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Predicted Paper 3H
14th June 2023
Mathematics
Higher Tier

You must have: Ruler graduated in centimetres and millimetres,

protractor, pairs of compasses, pen, HB pencil, eraser.
Tracing paper may be used.
**No-one can know for sure what will appear on Paper 3. This paper is not a guarantee of the
topics you will see on the next paper, but is a good guess based on what has come up lots on
previous years, and taking into consideration the topics we’ve already seen on Paper 1 & 2.
All of these questions are taken from various Edexcel Past Papers. I hope you find it helpful.
You can find the solutions on my YouTube channel, and I’ll be LIVE on YouTube and
TikTok on Tuesday evening (13th June, 7-8pm for Foundation and 8-9pm for Higher)! J
@hannahkettlemaths

Question No Topic
1 Index Laws
2 Percentage Increase
3 Plotting Quadratics
4 Mean from a Frequency Table
5 Metric Conversions
6 Speed Distance Time
7 Standard Form
8 Angles in Polygons
9 Box Plot
10 Enlargement
11 Area of a Sector
12 Algebraic Proof
13 Speed Time Graph
14 Algebraic Fraction
15 Cosine Rule / 1/2absinC
16 Density Mass Volume
17 Population Growth
18 Expand Triple Brackets
19 Sine / Cosine Graph
20 Complete the Square and Solve Quadratic
21 Rotations / Translation / Invariant Point
22 Cosine / Sine Rule / Bearings
 Answer ALL questions.

Write your answers in the spaces provided.

You must write down all the stages in your working.

1 (a) Simplify n3 × n5

................................................
(1)
c 3d 4
(b) Simplify
c2d

................................................
(2)
(Total for Question 1 is 3 marks)
___________________________________________________________________________

2 Last year Jo paid £245 for her car insurance.

This year she has to pay £883 for her car insurance.
Work out the percentage increase in the cost of her car insurance.

.......................................................%
(Total for Question 2 is 3 marks)
__________________________________________________________________________
 3 (a) Complete this table of values for y = x2 + x 2– 4
3 (a) Complete this table of values for y = x + x – 4
DO NOT WRITE IN THIS AREA

x –3 –2 –1 0 1 2 3
x –3 –2 –1 0 1 2 3
yy –2
–2 –4 –2
–2

(2)(2)
(b)(b)
On theOn the draw
grid, grid, the
drawgraph of y =ofx2y+=xx–2 +4 xfor
the graph – 4values
for values of x from
of x from –3 to–3
3 to 3

y
15
DO NOT WRITE IN THIS AREA

10

–3 –2 –1 O 1 2 3 x

–5
DO NOT WRITE IN THIS AREA

–10
(2)(2)
2
(c)(c)Use the
Use the graph
graph to estimate
to estimate a solution
a solution to x2 to
+ xx –+4x=–04 = 0

.......................................................
.......................................................

(1)(1)
(Total for Question 3 is 5 marks)
(Total for Question 3 is 5 marks)
__________________________________________________________________________

3
4 The table gives information about the times taken, in seconds, by 18 students to run a race.

Time (t seconds) Frequency

5 < t ⩽ 10 1
10 < t ⩽ 15 2
15 < t ⩽ 20 7
20 < t ⩽ 25 8

Work out an estimate for the mean time.

Give your answer correct to 3 significant figures.

....................................................... seconds

(Total for Question 4 is 3 marks)

___________________________________________________________________________
5 Write 37 cm3 in mm3

.......................................................mm3

(Total for Question 5 is 1 mark)

___________________________________________________________________________

6 Nimer was driving to a hotel.

He looked at his Sat Nav at 13 30

Time 13 30
Distance to destination 65 miles

Nimer arrived at the hotel at 14 48

Work out the average speed of the car from 13 30 to 14 48
You must show all your working.

.......................................................mph
(Total for Question 6 is 4 marks)
__________________________________________________________________________
7 (a) Write 1.63 × 10−3 as an ordinary number.

.......................................................
(1)
(b) Write 438 000 in standard form.

.......................................................
(1)
(c) Work out (4 × 103) × (6 × 10−5)
Give your answer in standard form.

.......................................................
(2)
(Total for Question 7 is 4 marks)
___________________________________________________________________________
8 The diagram shows a regular pentagon and a parallelogram.

Work out the size of the angle marked x.

You must show all your working.

.......................................................°
(Total for Question 8 is 4 marks)
___________________________________________________________________________
9 The box plot shows information about the length of time, in minutes, some people waited
to see a doctor at a hospital on Monday.

(a) Work out the interquartile range of the information in the box plot.

....................................................... minutes
(2)
Becky says,
“50% of the people waited for at least 2 hours.”
(b) Is Becky correct?
Explain why.

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................
(1)
The table gives information about the length of time, in minutes, some people waited
to see a doctor at the same hospital on Tuesday.

Waiting time (minutes)

Shortest time 20

Lower quartile 50

Median 100

Upper quartile 140

Longest time 210

 Becky was asked to compare the distribution of the lengths of times people waited on
Monday with the distribution of the lengths of times people waited on Tuesday.
She wrote,

“People had to wait longer on Tuesday than on Monday.”

(c) Give one reason why Becky may be wrong.

......................................................................................................................................................

......................................................................................................................................................

......................................................................................................................................................
(1)
(Total for Question 9 is 4 marks)
___________________________________________________________________________
10

Enlarge triangle A by scale factor 2.5 with centre (0, 1)

(Total for Question 10 is 2 marks)

______________________________________________________________________
 11
17
N
DO NOT WRITE IN THIS AREA

Q B O
ONQ is a sector of a circle with centre O and radius 11 cm.
ONQ is a sector of a circle with centre O and radius 11 cm.
A Aisisthe
thepoint
pointononONONand
andBBisisthe
thepoint
pointon
onOQ
OQsuch
suchthat
thatAOB
AOB
isisananequilateral triangle of side 7 cm.
equilateral triangle of side 7 cm.
Calculate
Calculatethe
thearea
areaofofthe
theshaded
shadedregion
regionasasa apercentage
percentageofofthe
thearea
areaofofthe
thesector
sectorONQ.
ONQ.
DO NOT WRITE IN THIS AREA

Give
Giveyour
youranswer
answercorrect
correcttoto1 1decimal
decimalplace.
place.
DO NOT WRITE IN THIS AREA

......................................................%
(Total for Question 11 is 5 marks)
___________________________________________________________________________

...................................................... %

(Total for Question 17 is 5 marks)

17
12 Prove algebraically that the sum of the squares of any two consecutive even numbers is
always a multiple of 4

(Total for Question 12 is 3 marks)

___________________________________________________________________________
13 A car moves from rest.
The graph gives information about the speed, v metres per second, of the car t seconds
after it starts to move.

(a) (i) Calculate an estimate of the gradient of the graph at t = 15

.......................................................
(3)
(ii) Describe what your answer to part (i) represents.

......................................................................................................................................................
(1)
 (b) Work out an estimate for the distance the car travels in the first 20 seconds of its journey.
Use 4 strips of equal width.

.......................................................m
(3)
(Total for Question 13 is 7 marks)
___________________________________________________________________________

1 3
14 Solve + =1
2x -1 x -1
Give your answers to 3 significant figures.

.......................................................
(Total for Question 14 is 4 marks)
__________________________________________________________________________
15 Here is triangle ABC.

(a) Find the length of BC.

Give your answer correct to 3 significant figures.

....................................................... cm
(3)
(b) Find the area of triangle ABC.
Give your answer correct to 3 significant figures.

....................................................... cm2
(2)
(Total for Question 15 is 5 marks)
16 The density of ethanol is 1.09 g/cm3
The density of propylene is 0.97 g/cm3
60 litres of ethanol are mixed with 128 litres of propylene to make 188 litres of antifreeze.
Work out the density of the antifreeze.
Give your answer correct to 2 decimal places.

....................................................... g/cm3
(Total for Question 16 is 4 marks)

17 The number of animals in a population at the start of year t is Pt

The number of animals at the start of year 1 is 400
Given that
Pt + 1 = 1.01Pt
work out the number of animals at the start of year 3

.......................................................
(Total for Question 17 is 2 marks)
_____________________________________________________
18 Show that (m + 4)(2m − 5)(3m + 1) can be written in the form am3 + bm2 + cm + d
where a, b, c and d are integers.

(Total for Question 18 is 3 marks)

___________________________________________________________________________
19

The diagram shows a sketch of part of the curve with equation y = cos x°
P is a minimum point on the curve.
Write down the coordinates of P.

( ............................ , ............................ )
(Total for Question 19 is 2 marks)
___________________________________________________________________________
20 Sketch the graph of
y = 2x2 – 8x – 5

showing the coordinates of the turning point and the exact coordinates of any intercepts
with the coordinate axes.

(Total for Question 20 is 5 marks)

___________________________________________________________________________
21
20
y

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4

2
A

–4 –2 O 2 4 x

–2

–4

DO NOT WRITE IN THIS AREA

Triangle
TriangleAAisistransformed
transformedbybythethecombined
combinedtransformation
transformationofofaarotation
rotationofof180°
180°about
aboutthe
the
−
 ⎛ −3 ⎞
3
point (−2, 0) followed by a translation with vector ⎜  ⎟
 ⎝ 22⎠
One point on triangle A is invariant under the combined transformation.
One point on triangle A is invariant under the combined transformation.
Find
Findthe
thecoordinates
coordinatesofofthis
thispoint.
point.

...................... , ............................)
(............................(. . .,. . .............................)
(Total
(Total forfor Question
Question 2021
is is 2 marks)
2 marks)
__________________________________________________________________________
TOTAL FOR PAPER IS 80 MARKS
DO NOT WRITE IN THIS AREA

20
22 The diagram shows the positions of three towns, Acton (A), Barston (B) and Chorlton (C).

Barston is 8 km from Acton on a bearing of 037°

Chorlton is 9 km from Barston on a bearing of 150°
Find the bearing of Chorlton from Acton.
Give your answer correct to 1 decimal place.
You must show all your working.

.......................................................°
(Total for Question 22 is 5 marks)

TOTAL FOR PAPER IS 80 MARKS