Mathematics, Unit 2 Intermediate Tier

Name
Class
Question / Mark / Maximum mark
1 / 4
2 / 3
3 / 3
4 / 5
5 / 6
6 / 4
7 / 2
8 / 4
9 / 4
10 / 6
11 / 4
12 / 2
13 / 2
14 / 4
15 / 6
16 / 5
17 / 5
18 / 3
19 / 4
20 / 4
Total / 80

Predicted Paper
November 2017

Mathematics, Unit 2 Intermediate Tier

WJECStyle

Calculator-allowed

Time: 1 hour 45 minutes

Marks Available: 80 marks

Commissioned by The PiXL Club Ltd.

Using only the numbers in the following list,

41, 42, 43, 44, 45, 46, 47, 48, 49, 50

Write down

(a)a prime number, [1]

………………………………………………………………………………………………………………………………………………………

(b)a square number, [1]

………………………………………………………………………………………………………………………………………………………

(c)a factor of 188, [1]

………………………………………………………………………………………………………………………………………………………

(d)a multiple of 12.5. [1]

………………………………………………………………………………………………………………………………………………………

Circle the correct answer for each of the following statements.

(a)Two angles in an isosceles triangle add to 90.

The other angle must be

obtuseacuteright-angledreflex [1]

(b)Three of the angles in a parallelogram add up to 303.

The size of the fourth angle must be

6712357151.5180 [1]

(c)One of the angles in a right-angled triangle is 89.

One of the other angles must be

910.5811791 [1]

Shade the least number of squares in the lower two quadrants so that the grid has rotational symmetry of order 2. [3]

4.The diagram below shows a number machine.

Using the number machine, calculate:

(a)the INPUT when the OUTPUT is 77, [1]

……………………………………………………………………………………………………………………………………………….

(b)the OUTPUT when the INPUT is , [2]

……………………………………………………………………………………………………………………………………………….

(c)the INPUT when the OUTPUT is . [2]

……………………………………………………………………………………………………………………………………………….

5.The table shows the minimum temperature recorded on 10th November in six cities around the world.

City / Berlin / Cardiff / Chicago / Milan / New-York / Vancouver
Temperature (C) / 0 / 7 / -3 / 11 / -5 / -35

(i)What is the difference in temperature between the warmest and coldest cities? [2]

……………………………………………………………………………………………………………………………………………….

(ii)What is the median temperature recorded? [2]

……………………………………………………………………………………………………………………………………………….

(iii)On November 10th, the temperature in Vancouver was 5C lower than the temperature in Calgary.

What was the temperature in Calgary? [1]

……………………………………………………………………………………………………………………………………………….

(iv)On November 10th, the temperature in Chicago was 11 higher than the temperature in Moscow.

What was the temperature in Moscow? [1]

……………………………………………………………………………………………………………………………………………….

6. Show clearly whether the following statement is true or false. [4]

‘The value of Michael’s flat decreased by 10% in 2015. In 2016, the value of his flat increased by 15%. Overall, Michael’s flat increased in value by 5%’.

…………………………………………………………………………………………………………………………………………………………….

7.Circle TRUE or FALSE for each statement written in the table below [2]

STATEMENT
All triangles with equal areas are congruent. / TRUE / FALSE
All squares with equal perimeters are congruent. / TRUE / FALSE
All regular pentagons are congruent. / TRUE / FALSE
All isosceles triangles with base angles of 70 are congruent. / TRUE / FALSE

8.Damon is playing a game that uses cards, numbered 1 - 20.

The game requires him to calculate the range, mean and median of the numbers on five cards.

Damon has these five cards.

Damon has one final turn in which he must replace exactly two of his tiles with different tiles. To win the game, he needs to:

increase the mean by 1
increase the median by 1
keep the same range.

Fill in the numbers on the square cards below to show the three cards he has kept, and the new numbers on the two tiles he has replaced, if he is to win.

……………………………………………………………………………………………………………………………………………..

[4]

9. (a) Calculate to 2 decimal places. [2]

……………………………………………………………………………………………………………………………………………………

(b) Calculate the reciprocal of -0.0021 to 2 significant figures. [2]

……………………………………………………………………………………………………………………………………………………

10.(a)Write down the term of the following sequence. [2]

12,18,24,30,36, ………….

……………………………………………………………………………………………………………………………………………….

(b)(i) The term of a different sequence is given by . [2]

……………………………………………………………………………………………………………………………………………...

……………………………………………………………………………………………………………………………………………....

……………………………………………………………………………………………………………………………………………….

The first three terms are ……….….. , …………… and …………….

(ii) Which term in this sequence is the first that has a value greater than 125?

[2]

……………………………………………………………………………………………………………………………………………...

……………………………………………………………………………………………………………………………………………....

……………………………………………………………………………………………………………………………………………….

Answer = ……………………….

11.Using only the expressions in the following list,

Simplify the following expressions.

(a)÷ = [1]

…………………………………………………………………………………………………………………………………………………………….

(b)× = [1]

…………………………………………………………………………………………………………………………………………………………….

(d)= [1]

…………………………………………………………………………………………………………………………………………………………….

12.Circle the correct answer for each of the following.

(a)( = [1]

(b)A coach travels miles in 120 minutes.

Its average speed in miles per hour is [1]

120

13. Reflect triangle in the line . [2]

14.A solution to the equation

lies between 2 and 3.

Use the method of trial and improvement to find this solution correct to 1 decimal place.

You must show all your working. [ 4 ]

……………………………………………………………………………………………………………………………………………………

…………………………………………………………………………………………………………………………………………………..

……………………………………………………………………………………………………………………………………………………

15.(a) Calculate the length of the side FE in the triangle EFG shown below. [3]

………………………………………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………………………………….

………………………………………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………………………………….

(b)Calculate the size of the angle [3]

………………………………………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………………………………….

………………………………………………………………………………………………………………………………………………

……………………………………………………………………………………………………………………………………………….

16. (a) The diagram below shows the graph of a straight line for values of from -3 to 3.

(i)Write down the gradient of the above line. [1]

…………………………………………………………………………………………………………………………………………………………….

(ii)Write down the equation of the line in the form where and are whole numbers. [2]

…………………………………………………………………………………………………………………………………………………………….

Line / Equation
A /
B /
C /
D /
E /

(b) Which two of the above lines are parallel? You must give a clear reason for your answer. [2]

……......

……………………………………………………………………………………………………………………………………………….

17.Phil is a professional darts player. He believes that, with any throw, he can hit the bull’s eye with a probability of 50%.

Sid challenges him to prove this by throwing 5 sets of 10 darts.

Phil’s results are recorded in the table below.

Number of throws / First 10 / Second 10 / Third 10 / Fourth 10 / Fifth 10
Number of bull’s eyes hit / 6 / 4 / 8 / 7 / 2

(a)After 30 throws, the relative frequency of hitting a bullseye was calculated as = 0.6.

What is the relative frequency after 40 throws?

Give your answer as a decimal. [1]

……………………………………………………………………………………………………………………………………………….

(b) What is the relative frequency after 50 throws?

Give your answer as a decimal. [1]

……………………………………………………………………………………………………………………………………………….

You must give a reason for your answer. [1]

Reason: ………………………………………………………………………………………………………………………………….

……………………………………………………………………………………………………………………………………………….

(d) In 1200 throws, how many times would you expect Phil to hit bull’s eye? [2]

……………………………………………………………………………………………………………………………………………….

18.In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The diagram shows a regular hexagon.

Calculate the size of angle

You must show all your working to support your answer. [3]

…………………………………………………………………………………………………………………………………………………………….

19.82% of first class parcels posted before 1pm on Monday arrive at their destination the next day. 12% of first class parcels posted before 1pm on Monday arrive at their destination on Wednesday.

(a)Complete the following tree diagram to show the probabilities of what can happen when two first class parcels are posted independently before 1pm on a Monday. [2]

[2]

(b)Calculate the probability that both parcels arrive on Wednesday.

…………………………………………………………………………………………………………………………………………………………….

20. Solve the equation [ 4 ]

…………………………………………………………………………………………………………………………………………………..

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