cambridge-mathematics-7-end-of-unit-test-units-8-15

Total: 50 marks

Instructions

Answer all 30 questions.

In Section 1, choose one correct answer for each question.

In Section 2, give your answers with the appropriate units.

In Section 3, show your working and explain your reasoning clearly.

A calculator may be used.

Do not measure lengths or angles from the diagrams.

SECTION 1. MULTIPLE CHOICE QUESTIONS (15 marks)

Choose one correct answer, A, B, C or D, for each question. Each question is worth 1 mark.

Question 1. How many lines of symmetry does a rectangle that is not a square have?

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Question 2. The diagram shows a regular pentagon. What is its order of rotational symmetry?

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Question 3. In the diagram, $O$ is the centre of the circle and $AB$ passes through $O$. Which segment is a diameter?

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Question 4. Which pair of rectangles consists of two congruent shapes?

Question 5. The diagram shows a triangular prism. How many vertices does it have?

[A triangular prism with two triangular faces and three rectangular faces, without vertex labels.]

Question 6. Convert $0.46$ cm² to mm².

Question 7. Convert $32 000$ cm² to m².

Question 8. A nature reserve has an area of $0.72$ ha. What is its area in square metres?

Question 9. Triangle $ABC$ has base $BC=14$ cm and perpendicular height $AH=9$ cm. What is its area?

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Question 10. A cube has side length $4$ cm. What is its volume?

Question 11. A closed cuboid has length $7$ cm, width $4$ cm and height $3$ cm. What is its total surface area?

Question 12. The total surface area of a cube is $150$ cm². What is its side length?

Question 13. Which statement must be true for every regular polygon?

Question 14. A cylinder stands upright on one of its circular faces. What is the shape of its top view?

[An upright cylinder standing on a circular base.]

Question 15. The base of a triangle is doubled, but its perpendicular height stays the same. What happens to its area?

SECTION 2. SHORT ANSWER AND WORD PROBLEMS (20 marks)

Answer all ten questions. Each question is worth 2 marks. Include units where appropriate.

Question 1 (2 marks). A sheet of card has an area of $0.85$ m². Express this area in square centimetres.

Answer: ______________________________________________________________________________

Question 2 (2 marks). A rectangular school garden is $120$ m long and $75$ m wide. Calculate its area in hectares.

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Answer: ______________________________________________________________________________

Question 3 (2 marks). A triangular banner has a base of $80$ cm and a perpendicular height of $45$ cm. Calculate its area in square centimetres.

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Answer: ______________________________________________________________________________

Question 4 (2 marks). A rectangular label is $18$ cm long and $25$ mm wide. Calculate its area in square centimetres.

Answer: ______________________________________________________________________________

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Question 5 (2 marks). The internal dimensions of a rectangular storage box are $40$ cm by $25$ cm by $30$ cm. Calculate the volume of space inside the box in cubic centimetres.

Answer: ______________________________________________________________________________

[A cuboid representing the storage space inside the box, with internal length 40 cm, width 25 cm and height 30 cm.]

Question 6 (2 marks). A solid wooden cube has side length $6$ cm. Calculate its volume.

Answer: ______________________________________________________________________________

[A wooden cube with an edge labelled 6 cm.]

Question 7 (2 marks). A closed gift box is a cuboid with length $12$ cm, width $8$ cm and height $5$ cm. Calculate its total surface area.

Answer: ______________________________________________________________________________

[A closed cuboid gift box, 12 cm long, 8 cm wide and 5 cm high, with hidden edges dashed.]

Question 8 (2 marks). Triangle $ABC$ is congruent to triangle $DEF$, with corresponding vertices $A\leftrightarrow D$, $B\leftrightarrow E$ and $C\leftrightarrow F$. Given that $BC=10$ cm and $AC=6$ cm, find:

a) the length of $EF$;

b) the length of $DF$.

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Answer:

a)______________________________________________________________________________

b)______________________________________________________________________________

Question 9 (2 marks). A cuboid is $9$ cm long, $4$ cm deep and $7$ cm high. The front face measures $9$ cm by $7$ cm.

[A cuboid nine centimetres long, four centimetres deep and seven centimetres high.]

Write down the dimensions of:

a) the top view; ___________________________________________________________________

b) the side view.___________________________________________________________________

Question 10 (2 marks). A rectangular floor measures $3.6$ m by $2.4$ m. It is covered with square tiles of side length $30$ cm. The tiles fit exactly, with no gaps, overlaps or wastage. How many tiles are needed?

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Left: floor. Right: one square tile.

Answer: ______________________________________________________________________________

SECTION 3. EXTENDED RESPONSE AND EXPLANATION (15 marks)

Answer all five questions. Each question is worth 3 marks. Show your working and give clear explanations.

Question 1 (3 marks). Maya writes:

“$0.36$ m² is equal to $3600$ mm² because I multiply by $10 000$.”

a) Explain why Maya has used an incorrect conversion factor.

Answer: ______________________________________________________________________________

b) Calculate the correct value of $0.36$ m² in square millimetres.

Answer: ______________________________________________________________________________

Question 2 (3 marks). A rectangular piece of card is $12$ cm long and $8$ cm wide. A rectangle measuring $5$ cm horizontally and $3$ cm vertically is cut from its top-right corner, leaving an L-shaped piece of card.

a) Calculate the area of the remaining card in square centimetres.

Answer: ______________________________________________________________________________

b) Express your answer in square millimetres.

Answer: ______________________________________________________________________________

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The dashed lines show the original top-right corner before it was cut away.

Question 3 (3 marks). A closed cuboid has length $20$ cm, width $12$ cm and height $50$ mm. Leo writes:

“Volume $=12 000$ cm³.
Total surface area $=800$ cm².”

Check each of Leo’s answers. State whether each answer is correct or incorrect, and justify your decisions with calculations. Explain the likely mistake in any incorrect answer.

Answer: ______________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

[Leo's closed cuboid with length 20 cm, width 12 cm and height 50 mm. The drawing uses consistent proportions while retaining the given units on its labels.]

Question 4 (3 marks). A farmer has a triangular field with base $160$ m and perpendicular height $125$ m. Fertiliser is applied at a rate of $150$ kg per hectare and costs $0.80$ dollars per kilogram.

a) Calculate the area of the field in hectares.

Answer: ______________________________________________________________________________

b) The farmer has a budget of $130$ dollars for fertiliser. Is this enough to treat the whole field? Show your calculations.

Answer: ______________________________________________________________________________

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Question 5 (3 marks). Rectangle $A$ measures $9$ cm by $3$ cm. Rectangle $B$ measures $7$ cm by $5$ cm. Sam says:

“The rectangles have the same perimeter, so they must be congruent.”

a) Calculate the perimeter and area of each rectangle.

Answer: ______________________________________________________________________________

b) Decide whether Sam’s conclusion is correct. Explain your answer using the meaning of congruent shapes.

Answer: ______________________________________________________________________________

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Both rectangles are drawn using the same scale

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--------- THE END OF UNIT TEST ---------
Candidate name: ................................................ Class: ........................