Please read this page, but do not open your booklet until your teacher tells you to start. Write your name and the name of your school in the spaces below.
First name Last name School
The test is 1 hour long. You may use a calculator for any question in this test. You will need: pen, pencil, rubber, ruler and a scientific or graphic calculator. Some formulae you might need are on page 2. This test starts with easier questions. Try to answer all the questions. Write all your answers and working on the test paper – do not use any rough paper. Marks may be awarded for working. Check your work carefully. Ask your teacher if you are not sure what to do.
For marker’s use only
Total marks Borderline check
This means write down your answer or show your working and write down your answer.
You may use a calculator to answer any question in this test.
You might need to use these formulae
1 (a + b)h 2
Volume = area of cross-section t length
Ratio of ages
Paul is 14 years old. His sister is exactly 6 years younger, so this year she is 8 years old. This year, the ratio of Paul’s age to his sister’s age is 14 : 8 14 : 8 written as simply as possible is 7 : 4
(a) When Paul is 21, what will be the ratio of Paul’s age to his sister’s age? Write the ratio as simply as possible.
(b) When his sister is 36, what will be the ratio of Paul’s age to his sister’s age? Write the ratio as simply as possible.
(c) Could the ratio of their ages ever be 7 : 7? Tick ( ) Yes or No. Yes Explain how you know. No
The information in the box describes three different squares, A, B and C.
The area of square A is 36cm2 The side length of square B is 36 cm The perimeter of square C is 36cm
Put squares A, B and C in order of size, starting with the smallest. You must show calculations to explain how you work out your answer.
The squared paper shows the nets of cuboid A and cuboid B.
(a) Do the cuboids have the same surface area? Show calculations to explain how you know.
(b) Do the cuboids have the same volume? Show calculations to explain how you know.
Two beaches are very similar. A survey compared the number of animals found in one square metre on each beach.
One beach had not been cleaned. The other beach had been cleaned.
(a) The data for the beach that had not been cleaned represent 1620 animals. Complete the table to show how many of each animal were found.
(b) The data for the beach that had been cleaned represent 15 animals. Complete the table to show how many of each animal were found on the cleaned beach.
(c) Cleaning the beach changes the numbers of animals and the proportions of animals. Write a sentence to describe both these changes.
Find the values of t and r
2 t = 3 6
2 5 = r 3
This pattern has rotation symmetry of order 6 (a) What is the size of angle w ? Show your working.
Not drawn accurately
(b) Each quadrilateral in the pattern is made from two congruent isosceles triangles. What is the size of angle y ? Show your working.
Not drawn accurately
Ks and ms
On the square grids below you can join dots with two different length lines. Length m is greater than length k
(a) Draw a shape with each...
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