Foundation Tier - Year 10

Year 10 Paper 3: Shape and Measures

Covers area, volume and measures, angles and geometrical reasoning, fractions, decimals and percentages, indices and standard form, graphs and coordinates, ratio and proportion, and sequences.

23 questions - 60 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 [1 marks]

Angles and Geometrical Reasoning

Circle the angle below that is a reflex angle. A) 45 degrees B) 90 degrees C) 135 degrees D) 200 degrees

Question 2 [2 marks]

Ratio and Proportion

On a school trip, the ratio of adults to children on a coach is 4:9.

Write the number of adults as a fraction of the number of children.

Write the number of children as a fraction of the total number of people on the coach.

Question 3 [2 marks]

Graphs and Coordinates

On the grid provided, draw the following straight lines.

Draw the graph of x = -3.

Draw the graph of y = 2.

Question 4 [3 marks]

Sequences

Three sequences are shown below. Sequence A: 7, 11, 15, 19 Sequence B: 4, 12, 36, 108 Sequence C: 3, 6, 11, 18

State whether Sequence A is arithmetic, geometric, or neither of these. Give a reason for your answer.

State whether Sequence B is arithmetic, geometric, or neither of these. Give a reason for your answer.

State whether Sequence C is arithmetic, geometric, or neither of these. Give a reason for your answer.

Question 5 [3 marks]

Area, Volume and Measures

Priya makes an open-topped rectangular planter (no lid) with length 120 cm, width 40 cm and height 50 cm. Work out the total surface area of the planter, including the base but not the open top.

Question 6 [3 marks]

Indices and Standard Form

Four identical square tiles, each with area 100 cm^2, are arranged edge-to-edge (2 tiles by 2 tiles) to form one larger square.

Question 7 [4 marks]

Fractions, Decimals and Percentages

A piece of ribbon is 96 cm long. Ben cuts off 3/8 of the ribbon.

Work out the length of ribbon that Ben cuts off.

Chloe then cuts off 3/5 of the ribbon that remains after Ben's cut. Work out the length of ribbon that is left.

Question 8 [1 marks]

Ratio and Proportion

Work out £88 in Canadian dollars. Use the exchange rate 1 GBP = 1.68 CAD.

Question 9 [2 marks]

Graphs and Coordinates

Find the gradient of the straight line joining the points (1, 1) and (4, 7).

Question 10 [2 marks]

Fractions, Decimals and Percentages

Simplify 42/56 to its lowest terms.

Question 11 [2 marks]

Angles and Geometrical Reasoning

The diagram shows a flat solid made from three 1 cm cubes on a 2 by 2 grid (one grid position is empty).

Which of these is the correct plan of the solid?

Even though the plan is an L-shape, the front elevation of this solid is a plain 2 cm by 1 cm rectangle, with no gap visible. Give a reason why.

Question 12 [1 marks]

Fractions, Decimals and Percentages

Work out 5/12 of 84 cm.

Question 13 [2 marks]

Indices and Standard Form

Work out (2 x 10^5) x (3 x 10^3). Give your answer in standard form.

Question 14 [2 marks]

Area, Volume and Measures

Convert 3.2 m^2 to cm^2.

Question 15 [3 marks]

Indices and Standard Form

Simplify 6^2 ÷ 6^1.

Question 16 [3 marks]

Graphs and Coordinates

The diagram shows two straight lines, l1 and l2, drawn on the same grid. l1 has equation y = 2x - 1 and l2 has equation y = -x + 5.

Write down the coordinates of the point where l1 and l2 intersect.

Hence write down the solution to the simultaneous equations y = 2x - 1 and y = -x + 5.

Question 17 [3 marks]

Indices and Standard Form

Simplify each of the following.

a^5 x a^2

b^9 / b^4

(c^3)^3

Question 18 [3 marks]

Ratio and Proportion

A shipping container holds gravel with a mass of 3.6 tonnes and a volume of 2.4 m^3. Work out the density of the gravel in kg/m^3.

Question 19 [3 marks]

Indices and Standard Form

Work out 4^3 and give the answer in standard form if needed.

Question 20 [3 marks]

Ratio and Proportion

A coach travels at an average speed of 56 km/h for 2 hours 30 minutes. Work out the distance travelled.

Question 21 [4 marks]

Angles and Geometrical Reasoning

Town P is due west of town Q. A plane leaves P and flies to R on a bearing of 030 degrees. Work out (i) the bearing of Q from P, and (ii) the bearing of P from R. Show your working for both.

Question 22 [4 marks]

Graphs and Coordinates

On a coordinate grid, a line goes through (-2, 1) and (2, 3). (a) Work out the gradient of the line. (b) Hence or otherwise find the y-intercept.

Question 23 [4 marks]

Area, Volume and Measures

A recipe for flapjacks that serves 6 people uses 750 g of oats.

Write 750 g in kilograms.

Bilal wants to make enough flapjacks to serve 15 people, using the recipe in the same proportions. Work out how many kilograms of oats he needs.

Model solutions

Mark scheme for Question 1 [1 mark]
Question 1[1 mark]
Answer or working	Marks
D circled	B1cao
Final answer: D) 200 degrees

Mark scheme for Question 2 [2 marks]
Question 2[2 marks]
Answer or working	Marks
4/9	B1oe
9/13	B1oe
Final answer: 4/9 \| 9/13

Mark scheme for Question 3 [2 marks]
Question 3[2 marks]
Answer or working	Marks
correct vertical line drawn through x = -3	B1
correct horizontal line drawn through y = 2	B1
Final answer: Vertical line through every point with x-coordinate -3. \| Horizontal line through every point with y-coordinate 2.

Mark scheme for Question 4 [3 marks]
Question 4[3 marks]
Answer or working	Marks
arithmetic, since the terms have a common difference of 4	B1oe
geometric, since the terms have a common ratio of 3	B1oe
neither, since the differences (3, 5, 7) are not constant and the ratios are not constant	B1oe
Final answer: Arithmetic (common difference of 4) \| Geometric (common ratio of 3) \| Neither (it is a quadratic sequence)

Mark scheme for Question 5 [3 marks]
Question 5[3 marks]
Answer or working	Marks
base area 120 x 40 (= 4800) seen	M1
complete method for the four side faces, e.g. 2(120x50) + 2(40x50) (= 16000)	M1
20800 cm^2	A1cao

Mark scheme for Question 6 [3 marks]
Question 6[3 marks]
Answer or working	Marks
sqrt(100) = 10 cm, the side length of one small tile	M1
20 cm (2 x 10) identified as the side length of the larger square	M1
400 cm^2 cao (units required)	A1
Final answer: 400 cm^2

Mark scheme for Question 7 [4 marks]
Question 7[4 marks]
Answer or working	Marks
96/8 = 12 oe (dividing by the denominator)	M1
36 (cm)	A1cao
96 - 36 = 60 (ft from part (a)), then 3/5 x 60 = 36 oe, Chloe's cut	M1
24 (cm)	A1cao
Final answer: 36 cm \| 24 cm

Mark scheme for Question 8 [1 mark]
Question 8[1 mark]
Answer or working	Marks
88 × 1.68 = 147.84	B1cao
Final answer: 147.84 CAD

Mark scheme for Question 9 [2 marks]
Question 9[2 marks]
Answer or working	Marks
(7 - 1)/(4 - 1), oe substitution into the gradient formula	M1
2	A1cao

Mark scheme for Question 10 [2 marks]
Question 10[2 marks]
Answer or working	Marks
divide numerator and denominator by a common factor, e.g. 14	M1oe
3/4	A1cao

Mark scheme for Question 11 [2 marks]
Question 11[2 marks]
Answer or working	Marks
B	B1cao
correct reason, e.g. Column 2 still has a cube in Row 1, so that column still shows height 1 from the front; the missing cube in Row 2 is hidden behind it	B1oe
Final answer: B \| The empty grid position is hidden behind a cube in the other row of the same column, so the front elevation still shows full height across both columns.

Mark scheme for Question 12 [1 mark]
Question 12[1 mark]
Answer or working	Marks
35 cm	B1cao

Mark scheme for Question 13 [2 marks]
Question 13[2 marks]
Answer or working	Marks
2 x 3 = 6 and 10^5 x 10^3 = 10^8 seen, or 6 x 10^8 oe unsimplified	M1
6 x 10^8	A1cao

Mark scheme for Question 14 [2 marks]
Question 14[2 marks]
Answer or working	Marks
3.2 x 10000, using 1 m^2 = 10000 cm^2	M1
32000 (cm^2)	A1cao
Final answer: 32000 cm^2

Mark scheme for Question 15 [3 marks]
Question 15[3 marks]
Answer or working	Marks
use law 6^2 ÷ 6^1 = 6^(2-1) or show 36 ÷ 6	M1
6	A1cao
accept explanation using index rule	B1

Mark scheme for Question 16 [3 marks]
Question 16[3 marks]
Answer or working	Marks
(2, 3)	B1
x = 2 (ft from (a))	B1
y = 3 (ft from (a))	B1
Final answer: (2, 3) \| x = 2, y = 3

Mark scheme for Question 17 [3 marks]
Question 17[3 marks]
Answer or working	Marks
a^7	B1cao
b^5	B1cao
c^9	B1cao
Final answer: a^7 \| b^5 \| c^9

Mark scheme for Question 18 [3 marks]
Question 18[3 marks]
Answer or working	Marks
3.6 tonnes = 3600 kg	M1oe
3600 / 2.4	M1dep
1500 (kg/m^3)	A1cao
Final answer: 1500 kg/m^3

Mark scheme for Question 19 [3 marks]
Question 19[3 marks]
Answer or working	Marks
calculate 4^3 = 4 x 4 x 4 or show method	M1
64	A1cao
if standard form required: 6.4 x 10^1 cao (award if student gives this form)	B1

Mark scheme for Question 20 [3 marks]
Question 20[3 marks]
Answer or working	Marks
2 hours 30 minutes = 2.5 hours	M1oe
56 x 2.5	M1dep
140 (km)	A1cao
Final answer: 140 km

Mark scheme for Question 21 [4 marks]
Question 21[4 marks]
Answer or working	Marks
recognise 'P is due west of Q' means Q is due east of P	M1
(i) 090 degrees	A1cao
back bearing of P from R: since the bearing P->R is less than 180, add 180: 030 + 180	M1
(ii) 210 degrees	A1cao
Final answer: (i) 090 degrees (ii) 210 degrees

Mark scheme for Question 22 [4 marks]
Question 22[4 marks]
Answer or working	Marks
gradient = (3 - 1)/(2 - (-2)) = 2/4 = 1/2	M1
1/2	A1cao
use y = mx + c with m = 1/2 and substitute a point, e.g. 1 = (1/2)(-2) + c	M1
y-intercept = 2	A1cao
Final answer: 1/2 \| y-intercept = 2 (so equation y = 1/2 x + 2)

Mark scheme for Question 23 [4 marks]
Question 23[4 marks]
Answer or working	Marks
0.75	B1cao
750 / 6 (= 125), finding the oats needed per person	M1
their 125 x 15	M1dep
1.875 (kg) oe cao (accept 1875 g)	A1
Final answer: 0.75 kg; 1.875 kg