Nov 2018 Paper 1 Q21
A
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1
M
P
O
N
B
OAB is a triangle.
OPM and APN are straight lines.
M is the midpoint of AB.
o
OB = b
OP : PM = 3 : 2
Work out the ratio ON : NB
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o
OA = a
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(Total for Question is 5 marks)
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19
Turn over
2
Nov 2017 Paper 3 Q21
N
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A
P
O
M
B
OAN, OMB and APB are straight lines.
AN = 2OA.
M is the midpoint of OB.
l=a
l=b
OA
OB
l
AP = k l
AB where k is a scalar quantity.
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Given that MPN is a straight line, find the value of k.
(Total for Question is 5 marks)
20
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3
June 2017 Paper 1 Q19
A
B
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a
O
c
C
OABC is a parallelogram.
o
o
OA = a and OC = c
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X is the midpoint of the line AC.
OCD is a straight line so that OC : CD = k : 1
o
1
Given that XD = 3cí a
2
find the value of k.
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k = .......................................................
(Total for Question is 4 marks)
16
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4
Sample Paper 3 Q18
O
A
N
C
B
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M
OMA, ONB and ABC are straight lines.
M is the midpoint of OA.
B is the midpoint of AC.
→
→
→
OA = 6a
OB = 6b
ON = kb where k is a scalar quantity.
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Given that MNC is a straight line, find the value of k.
18
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Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics - Sample Assessment Materials (SAMs) - Issue 2 - June 2015
© Pearson Education Limited 2015
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(Total for Question is 5 marks)
5
Mock Set 1 Paper 2 Q21
A
O
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X
Z
Y
B
OAB is a triangle.
A is the midpoint of OZ
Y is the midpoint of AB
X is a point on OB
→
→
→
OA = a OX = 2b XB = b
Prove that XYZ is a straight line.
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20
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(Total for Question is 5 marks)
Specimen 2 Paper 3 Q20
6
A
O
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2a
P
2b
B
OAB is a triangle.
P is the point on AB such that AP : PB = 5:3
→
OA = 2a
→
OB = 2b
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→
OP = k(3a + 5b) where k is a scalar quantity.
Find the value of k.
(Total for Question is 4 marks)
18
170
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Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics Specimen Papers Set 2 - September 2015 © Pearson Education Limited 2015
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7
The diagram shows a square ABCD with sides of length 20 cm.
It also shows a semicircle and an arc of a circle.
D
A
C
20 cm
B
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AB is the diameter of the semicircle.
AC is an arc of a circle with centre B.
Show that
π
area of shaded region
=
8
area of square
*P55584A0620*
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(Total for Question is 4 marks)
6
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Nov 2018 Paper 1 Q7
Mock Set 1 Paper 2 Q15
A
B
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80° 30 cm
O
AB is a chord of a circle centre O.
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8
The radius of the circle is 30 cm.
Angle AOB = 80°
14
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(Total for Question is 5 marks)
%
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. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Work out what percentage of the area of the circle is shaded.
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9 The diagram shows a pyramid with base ABC.
Mock Set 1 Paper 3 Q19
D
45°
A
C
34° 20 cm
60°
B
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CD is perpendicular to both CA and CB.
Angle CBD = 34°
Angle ADB = 45°
BC = 20 cm.
Angle DBA = 60°
Calculate the size of the angle between the line AD and the plane ABC.
Give your answer correct to 1 decimal place.
. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
°
(Total for Question is 5 marks)
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17
Turn over
30°
n
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30°
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30°
Mock Set 3 Paper 1 Q20
y
22
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(Total for Question is 4 marks)
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3
n
4
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Prove that y =
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The diagram shows three right-angled triangles.
11
Nov 2018 Paper 2 Q21
A
O
C
R
B
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P
A, B, R and P are four points on a circle with centre O.
A, O, R and C are four points on a different circle.
The two circles intersect at the points A and R.
CPA, CRB and AOB are straight lines.
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Prove that angle CAB = angle ABC.
20
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(Total for Question is 4 marks)
12 Here is a shaded shape ABCD.
Nov 2018 Paper 3 Q16
O
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B
D
C
A
The shape is made from a triangle and a sector of a circle, centre O and radius 6 cm.
OCD is a straight line.
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AD = 14 cm
Angle AOD = 140°
Angle OAD = 24°
Calculate the perimeter of the shape.
Give your answer correct to 3 significant figures.
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(Total for Question is 5 marks)
16
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cm
13 The two triangles in the diagram are similar.
x cm
B
8 cm
A
12 cm
E
3 cm
D
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C
Nov 2017 Paper 1 Q22
There are two possible values of x.
Work out each of these values.
State any assumptions you make in your working.
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(Total for Question is 5 marks)
18
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14 The diagram shows a hexagon ABCDEF.
B
June 2017 Paper 1 Q22
A
P
F
C
E
Q
D
Given that angle ABC = 30°,
prove that
cos PBQ = 1 −
(2 − 3 ) 2
x
200
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ABEF and CBED are congruent parallelograms where AB = BC = x cm.
P is the point on AF and Q is the point on CD such that BP = BQ = 10 cm.
(Total for Question is 5 marks)
*P48147A01920*
19
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15
June 2017 Paper 2 Q17
N
A
Q
B
O
ONQ is a sector of a circle with centre O and radius 11 cm.
Calculate the area of the shaded region as a percentage of the area of the sector ONQ.
Give your answer correct to 1 decimal place.
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A is the point on ON and B is the point on OQ such that AOB
is an equilateral triangle of side 7 cm.
......................................................
%
(Total for Question is 5 marks)
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17
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16 The diagram shows 3 identical circles inside a rectangle.
Each circle touches the other two circles and the sides of the rectangle, as shown in
the diagram.
June 2017 Paper 2 Q21
Work out the area of the rectangle.
Give your answer correct to 3 significant figures.
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The radius of each circle is 24 mm.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .
mm2
(Total for Question is 4 marks)
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21
Turn over
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17 The diagram shows a triangular prism.
F
June 2019 Paper 2 Q19
E
C
B
35°
D
15 cm
15 cm
A
The base, ABCD, of the prism is a square of side length 15 cm.
Angle ABE and angle CBE are right angles.
Angle EAB = 35°
M is the point on DA such that
Calculate the size of the angle between EM and the base of the prism.
Give your answer correct to 1 decimal place.
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DM : MA = 2 : 3
.......................................................
°
(Total for Question is 4 marks)
*P54214A01920*
19
Turn over
18 The diagram shows a rectangle, ABDE, and two congruent triangles, AFE and BCD.
A
B
30°
30°
24 cm
24 cm
F
C
E
area of rectangle ABDE
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June 2019 Paper 3 Q14
D
area of triangle AFE area of triangle BCD
AB : AE
1:3
Work out the length of AE.
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(Total for Question is 4 marks)
cm
Sample Paper 1 Q25
l
19 A(−2, 1), B(6, 5) and C(4, k) are the vertices of a right-angled triangle ABC.
Angle ABC is the right angle.
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Find an equation of the line that passes through A and C.
Give your answer in the form ay + bx = c where a, b and c are integers.
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(Total for Question is 5 marks)
20
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Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics - Sample Assessment Materials (SAMs) - Issue 2 - June 2015
© Pearson Education Limited 2015
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20 Here is a sketch of a vertical cross section through the centre of a bowl.
Mock Set 1 Paper 1 Q15
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y
O
x
The cross section is the shaded region between the curve and the x-axis.
The curve has equation
y=
x2
− 3x
10
where x and y are both measured in centimetres.
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Find the depth of the bowl.
.........................................
cm
(Total for Question is 4 marks)
*S52624A01324*
13
Turn over
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21
Mock Set 4 Paper 1 Q21
y
A
B
O
x
C (6, −8)
The diagram shows the circle with equation x2 + y2 = 100
The unit of length on both axes is one centimetre.
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The circle intersects the positive y-axis at the point A.
The point C on the circle has coordinates (6, −8)
The straight lines AB and CB are tangents to the circle.
Find the area of quadrilateral ABCO.
.......................................................
cm2
(Total for Question is 4 marks)
*S59726A02121*
21
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22 A solid is made by putting a hemisphere on top of a cone.
Specimen 2 Paper 1 Q11
x
Volume of cone =
1 2
πr h
3
h
r
5x
4
Volume of sphere = πr 3
3
r
2x
h
A cylinder has the same volume as the solid.
The cylinder has radius 2x and height h
All measurements are in centimetres.
Find a formula for h in terms of x
Give your answer in its simplest form.
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The total height of the solid is 5x
The radius of the base of the cone is x
The radius of the hemisphere is x
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(Total for Question is 5 marks)
*S50156A0916*
Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics Specimen Papers Set 2 - September 2015 © Pearson Education Limited 2015
9
105
Turn over
23 LMN is a right-angled triangle.
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Specimen 2 Paper 1 Q18
N
P
L
Q
M
Angle NLM = 90°
PQ is parallel to LM.
The area of triangle PNQ is 8 cm2
The area of triangle LPQ is 16 cm2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .
cm2
(Total for Question is 4 marks)
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Work out the area of triangle LQM.
*S50156A01316*
Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics Specimen Papers Set 2 - September 2015 © Pearson Education Limited 2015
13
109
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24 Specimen 2 Paper 2 Q20
R
O
U
P
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S
Q
T
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PQRST is a regular pentagon.
R, U and T are points on a circle, centre O.
QR and PT are tangents to the circle.
RSU is a straight line.
Prove that ST = UT.
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(Total for Question is 5 marks)
22
142
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Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics Specimen Papers Set 2 - September 2015 © Pearson Education Limited 2015
Mock Set 2 Paper 1 Q22
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25 The diagram shows a quadrilateral XBYA.
X
A
M
B
Y
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The diagonals AB and XY intersect at the point M.
Given that the area of triangle AXB is equal to the area of triangle AYB,
prove that XY is bisected by AB.
(Total for Question is 4 marks)
*S53603A01920*
19
Nov 2019 Paper 3 Q18
26 The diagram shows triangle ABC.
B
6.1 cm
D
3.4 cm
C
6.2 cm
A
AB = 3.4 cm
AC = 6.2 cm
BC = 6.1 cm
D is the point on BC such that
size of angle DAC =
size of angle BCA
Calculate the length DC.
Give your answer correct to 3 significant figures.
You must show all your working.
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(Total for Question is 5 marks)
*P58876RA01624*
cm
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27
The diagram shows a cycle track.
Mock Set 2 Paper 2 Q5
27 m
40 m
The track has two straight sides each of length 40 m.
Each end of the track is a semicircle of radius 27 m.
The diameter of each wheel of Ian’s bike is 590 mm.
Ian is going to ride his bike around the track once.
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Calculate how many complete revolutions each wheel of his bike will make.
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(Total for Question is 5 marks)
*S53605A0524*
5
Turn over
R
n is an integer.
Find the least possible value of n.
You must show all of your working.
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(Total for Question is 5 marks)
14
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The area of R is greater than the area of a circle of radius (n + 13) cm.
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The outer circle has radius (2n + 6)
The inner circle has radius (n – 1)
All measurements are in centimetres.
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n–1
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2n + 6
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Mock Set 3 Paper 1 Q12
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28 The region R, shown shaded in the diagram, is the region between two circles with the
same centre.
29 The diagram shows a sector OACB of a circle with centre O.
The point C is the midpoint of the arc AB.
The diagram also shows a hollow cone with vertex O.
The cone is formed by joining OA and OB.
Volume of cone =
h
2
Curved surface area of cone =
Nov 2019 Paper 3 Q23
O
A
O
C
B
A
B
C
The cone has volume 56.8 cm3 and height 3.6 cm.
Calculate the size of angle AOB of sector OACB.
Give your answer correct to 3 significant figures.
You must show all your working.
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(Total for Question is 5 marks)
*P58876RA02024*
°
30 A, B, C and D are four points on a circle.
November 2019 Paper 1 Q22
A
D
B
E
C
AEC and DEB are straight lines.
Triangle AED is an equilateral triangle.
Prove that triangle ABC is congruent to triangle DCB.
(Total for Question 22 is 4 marks)
TOTAL FOR PAPER IS 80 MARKS
*P58866A02124*
James and Peter cycled along the same 50km route.
1
James took 2 hours to cycle the 50 km.
2
Nov 2017 Paper 1 Q9
Peter started to cycle 5 minutes after James started to cycle.
Peter caught up with James when they had both cycled 15 km.
James and Peter both cycled at constant speeds.
Work out Peter’s speed.
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31
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km/h
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(Total for Question is 5 marks)
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9
Turn over
The second part of the journey took 25 minutes longer than the first part of the journey.
(b) Find the value of x.
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4)
(Total for Question is 8 marks)
14
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(4)
mph
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(a) Find Ayshab’s average speed for the whole journey.
Give your answer as a mixed number.
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Mock Set 4 Paper 1 Q14
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32 Ayshab walked x miles at 4 mph.
She then walked 2x miles at 3 mph.
June 2017 Paper 1 Q14
The ratio of the number of white shapes to the number of black shapes is 3:7
The ratio of the number of white circles to the number of white squares is 4:5
The ratio of the number of black circles to the number of black squares is 2: 5
Work out what fraction of all the shapes are circles.
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33 White shapes and black shapes are used in a game.
Some of the shapes are circles.
All the other shapes are squares.
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(Total for Question is 4 marks)
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Specimen 2 Paper 2 Q21
2x − 1 : x − 4 = 16x + 1 : 2x − 1
find the possible values of x.
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34 Given that
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(Total for Question is 5 marks)
*S50158A02324*
Pearson Edexcel Level 1/Level 2 GCSE (9-1) in Mathematics Specimen Papers Set 2 - September 2015 © Pearson Education Limited 2015
23
143
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35
A shop sells packs of black pens, packs of red pens and packs of green pens.
June 2019 Paper 1 Q6
There are
2 pens in each pack of black pens
5 pens in each pack of red pens
6 pens in each pack of green pens
On Monday,
number of packs
number of packs
:
of black pens sold
of red pens sold
:
number of packs
= 7:3:4
of green pens sold
A total of 212 pens were sold.
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Work out the number of green pens sold.
.......................................................
(Total for Question is 4 marks)
*P53836A0724*
7
Turn over
June 2019 Paper 1 Q17
x 2 : (3x + 5) = 1 : 2
find the possible values of x.
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36 Given that
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(Total for Question is 4 marks)
*P53836A01724*
17
Turn over
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37 Ben fills a glass with orange juice and lemonade in the ratio 1 : 4 by volume.
He mixes the liquid that is in the glass.
Mock Set 4 Paper 1 Q13
1
of this liquid.
4
He then fills the glass using orange juice.
Ben drinks
Work out the ratio of orange juice to lemonade, by volume, that is now in the glass.
Give your ratio in its simplest form.
.......................................................
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(Total for Question is 3 marks)
*S59726A01321*
13
Turn over
38 There are only Ured counters and g green counters in a bag.
The probability that the counter is green is
The counter is put back in the bag.
3
7
2 more red counters and 3 more green counters are put in the bag.
A counter is taken at random from the bag.
6
The probability that the counter is green is
13
Find the number of red counters and the number of green counters that were in the bag originally.
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A counter is taken at random from the bag.
June 2019 Paper 1 Q22
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green counters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(Total for Question is 5 marks)
22
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red counters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Mock Set 2 Paper 2 Q25
39 There are some red counters and some white counters in a bag.
At the start, 7 of the counters are red, the rest of the counters are white.
Alfie takes at random a counter from the bag.
He does not put the counter back in the bag.
Alfie then takes at random another counter from the bag.
The probability that the first counter Alfie takes is white and the second counter Alfie
21
takes is red is
80
Work out the number of white counters in the bag at the start.
.......................................................
(Total for Question is 5 marks)
*S53605A02124*
21
13
36
The probability that the first counter is red and the second counter is not red is
1
4
Seb takes at random a counter from the bag.
Work out the probability that Seb takes a yellow counter.
You must show all your working.
22
*S59728A02224*
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(Total for Question is 5 marks)
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The probability that both counters are red or that both counters are yellow is
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Kevin takes at random a counter from the bag.
He puts the counter back in the bag.
Lethna takes at random a counter from the bag.
She puts the counter back in the bag.
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Mock Set 4 Paper 2 Q21
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40 There are only red counters, yellow counters and blue counters in a bag.
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Mock Set 2 Paper 3 Q17
41 a, b, c are positive integers such that a > b > c
N is the largest three digit number that has the digits a, b and c.
K is the smallest three digit number that has the digits a, b and c.
(a) Use algebra to show that the difference between N and K is always a multiple of 99
(3)
(b) If a > b and b = c will the difference between N and K still be a multiple of 99?
Justify your answer.
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(1)
(Total for Question is 4 marks)
*S53607A01520*
15
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Mock Set 3 Paper 1 Q14
42 A particle P is moving in a straight line.
O is a fixed point on the straight line.
The distance, s metres, of P from O at time t seconds is given by
16
*S57492A01624*
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(Total for Question is 4 marks)
metres
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.......................................................
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Use algebra to find the greatest distance of P from O when 0  t  16
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t
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O
s = 80t – 5t 2
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s
Mock Set 3 Paper 2Q21
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43 The diagram shows an acute-angled triangle ABC.
A
b
c
B
a
1
ab sin C
2
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Prove that area of triangle ABC =
C
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(Total for Question is 3 marks)
*S57494A02124*
21
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