Phase test
Calculator allowed
Please read this page, but do not turn over until your teacher tells you to start.
Write your details in the spaces below.
Name ______
Class ______
Teacher ______
Date ______
Remember
§ The test is one hour long.
§ You will need: pen, pencil, rubber, ruler and a protractor.
§ Try to answer all the questions.
§ Write all your answers and working on the test paper.
§ Check your work carefully.
§ Ask your teacher if you are not sure what to do.
For marker’suse only / Total marks
Calculator allowed 60 marks total
1 a Write down the prime factor decomposition of 120.
______(1 mark)
b What is the highest common factor of 120 and 36?
______(1 mark)
2 The radius of circle A = 3.5 cm.
a What is the circumference of A to 1 decimal place?
(For this question, use p = 3.14)
______cm (2 marks)
2 cont.
b What is the area of circle A to 2 dp?
______cm2 (1 mark)
Circle B has an area of 201.06 cm2.
c Calculate the radius of circle B to 1 dp.
______cm (2 marks)
3 Six children enter a race on sports day.
Their probabilities of winning are given in the table.
Anna / Jack / Mike / Ahmed / Alice / Melissa0.16 / 0.35 / 0.24 / 0.07
Alice and Melissa both have the same chance of winning.
a Fill in their probabilities on the table. (2 marks)
b What is the probability of a boy winning?
______(2 marks)
4 Here are some fractions.
a Which of the fractions are larger than ?
Circle your answer(s). (1 mark)
b Which of the fractions below are equivalent to ?
(1 mark)
c Calculate
i +
______(1 mark)
ii –
______(1 mark)
5 Louise goes to the shops to buy shoes.
a A pair of shoes was originally £70.
They are reduced by 60% in the sale.
What is the sale price?
£ ______(2 marks)
b A pair of sandals was £50 and now they cost £20.
What is the percentage reduction?
£ ______(2 marks)
c A pair of shoes costs £79.95 in the sale.
They have been reduced by 35%.
What was their original price?
£ ______(2 marks)
6 DE and FG are parallel lines. Right-angled triangle ABC is drawn between them.
a Find b and c.
b = ______°
c = ______° (2 marks)
b What type of triangle is ABC? Choose from the list below:
Equilateral Scalene Isosceles Regular
Give a reason for your answer.
______
______(1 mark)
7 Solve the equations.
a (3x − 4) = 3x + 21
x = ______(2 marks)
b + 5 = 11
x = ______(2 marks)
8 a Make R the subject of the formula I =
______(1 marks)
b Make u the subject of the formula s = t
______(2 marks)
9 Here are five cards.
a Which cards have a vertical line of symmetry?
______(1 mark)
b Which have both a vertical and a horizontal line of symmetry?
______(1 mark)
Claire says Shape 1, which is a rectangle with a diagonal line, does not have any lines of symmetry but Doctor McAllister says it does have a line of symmetry.
c Who is right? Explain your answer.
______
______(1 mark)
10 A set of patterns is made out of counters.
They are labelled T1, T2, …, Tn
a Complete this table to show the number of counters in each of the first seven patterns.
Triangle number (n) / 1 / 2 / 3 / 4 / 5 / 6 / 7Number of Counters (c)
(2 marks)
The position to term rule is C =
b How many counters are there in the twentieth pattern?
______(2 marks)
11 This grouped frequency table shows the time, t hours, that
20 children spend at a computer.
Frequency / 1 / 4 / 13 / 2
Emily is investigating her hypothesis that ‘it is unhealthy to spend more than 1.5 hours on the computer per day’.
Emily wants to work out the exact percentage of the class that spends more than 1.5 hours at a computer.
a Why can she not work this out?
______
______(1 mark)
b How could Emily resolve this problem in a future survey?
______
______(1 mark)
c What fraction of the children spend less than half an hour per day on a computer?
______(1 mark)
12 Raymond has two cats, Bits and Bobs.
Bits gives birth to six kittens.
a What is the ratio of adult cats to kittens in its simplest form?
______(1 mark)
Bobs then gives birth to eight kittens.
b What is the new ratio of adult cats to kittens?
______(1 mark)
c What percentage of all the cats are kittens?
______% (1 mark)
13 A survey was done of the colour of 120 cars. Here are the results.
Blue / 9
Red / 15
Silver / 66
Black / 30
a Fill in this table for the percentage of cars that were each colour.
Blue
Red
Silver
Black
(2 marks)
b Show this data on a pie chart.
You must label each sector of the chart.
(3 marks)
14 Use this equation to answer the questions below:
6x2 + 4 = 28
a What is the value of 3x2 + 2?
______(1 mark)
b What is the value of x2?
______(2 marks)
c What is the value of x?
______(1 mark)
15 The cross-section of a prism is made from a rectangle and a square.
The prism is 5 cm deep.
a What is the area of the shaded face of the prism?
______cm2 (2 marks)
b Find the surface area of the prism.
______cm2 (3 marks)
c What is the volume of the prism?
______cm3 (2 marks)