Name
Class
Question
Pre Public Exam Unit
June 2016
Mathematics
Intermediate Tier
WJEC Style
Non-Calculator
Time
1 hour 45 minutes
Marks Available
80 marks
Maximum
mark
1
6
2
6
3
3
4
4
5
5
6
7
7
4
8
8
9
6
10
4
11
4
12
6
13
3
14
3
15
4
16
4
17
3
Total
80
Commissioned by The PiXL Club Ltd.
1
Mark
2
1. Calculate the following.
(a) 10² × 23
[2]
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(b) 0·4 × 0·6
[1]
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(c) 6·7 - 3·25
[1]
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(d)
-
[2]
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3
2. (a) Write down the next two numbers in the following sequence.
18
14
10
6
.........
[2]
.........
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(b)
Simplify the expression 9x + 4y - 7x - 6y.
[2]
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(c)
Using the formula Q = 7P + 2S, find the value of S when Q = 36 and P = 4
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4
[2]
3.
Showing all of your workings, find which of the quantities
9
20
, 0.46 and 43% is
(i) the smallest, (ii) the largest
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(i)
4.
Smallest = ………………………(ii)
Largest = ………………………….
[3]
Calculate 30% of ¼ of 160
[4]
5
5.
(a)
Find the size of angle x.
[2]
𝑥
65
Diagrams not drawn to scale
(b)
Find the size of angle y
[3]
yº
78º
134º
88º
6
6.
(a) Solve the equation
5 + 9x = 29 + 3x
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(b) Simplify
[3]
𝑦10 × 𝑦 2
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[2]
(c) Expand and simplify 5(2x + 4) – 2(2x + 7)
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7
[2]
7.
(a) For each of the following statements, circle whether it is true or false.
You must give an explanation for your choice.
(i) All prime numbers are always odd.
True / False
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[1]
(ii) If you halve any whole number ending in 8 you will always get a number ending in 4.
True / False
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[1]
(b) Matthew says
“When I multiply any whole number by its previous number, the result is always
an even number.”
Explain whether or not he is correct.
[2]
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8
8.
A game is played by selecting two different cards. One pack is coloured black and the other
pack is coloured pink.
The black pack has three cards numbered.
11
14
15
The pink pack has four cards numbered
11
13
12
33
4
31
In the game, a player chooses one card from the black pack and one card from the pink pack.
To calculate the player’s score you find the product of the two numbers.
For example, if the number on the black card is 1 and the number of the pink card is 2, the score is
worked out by 1 x 2 = 2 and the player scores 2.
(a) Complete the following table to show all the possible scores.
Pink Cards
Black Cards
9
[2]
(a) A player wins a prize by gettering a score of 10 or more.
(i) What is the probability that a player wins a prize?
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(ii)
[2]
120 people each place the game once.
Aproximately how many would you expect to win a prize?
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(iii)
[2]
It costs 80p to play the game once. The prize for getting a score of 10 or more is £1.50. If the
120 people people each play the game once, approximately how much profit do you expect the
game to make?
…………………………………………………………………………………………………………………………………………
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10
[2]
9.
You will be assessed on the quality of your organsation, communication and
accuracy in writing in this question.
The area of the trapezium is equal to the area of the right-angled triangle.
4 cm
5 cm
10 cm
12 cm
x cm
Diagrams not drawn to scale
Calculate the value of x.
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11
[6]
10.
1
Seven single digit numbers have a median of 6 and a range of 8.
The mode of seven numbers is 3. Find the seven numbers.
Write your single digit numbers in order in the boxes below.
1
1
1
1
1
1
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12
[4]
11.
The table below shows some values of y = x³ - 3x + 4 for values of x from -3 to 3.
x
-3
y = x³ - 3x + 4
-14
-2
-1
0
1
2
6
4
2
6
3
(a) Complete the table above.
[2]
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(b) On the graph paper below draw the graph of y = x³ - 3x + 4 for the values of x from -3 to 3.
13
[2]
12.
Gwyn either walks, cycles, travels by car or travels by bus to work each day.
Her method of travel each day is independent of her method of travel on any other day.
The table below shows the probability for three of her methods of travel on any randomly chosen
day.
Method of travel
Probability
(a)
Walk
Bike
Car
Bus
0·35
0·2
0·05
Calculate the probability that, on any randomly chosen day, she walks to work.
[2]
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(b)
What is the probability that, on any randomly chosen day, she either travelled to work by car or by
bus?
[2]
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(c)
What is the probability that, in any randomly chosen week, Gwyn travelled to work by car on the
Monday and by bus on the Tuesday?
[2]
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14
13.
The diagram below shows part of a regular polygon.
Diagram not drawn to scale
How many sides does this regular polygon have?
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[3]
15
14.
Circle your answer in each of the following.
(a)
1/15
The value of 5 – 3 as a fraction in its simplest form is
-1/15
1/125
-1/125
15/125
[1]
(b)
4/9 as a recurring decimal is
0·49494949……
0·499999…….
0·949494…..
0·4444444….
0·9444444….
[1]
(c) 13 0 is equal to
13
1
0
1/3
16
1·3
[1]
15.
(a) Draw the reflection of the triangle A in the line y=x. Label the image C.
(b) Rotate the triangle B through 90° clockwise about the point (–1, 2).
Label the image D.
17
[2]
[2]
16.
Find, in standard form, the value of
i 4.5 × 106
[2]
30000
..………………………………………………………………………………………………………………………………………………………
.
.……………………………………………………………………………………………………………………………………………………….
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ii
(1·5 × 103) + (3 × 106).
[2]
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17.
Solve
x² + 2x – 15 = 0
[3]
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18