Foundation Tier - Year 10

OCR-Style Year 10 Foundation Paper 3

An OCR-style Year 10 Foundation Paper 3: 100 marks, 90 minutes, calculator, matching OCR J560's published paper format. Covers the same nine Year 10 topics as the board-agnostic set: number and calculation, fractions, decimals and percentages, ratio and proportion, indices and standard form, linear algebra, graphs and coordinates, sequences, angles and geometrical reasoning, and area, volume and measures.

43 questions - 100 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.

Download printable PDF

Questions

Question 1 [1 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (2, 3) and (5, 12).

Question 2 [1 marks]

Angles and Geometrical Reasoning

Write down the sum of the angles on a straight line.

Question 3 [2 marks]

Linear Algebra

Solve 20 / x = 4

Question 4 [2 marks]

Ratio and Proportion

The table shows the cost of buying ribbon. The cost is in direct proportion to the length. Length (m) | Cost (GBP) 2 | 3.00 5 | ? 8 | ?

Work out the cost of 5 m of ribbon.

Work out the cost of 8 m of ribbon.

Question 5 [2 marks]

Number and Calculation

Jamal's bank balance is -£18.50. He spends another £6.75 using his card. Work out his new balance.

Question 6 [2 marks]

Linear Algebra

Simplify 6p + 3q - 2p + 5q

Question 7 [3 marks]

Area, Volume and Measures

A square patio has an area of 49 m^2. Work out the perimeter of the patio.

Question 8 [3 marks]

Sequences

The nth term of a sequence is 6n - 4.

Work out the first three terms of the sequence.

Work out the 20th term of the sequence.

Question 9 [4 marks]

Fractions, Decimals and Percentages

A school trip costs £256 per student at full price. Students who book early pay only 5/8 of the full cost. Zainab books early. Her parents pay 3/4 of Zainab's early-booking cost, and Zainab pays the rest from her own savings. Work out how much Zainab pays from her own savings.

Question 10 [4 marks]

Indices and Standard Form

Write down the value of each power.

2^2

10^2

5^2

1^5

Question 11 [4 marks]

Angles and Geometrical Reasoning

A rectangular kitchen measures 4.8 m by 3.6 m in real life. A scale drawing is made using a scale of 1 : 60.

Work out the dimensions of the kitchen on the scale drawing, in centimetres.

Work out the area of the kitchen on the scale drawing, in cm^2.

Question 12 [4 marks]

Area, Volume and Measures

This question is about converting between different time formats.

A yoga class lasts 1 5/6 hours. Work out how many minutes this is.

A cyclist's finish time is recorded as 2:18:37 (hours:minutes:seconds). Work out this time in minutes, giving your answer correct to the nearest minute.

Question 13 [1 marks]

Number and Calculation

Work out 0.345 multiplied by 10.

Question 14 [1 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (-3, -4) and (1, -4).

Question 15 [1 marks]

Number and Calculation

Write down the bounds for a number given as 5, correct to 1 significant figure, using inequality notation.

Question 16 [2 marks]

Linear Algebra

a = 6 and c = 2. Work out the value of a^2 - c^2.

Question 17 [1 marks]

Number and Calculation

Round 0.995 to 1 significant figure.

Question 18 [1 marks]

Fractions, Decimals and Percentages

Write 175% as a fraction in its simplest form.

Question 19 [1 marks]

Number and Calculation

Write as an integer: 3 hundreds + 2 tens + 7 ones.

Question 20 [2 marks]

Angles and Geometrical Reasoning

Find the sum of the interior angles of a pentagon.

Question 21 [2 marks]

Linear Algebra

A delivery service charges a fixed fee of £1.20 plus £0.35 for each item ordered. Write an expression for the total cost if m items are ordered.

Question 22 [1 marks]

Number and Calculation

Round 92,715 to the nearest 1,000.

Question 23 [1 marks]

Angles and Geometrical Reasoning

Write down the vector from point P to point Q. P has position vector (2, 3) and Q has position vector (5, 1).

Question 24 [1 marks]

Number and Calculation

Write down the lower bound and upper bound for a number which is 12, correct to the nearest integer, using inequality notation.

Question 25 [2 marks]

Area, Volume and Measures

A delivery van arrives at a warehouse at 13:10 after a journey lasting 2 hours 45 minutes. Work out the time the van left.

Question 26 [2 marks]

Fractions, Decimals and Percentages

A restaurant automatically adds a service charge of 12.5% to the price of a meal. The total bill, including the service charge, is £81.00. Work out the price of the meal before the service charge was added.

Question 27 [1 marks]

Number and Calculation

Round 82.56 to 1 significant figure.

Question 28 [2 marks]

Area, Volume and Measures

A cone has base radius 3 cm and slant height 8 cm. Calculate the curved surface area of the cone. Give your answer correct to 3 significant figures.

Question 29 [2 marks]

Number and Calculation

Work out 306 x 7.

Question 30 [2 marks]

Fractions, Decimals and Percentages

£5000 is invested for 2 years at a rate of 2.4% per year compound interest. Work out the value of the investment at the end of 2 years, giving your answer to the nearest penny.

Question 31 [1 marks]

Number and Calculation

Work out (-5) - (-9).

Question 32 [3 marks]

Area, Volume and Measures

A student's working to find the area of a parallelogram with base 11 cm and perpendicular height 8 cm is shown below. Area = 11 + 8 = 19 cm^2

Identify the error in the student's method.

Work out the correct area of the parallelogram.

Question 33 [3 marks]

Graphs and Coordinates

Use your table of values from Question 3 for y = x^3 - 4.

Draw the graph of y = x^3 - 4 for -2 <= x <= 2 on the grid provided.

Write down the coordinates of the point where the graph crosses the y-axis.

Question 34 [3 marks]

Angles and Geometrical Reasoning

A shape has plan a cross shaped layout on a 3 by 3 grid: central square and the middle square on each side, so 5 unit squares in the plan. The front elevation shows the central column has height 3 and the four arm columns have height 1. Work out the total number of unit cubes used.

Question 35 [3 marks]

Ratio and Proportion

A gardener needs at least 9 kg of compost for a raised bed. Compost is sold in 2 kg bags at £3.20 and 5 kg bags at £7.00. Show that buying one 5 kg bag and two 2 kg bags is cheaper than buying five 2 kg bags or two 5 kg bags.

Question 36 [3 marks]

Graphs and Coordinates

Line L has equation 2y = 6x + 8. Write the equation of L in the form y = mx + c, and state the gradient and the y-intercept of L.

Question 37 [3 marks]

Linear Algebra

The circumference of a circle of radius r is given by the formula C = 2 * pi * r

Rearrange the formula to make r the subject.

A circular pond has a circumference of 18.84 metres. Work out the radius of the pond. Give your answer correct to 1 decimal place.

Question 38 [3 marks]

Area, Volume and Measures

A circular flower bed has area 50.24 m^2. Use pi = 3.14. Work out the radius of the flower bed, giving your answer to 2 decimal places.

Question 39 [4 marks]

Linear Algebra

Solve the simultaneous equations: y = 3x - 2 2x + y = 13

Question 40 [4 marks]

Ratio and Proportion

£1 = 1.18 euros and £1 = 1.32 US dollars. Work out how many US dollars are equivalent to 50 euros. Give your answer correct to 2 decimal places.

Question 41 [4 marks]

Fractions, Decimals and Percentages

Priya invests £2500 in a savings account that pays compound interest at a rate of 2.5% per year. Calculate the total interest she earns after 3 years. Give your answer to the nearest penny.

Question 42 [5 marks]

Indices and Standard Form

A rectangle has a width of 3^2 cm and a length of 3^5 cm.

Work out the area of the rectangle, giving your answer as a single power of 3.

A second rectangle has the same area as the rectangle in part (a). Its width is 3^3 cm. Work out its length, giving your answer as a single power of 3.

Question 43 [3 marks]

Fractions, Decimals and Percentages

A television costs £320. The price of the television increases by 8%. Work out the new price of the television.

Model solutions

Mark scheme for Question 1 [1 mark]
Question 1[1 mark]
Answer or working	Marks
3	B1cao

Mark scheme for Question 2 [1 mark]
Question 2[1 mark]
Answer or working	Marks
180 (degrees)	B1cao
Final answer: 180 degrees

Mark scheme for Question 3 [2 marks]
Question 3[2 marks]
Answer or working	Marks
both sides multiplied by x, or 20 divided by 4	M1oe
x = 5	A1cao

Mark scheme for Question 4 [2 marks]
Question 4[2 marks]
Answer or working	Marks
7.50	B1cao
12.00 cao	B1ft
Final answer: GBP 7.50 \| GBP 12.00

Mark scheme for Question 5 [2 marks]
Question 5[2 marks]
Answer or working	Marks
-18.50 - 6.75 seen or correct process	M1
-25.25 cao (pounds)	A1
Final answer: -£25.25

Mark scheme for Question 6 [2 marks]
Question 6[2 marks]
Answer or working	Marks
4p or 8q seen (one pair of like terms correctly collected)	M1
4p + 8q oe	A1cao
Final answer: 4p + 8q

Mark scheme for Question 7 [3 marks]
Question 7[3 marks]
Answer or working	Marks
finds the side length: sqrt(49) = 7	M1oe
4 x 7, ft their side length	M1
28	A1cao
Final answer: 28 m

Mark scheme for Question 8 [3 marks]
Question 8[3 marks]
Answer or working	Marks
at least one correct substitution, e.g. n=1 gives 2	M1
2, 8, 14 all correct	A1cao
116	B1cao
Final answer: 2, 8, 14 \| 116

Mark scheme for Question 9 [4 marks]
Question 9[4 marks]
Answer or working	Marks
256 / 8 = 32, 32 x 5 = 160 oe (Zainab's early-booking cost)	M1
160 / 4 = 40, 40 x 3 = 120 oe (dep, the amount Zainab's parents pay)	M1
160 - 120 = 40 oe (dep on both previous methods)	M1
40 (pounds)	A1cao
Final answer: £40

Mark scheme for Question 10 [4 marks]
Question 10[4 marks]
Answer or working	Marks
4	B1cao
100	B1cao
25	B1cao
1	B1cao
Final answer: 4 \| 100 \| 25 \| 1

Mark scheme for Question 11 [4 marks]
Question 11[4 marks]
Answer or working	Marks
480 / 60 or 360 / 60	M1
8 cm	A1
6 cm	A1
48 cm^2 ft from part (a)	B1
Final answer: 8 cm by 6 cm \| 48 cm^2

Mark scheme for Question 12 [4 marks]
Question 12[4 marks]
Answer or working	Marks
1 5/6 x 60, or 1 hour (= 60 minutes) plus 5/6 hour (= 50 minutes)	M1
110 minutes	A1cao
2 x 60 + 18 + 37/60 (= 138.61... minutes), correct method to combine all three units into minutes	M1
awrt 139 minutes	A1
Final answer: 110 minutes \| 139 minutes (awrt)

Mark scheme for Question 13 [1 mark]
Question 13[1 mark]
Answer or working	Marks
3.45	B1cao

Mark scheme for Question 14 [1 mark]
Question 14[1 mark]
Answer or working	Marks
0	B1cao

Mark scheme for Question 15 [1 mark]
Question 15[1 mark]
Answer or working	Marks
4.5 <= x < 5.5	B1cao

Mark scheme for Question 16 [2 marks]
Question 16[2 marks]
Answer or working	Marks
a^2 = 36 and c^2 = 4 both evaluated	M1oe
32	A1cao

Mark scheme for Question 17 [1 mark]
Question 17[1 mark]
Answer or working	Marks
1.0 or 1	B1cao
Final answer: 1.0 (to 1 s.f.), i.e. 1

Mark scheme for Question 18 [1 mark]
Question 18[1 mark]
Answer or working	Marks
7/4 oe (e.g. 1 3/4)	B1cao
Final answer: 7/4

Mark scheme for Question 19 [1 mark]
Question 19[1 mark]
Answer or working	Marks
327	B1cao

Mark scheme for Question 20 [2 marks]
Question 20[2 marks]
Answer or working	Marks
use formula (n - 2) x 180 with n = 5	M1
540 degrees	A1cao

Mark scheme for Question 21 [2 marks]
Question 21[2 marks]
Answer or working	Marks
identify fixed fee + variable cost, 1.20 + 0.35m or equivalent	M1
1.20 + 0.35m	A1cao

Mark scheme for Question 22 [1 mark]
Question 22[1 mark]
Answer or working	Marks
93,000	B1cao

Mark scheme for Question 23 [1 mark]
Question 23[1 mark]
Answer or working	Marks
vector PQ = (3, -2)	B1cao
Final answer: (3, -2)

Mark scheme for Question 24 [1 mark]
Question 24[1 mark]
Answer or working	Marks
11.5 <= x < 12.5	B1cao

Mark scheme for Question 25 [2 marks]
Question 25[2 marks]
Answer or working	Marks
subtract duration from arrival time, e.g. 13:10 - 2:45	M1oe
10:25	A1cao

Mark scheme for Question 26 [2 marks]
Question 26[2 marks]
Answer or working	Marks
81 / 1.125	M1oe
£72	A1cao

Mark scheme for Question 27 [1 mark]
Question 27[1 mark]
Answer or working	Marks
80	B1cao

Mark scheme for Question 28 [2 marks]
Question 28[2 marks]
Answer or working	Marks
pi x 3 x 8 oe (24 pi seen)	M1
awrt 75.4	A1
Final answer: 75.4 cm^2 (3 sf)

Mark scheme for Question 29 [2 marks]
Question 29[2 marks]
Answer or working	Marks
attempt to use long or column multiplication (e.g. 300 x 7 and 6 x 7 shown)	M1oe
2142	A1cao

Mark scheme for Question 30 [2 marks]
Question 30[2 marks]
Answer or working	Marks
5000 x 1.024^2 oe, or a correct year-by-year method	M1
5242.88 (pounds)	A1cao
Final answer: £5242.88

Mark scheme for Question 31 [1 mark]
Question 31[1 mark]
Answer or working	Marks
4	B1cao

Mark scheme for Question 32 [3 marks]
Question 32[3 marks]
Answer or working	Marks
States the student added the base and height instead of multiplying them	B1oe
Area = base x height = 11 x 8	M1
88 cm^2	A1cao
Final answer: The base and height were added instead of multiplied \| 88 cm^2

Mark scheme for Question 33 [3 marks]
Question 33[3 marks]
Answer or working	Marks
all 5 points from the table plotted correctly, ft candidate's table from Q3	B1
single smooth curve drawn through all the points, correct increasing s-shape with no turning points	B1
(0, -4)	B1cao
Final answer: Smooth curve through (-2,-12), (-1,-5), (0,-4), (1,-3), (2,4) \| (0, -4)

Mark scheme for Question 34 [3 marks]
Question 34[3 marks]
Answer or working	Marks
identify heights for each of the 5 plan positions: central 3, four arms 1 each	M1
calculate total 3 + 4 x 1 = 7	M1
7	A1cao

Mark scheme for Question 35 [3 marks]
Question 35[3 marks]
Answer or working	Marks
Calculate cost of 5 x 2 kg = 5 * £3.20 = £16.00	dM1cso
Calculate cost of 1 x 5 kg + 2 x 2 kg = £7.00 + £6.40 = £13.40	dM1cso
Conclude cheapest is 5 kg + 2x2 kg = £13.40 cao, less than both £16.00 and £14.00	A1
Final answer: 1 x 5 kg + 2 x 2 kg costs £13.40 and gives 9 kg. Five 2 kg bags cost £16.00 (10 kg). Two 5 kg bags cost £14.00 (10 kg). Since £13.40 is less than both £16.00 and £14.00, one 5 kg bag plus two 2 kg bags is the cheapest way to get at least 9 kg.

Mark scheme for Question 36 [3 marks]
Question 36[3 marks]
Answer or working	Marks
divides both sides by 2, e.g. y = 3x + 4	M1oe
gradient = 3	A1
y-intercept = 4 oe (0, 4)	A1
Final answer: y = 3x + 4; gradient = 3; y-intercept = (0, 4)

Mark scheme for Question 37 [3 marks]
Question 37[3 marks]
Answer or working	Marks
r = C/(2 * pi)	B1oe
substitutes C = 18.84 into r = C/(2 * pi), ft from part a	M1
awrt 3.0 (m)	A1
Final answer: r = C/(2 * pi) \| r = 3.0 m (1 dp)

Mark scheme for Question 38 [3 marks]
Question 38[3 marks]
Answer or working	Marks
use area = pi * r^2 and rearrange: r = sqrt(area / pi)	M1
substitute: r = sqrt(50.24 / 3.14)	M1
r = 4.00 m awrt (50.24 / 3.14 = 16; sqrt(16) = 4.00)	A1
Final answer: 4.00 m

Mark scheme for Question 39 [4 marks]
Question 39[4 marks]
Answer or working	Marks
substitutes y = 3x - 2 into the second equation	M1
forms and simplifies a single linear equation in x, e.g. 5x - 2 = 13	M1
x = 3	A1
y = 7	A1cao
Final answer: x = 3, y = 7

Mark scheme for Question 40 [4 marks]
Question 40[4 marks]
Answer or working	Marks
50 / 1.18 oe (convert euros to pounds)	M1
awrt 42.37	A1
their pounds x 1.32 (convert pounds to dollars)	M1ft
awrt 55.93	A1
Final answer: $55.93

Mark scheme for Question 41 [4 marks]
Question 41[4 marks]
Answer or working	Marks
1.025^3 (= 1.076890625)	M1
2500 x their 1.076890625 (= 2692.2265625, the total value)	M1
their total value - 2500 (method to find interest only)	M1
192.23 (pounds)	A1cao
Final answer: £192.23

Mark scheme for Question 42 [5 marks]
Question 42[5 marks]
Answer or working	Marks
3^2 x 3^5 seen (area = width x length)	M1
3^7	A1cao
recognises length = area / width, i.e. 3^7 / 3^3	P1oe
3^(7-3) seen	M1
3^4	A1cao
Final answer: 3^7 \| 3^4

Mark scheme for Question 43 [3 marks]
Question 43[3 marks]
Answer or working	Marks
8% of 320 (=25.6) found	M1oe
320 + 25.6	M1oe
£345.60	A1cao