degrees | |
| Question 9[4 marks] | |
|---|---|
| Answer or working | Marks |
| finding 1/6 of 480 = 80 | M1 |
| 480 - 80 = 400 | M1 |
| subtracting the further 30 litres | M1 |
| 370 litres | A1 |
| Question 10[4 marks] | |
|---|---|
| Answer or working | Marks |
| summing the six prices to get 84 | M1 |
| mean = 14 pounds | A1 |
| adding the seventh price: 84 + 30 = 114 | M1 |
| new mean = 114/7 = 16.29 pounds (2 d.p.) | A1 |
| Final answer: mean = 14 pounds, new mean = 16.29 pounds | |
| Question 11[4 marks] | |
|---|---|
| Answer or working | Marks |
| using adjacent angles in a parallelogram sum to 180 degrees | M1 |
| forming (4x + 10) + (2x + 26) = 180 | M1 |
| solving 6x + 36 = 180 to get x = 24 | M1 |
| angle W = 106 degrees | A1 |
| Final answer: x = 24; angle W = 106 degrees | |
| Question 12[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 | |
| Question 13[4 marks] | |
|---|---|
| Answer or working | Marks |
| 3^-2 = 1/9 | M1 |
| 2^0 = 1 | M1 |
| writing 1 as 9/9 | M1 |
| 10/9 | A1 |
| Question 14[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 | |
| Question 15[5 marks] | |
|---|---|
| Answer or working | Marks |
| multiplying 2/5 by 5/6 to find the amount poured out | M1 |
| 2/5 x 5/6 = 10/30 = 1/3 | M1 |
| 1/3 of the capacity is now in container B | A1 |
| subtracting 1/3 from 5/6, using a common denominator of 6 | M1 |
| 1/2 of the capacity remains in container A | A1 |
| Final answer: 1/3 in container B, 1/2 remains in container A | |
| Question 16[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 | |
| Question 17[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 |
| Question 18[5 marks] | |
|---|---|
| Answer or working | Marks |
| -340 + 155 = -185 | M1 |
| -185 - 210 = -395 | M1 |
| -395 + 98 = -297 | M1 |
| interpreting the negative result as below sea level | M1 |
| 297 m below sea level | A1 |
| Question 19[4 marks] | |
|---|---|
| Answer or working | Marks |
| 4^0 = 1 | M1 |
| 5^-2 = 1/25 | M1 |
| writing 1 as 25/25 | M1 |
| 26/25 | A1 |
| Question 20[5 marks] | |
|---|---|
| Answer or working | Marks |
| finding 2/3 of 5.4 = 3.6 m remaining after the first cut | M1 |
| finding 2/5 of 3.6 = 1.44 m | M1 |
| subtracting to leave 3.6 - 1.44 = 2.16 m | M1 |
| converting 2.16 m to centimetres | M1 |
| 216 cm | A1 |
| Question 21[5 marks] | |
|---|---|
| Answer or working | Marks |
| using the nth term formula a r^(n-1) | M1 |
| 5th term = 40 x (1/2)^4 | M1 |
| 2.5 | A1 |
| using the sum to infinity formula a/(1 - r) | M1 |
| sum to infinity = 80 | A1 |
| Final answer: 5th term = 2.5, sum to infinity = 80 | |