Mr.
Jacobs
Practise past
paper 2
Mathematics
Stage 8
Paper 1 2023
eacher
1 hour
Additional materials: Geometrical instruments
Tracing paper (optional)
INSTRUCTIONS
• Answer all questions.
• Write your answer to each question in the space provided.
• You should show all your working on the question paper.
• You are not allowed to use a calculator.
INFORMATION
• The total mark for this paper is 50.
• The number of marks for each question or part question is shown in brackets [ ].
Don’t answer questions
crossed out with a Red
3142_01_6RP
Cross
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2
1 Write down the coordinates of two possible points that are on the line y = x + 4
( , ) and ( , ) [1]
2 Write integers in the boxes to make each statement correct.
70 = IV A
,
720 ÷ 718 = 49VA ./.
720 18
72
-
[2]
3 Work out.
3 −1000
-03 = -1000 % 3-1000 = -10
-
-
10 As [1]
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3 , no
equal sign
4 Draw a line to match each formula, equation or expression to the correct description.
3x + 4 = 19
Formula
10mp A , all
Equation correct
A=b×h
Expression
y
↑
= 20
4
[1]
5 Complete this sentence. 35x1 6 .
=
355x5
As
35 miles is equal to 561 km. [1]
6 (a) Write down the gradient of the line y = 3x + 5
[1]
(b) Write down the y-intercept of the line y = 7 – 8x
[1]
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4
7 Work out.
4 2
8 −3
7 7
Give your answer as a mixed number in its simplest form.
1
:
60 .
23
=
3 = 57
59A [2]
8 When a fair spinner is spun the arrow is equally likely to point in any direction.
Chen has these four fair spinners.
I heoretical
probability P(R) 5 PCR) =
33
5
=
PCR) =
R S R S R S
pCr =
E S R T
T V T R T
V
He spins one of the spinners 600 times and the arrow points to the letter R 205 times.
Draw a ring around the spinner he is most likely to have used.
experimental probability= to the second spinner
[1]
9 Complete each sentence with the correct number.
L
A regular octagon has g lines of symmetry.
A
A regular hexagon has rotational symmetry of order G
[1]
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> use H C F
. .
5
and write with brackets
10 Factorise.
6x + 24
G(x + 4)
G(x+ 4) An
=
[1]
11 The diagram shows two straight lines crossing two parallel lines.
y°
x°
NOT TO
SCALE
42°
33°
Find the value of x and the value of y.
Give a geometrical reason for each answer.
x= because
y= because
[2]
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12 Complete the grid so that the three numbers in each row, each column and each diagonal
have the same total.
514 −12 A, V 3 Correct
−8 −1 6 A ~ all correct
10 −16 3
[2]
13 Find the value of each of these expressions when x = – 8 Substitute
10x2
10( 8)2 = 10(64)
A
-
=
640
5(12 − x)
= 5(12 -
C 8))
-
100
-
1
= 5(12 +8) [2]
=
5(20)
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14 The diagram shows a triangle with an exterior angle of 120°.
NOT TO
x°
65° SCALE
120°
Work out the value of x.
x= [1]
15 Expand the brackets.
5t(t2 + 2t − 3)
= 5t(2 2t *3) +
An
2
= 573 + 10t2 15t
-
5t + 10t -
157 [1]
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16 (a) Work out the area of this parallelogram.
15 cm
NOT TO
6 cm SCALE
7.5 cm
Area-base
height
: 15cm X 6cm
= 90 cm2
V Ai
90 cm2 cm2 [1]
(b) Work out the area of this trapezium.
4 mm NOT TO
SCALE
5 mm
10 mm
Area = (a +b) x
height
Mi
=
&(4 + ) + 5
~A
35 mm2
: 35mm? mm2 [2]
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17 The diagram shows two triangles, T and V.
y
8
7
6
5
V 4
3
2
1
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 x
–1
–2 T
–3
–4
–5
–6
–7
–8
(a) A transformation maps triangle T onto triangle V.
Complete these sentences.
The type of transformation is
The scale factor is
[2]
(b) Rotate triangle T by 270° anticlockwise about the point (–2, –3). [2]
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18 Mike has these four number cards.
2 2 2 5
He uses each card once to make a four-digit number.
Work out how many different four-digit numbers he could make.
A
4 [1]
19 Jamila has p pencils.
Hassan has 3 fewer pencils than Jamila.
Naomi has 4 times as many pencils as Hassan.
Write an expression, in terms of p, for the total number of pencils the three children have.
Write your expression in its simplest form.
p +
(p 3) + 4(p 3) M ,
-
-
12
=
p p
+ -
3 +
4p
um
-
Al vA
=
6p - 15
Gp-15 [3]
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20 Here is a table showing information about some linear number sequences.
Sequence First four terms of How the sequence is Term-to-
5th term
name sequence related to sequence A term rule
A 6, 10, 14, 18, … Add 4 22
Add 1 to each term in
B 7, 11, 15, 19, … Add 4 23
sequence A
C Add 4 20
Double each term in
D
sequence A
E –6, –10, –14, –18, …
Complete the table. [3]
<
Rangeofnumbersanoints
9
difficult Question for
21 n lies in the interval 3.5 < n < 3
SS
16
>
mark
Find a possible value of n.
Give your answer as a mixed number.
only I
.
7
< I A
56 3
16 In
n= [1]
114
< -
32
↓
113
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22 Draw a ring around the inequality that is equivalent to x ≤ 4
x–1≤5 2x < 8 x<5 x+1≤5 x–3≥1
[1]
An
23 Work out.
112 – 5 × 2.6 + 9 2 + 63
=
121 -
(13) + 81 +
63
An
= 121 -
13 + 144
~ roessary
= 121 -
13 =12 >
120 96 [2]
(2) 13 + 12 121-13-12
A,
= -
or
24 Rajiv has two pieces of string measuring 240 cm and 168 cm in length.
He cuts both pieces of string into smaller pieces that are all equal in length.
Work out the greatest possible length for each smaller piece.
cm [3]
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25 In June, eleven people take part in a long jump competition.
Here are the results for the distance, in metres, each person jumps.
2.6 2.4 3.6 2.8 4.2 3.8 5.1 3.0 4.5 3.3 4.6
(a) Complete the stem-and-leaf diagram for this information.
Key:
[3]
(b) In August, the same eleven people take part in another long jump competition.
The median distance jumped in August is 4.1 m.
Write down a comparison between the distances jumped in June and the distances
jumped in August.
You must use statistics to support your comparison.
[2]
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> not in exam (extension)
14
26 Here is square ABCD.
D C
A B
ABCD is drawn on a grid so that A is at (2, 1) and C is at (6, 5).
ABCD is reflected in the y-axis to make square A’B’C ’D’.
Write each of these points in the correct place in the table.
(3, –3) (–2, 3) (–5, 6) (–3, 3) (–2, 5)
On the edge of
Inside square Outside square A vertex of square
square A’B’C ’D’
A’B’C ’D’ A’B’C ’D’ A’B’C ’D’
but not a vertex
[2]
27 Lily thinks of a number.
She squares the number and the answer is 4.6225
There are two possible numbers she could be thinking of.
Write down the sum of these two numbers.
thinks of
let Xnumber that
= lily
* VA
x = 4 6225
.
[1]
*
=
= 4 6225
.
X = 12 15
.
. 15
2 + ( -
2 . 15)
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