alsttaaalsllkmel gcse mathematics practice tests: set 16
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Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 1
GCSE Mathematics Practice Tests: Set 16
Paper 1H (Non-calculator)
Time: 1 hour 30 minutes
You should have: Ruler graduated in centimetres and millimetres, protractor, pair of compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.
Instructions • Use black ink or ball-point pen. • Fill in the boxes at the top of this page with your name,
centre number and candidate number. • Answer all questions. • Answer the questions in the spaces provided
– there may be more space than you need. • Calculators may be used. • Diagrams are NOT accurately drawn, unless otherwise indicated. • You must show all your working out.
Information
• The total mark for this paper is 80 • The marks for each question are shown in brackets
– use this as a guide as to how much time to spend on each question. Advice
• Read each question carefully before you start to answer it. • Keep an eye on the time. • Try to answer every question. • Check your answers if you have time at the end.
AlsttAAAlsllkmeljustmalhs.co.uk
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 2
Answer all questions.
Write your answers in the spaces provided.
You must write down all the stages in your working.
1 (a) Write 2 840 000 000 in standard form.
...................................................... (1)
(b) Write 2.5 × 10–4 as an ordinary number.
.................................................. (1)
(Total for Question 1 is 2 marks) ___________________________________________________________________________
2 (a) Factorise fully 15y4 + 20uy3
...................................................... (2)
(b) Solve 4 – 3x = 5 - 8x
4
Show clear algebraic working.
x = ...................................................... (3)
(Total for Question 2 is 5 marks) ___________________________________________________________________________
2 84 109
0.00025
L C5 3 5 4
5y3 3ye Liu
16 122C 5 8
11 x
x I4
14
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 3
3 (a) Simplify (2x3y5)4
...................................................... (2)
(b) (i) Factorise x2 + 5x – 36
...................................................... (2)
(ii) Hence, solve x2 + 5x – 36 = 0
...................................................... (1)
(Total for Question 3 is 5 marks) ___________________________________________________________________________
242C2y20
16 1420
161420
436 2,18 3,12 19 4
act 9 Gc 4
x take 4
act 9 x 4 O
D 9 2 4
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 4
4 Ding is going to play one game of snooker against each of two of his friends, Marco and Judd.
The probability tree diagram gives information about the probabilities that Ding will win or lose each of these two games.
*P66297A01628*16
14 Ding is going to play one game of snooker against each of two of his friends, Marco and Judd.
The probability tree diagram gives information about the probabilities that Ding will win or lose each of these two games.
Ding wins
Ding wins
Ding loses0.4
0.6
0.1
0.9
0.75
0.25 Ding wins
Ding loses
Ding loses
Ding against Marco
Ding against Judd
(a) Work out the probability that Ding will win both games.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(b) Work out the probability that Ding will win exactly one of the games.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 14 is 5 marks)
(a) Work out the probability that Ding will win both games.
...................................................... (2)
(b) Work out the probability that Ding will win exactly one of the games.
...................................................... (3)
(Total for Question 4 is 5 marks) ___________________________________________________________________________
O 6 0.9 0 54
O 54
P W LJ O 6 0 I O 06
PCL w s 0.4 0.25 0 10 t
O 16
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 5
5 (a) Expand and simplify 4x(2x + 5) – 3x(2x – 3)
...................................................... (2)
Given that
y5 ´ yn
y6 = y13
(b) work out the value of n.
n = ...................................................... (2)
(c) (i) Solve the inequality 7t – 8 < 2t + 7
...................................................... (2)
(ii) On the number line below, represent the solution set of the inequality solved in part (c)(i)
*P66301A0728* Turn over 7
5 (a) Expand and simplify 4x(2x + 5) – 3x(2x – 3)
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
Given that y y
y
n5
6´
= y13
(b) work out the value of n.
n = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(c) (i) Solve the inequality 7t – 8 < 2t + 7
... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
(ii) On the number line below, represent the solution set of the inequality solved in part (c)(i)
–5 –4 –3 –2 –1 0 1 2 3 4 5 t
(1)
(Total for Question 5 is 7 marks)
(1)
(Total for Question 5 is 7 marks) ___________________________________________________________________________
8 2 202C 622 t 92C
2 2 29 x
Eth
ysxy y
n 1414
St 8C 7
St C 15t C 3
O
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 6
6 Expand and simplify 2x(x – 5)(x – 3)
......................................................
(Total for Question 6 is 3 marks) ___________________________________________________________________________
7
*P66301A0628*6
4
x
y7
6
5
4
3
2
1
1 2 3 4 5 6 7O
(a) On the grid, draw and label the straight line with equation
(i) x = 1.5
(ii) y = x
(iii) x + y = 6(3)
(b) Show, by shading on the grid, the region that satisfies all three of the inequalities
x 1.5 y x x + y 6
Label the region R.(1)
(Total for Question 4 is 4 marks)
(a) On the grid, draw and label the straight line with equation
(i) x = 1.5
(ii) y = x
(iii) x + y = 6 (3)
(b) Show, by shading on the grid, the region that satisfies all three of the inequalities
x 1.5 y x x + y 6 Label the region R.
(1)
(Total for Question 7 is 4 marks) ___________________________________________________________________________
2x 2 10x x 3
2 3 2 t 30
2 3 IGod 302C
IC il S
y x
q
ART
r
x ty 6
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 7
8 E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}
A = {odd numbers} B = {multiples of 3}
List the members of the set
(i) A ∩ B
........................................................................................................... (1)
(ii) A ∪ B
........................................................................................................... (1)
(Total for Question 8 is 2 marks) ___________________________________________________________________________
A 2L 23 25 27 29
B 21 24 27
21,27
21,23 24,25 27,29
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 8
9 Ava writes down five whole numbers. For these five numbers
the median is 7
the mode is 8
the range is 5
Find a possible value for each of the five numbers that Ava writes down.
.................................................................................
(Total for Question 9 is 3 marks) ___________________________________________________________________________
8 S 3
3 7 8 8
9could be
45OR
6
34788 OR 35788 or 36788
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 9
10 Make c the subject of the formula p =
ac + 83 + c
......................................................
(Total for Question 10 is 4 marks) ___________________________________________________________________________
11 Point A has coordinates (5, 8) Point B has coordinates (9, –4)
(a) Work out the gradient of AB.
...................................................... (2)
The straight line L has equation y = –4x + 5
(b) Write down the gradient of a straight line that is perpendicular to L.
...................................................... (1)
(Total for Question 11 is 3 marks) ___________________________________________________________________________
p2 ac 83 to
p2 3 e c act 8
3p2 p2c act 8
p2c ac 8 3p2 8 3psC 7p2 a
c p2 a 8 3p2
A gradient 128 g 4
i i5 9
4 xB 3
Lgradient 4
Lz Is4
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 10
12 A = 23 × 32 × 52 × 11
B = 24 × 3 × 54 × 13
Find the lowest common multiple (LCM) of A and B. Give your answer as a product of powers of prime numbers.
......................................................
(Total for Question 12 is 2 marks) ___________________________________________________________________________
Ucf 23 3 52
LCM 23 2 3 3 x 52 52 11 13
24 32 5 4 11 13
24 3454 11 13
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 11
13 Express
4x - 2
-3
x + 1 as a single fraction.
Give your answer in its simplest form.
......................................................
(Total for Question 13 is 3 marks) ___________________________________________________________________________
46cal 3 x 2
x 2 act l
42C 14 32C16x 2Cacti
10
Go 2 Xtc2C 110Go 2 Rtl
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 12
14 Some students were asked the following question.
“Which of the subjects Russian (R), French (F) and German (G) do you study?”
Of these students
4 study all three of Russian, French and German 10 study Russian and French 13 study French and German
6 study Russian and German 24 study German 11 study none of the three subjects the number who study Russian only is twice the number who study French only.
Let x be the number of students who study French only.
(a) Show all this information on the Venn diagram, giving the number of students in each appropriate subset, in terms of x where necessary.
E
*P66301A01728* Turn over 17
16 Some students were asked the following question.
“Which of the subjects Russian (R), French (F) and German (G) do you study?”
Of these students
4 study all three of Russian, French and German 10 study Russian and French 13 study French and German 6 study Russian and German 24 study German 11 study none of the three subjects the number who study Russian only is twice the number who study French only.
Let x be the number of students who study French only.
(a) Show all this information on the Venn diagram, giving the number of students in each appropriate subset, in terms of x where necessary.
R
G
EF
x
(3)
Given that the number of students who were asked the question was 80
(b) work out the number of these students that study Russian.
.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3)
(Total for Question 16 is 6 marks)
(3)
Given that the number of students who were asked the question was 80
(b) work out the number of these students that study Russian.
...................................................... (3)
(Total for Question 14 is 6 marks) ___________________________________________________________________________
Loc b
42 9
911
I 32C 80 Russian 26 6 14 2 38320 39 382C 13
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 13
15 Simplify fully
9t4w9
18t6w10
æ
èçö
ø÷
-2
......................................................
(Total for Question 15 is 3 marks) ___________________________________________________________________________
16 15 people were asked how long, in minutes, they had been waiting for a bus.
Here are the results.
2 3 3 4 5 6 6 8 9 10 11 13 14 15 18 Find the interquartile range of these times.
...................................................... minutes
(Total for Question 16 is 2 marks) ___________________________________________________________________________
18 tbwaatt they
t4w2
t4w2
x x x D x x x D a a D x x x
IQR 13 4
9
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 14
17 Show that
26 - 3 2
can be written in the form a + a
b where a and b are integers.
Show your working clearly.
(Total for Question 17 is 3 marks) ___________________________________________________________________________
2
G 3ozGt3b t352
2Cb t 352
36 1852 4852 18
124152183
231 as required
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 15
18 Given that (8 – x )(5 + x ) = y x + 21 where x is a prime number and y is an integer, find the value of x and the value of y. Show each stage of your working clearly.
x = ......................................................
y = ......................................................
(Total for Question 18 is 3 marks) ___________________________________________________________________________
racks TE
40 8Fa 5rad sa
40 t 3 Be a y TE t 21
1 40 2C 21
see 19
y 3 193
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 16
19 (a) Write down the value of y0
...................................................... (1)
(b) Work out
9.6 ´ 10141 + 6.4 ´ 10140
3.2 ´ 1016
Give your answer in standard form.
...................................................... (3)
(Total for Question 19 is 4 marks) ___________________________________________________________________________
I
rX XE
9 6 10141
G 4 10140
9.6 101411 0.64101411,02410141
10.2 4 10141
3 2 1016
3.2 101253 2 10125
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 17
20 Solve the simultaneous equations
x2 – 9y – x = 2y2 – 12
x + 2y – 1 = 0
Show clear algebraic working.
............................................................................................................
(Total for Question 20 is 5 marks) ___________________________________________________________________________
from ac I Lyx2 Ct Ly I 2g I Liye4g
swim
I 4yt4y2 9g d 2y 2y2 12
I lZyt4y2 I t y Ly2 12 0
Ly I ly t 12 0 2 12 24 Ig242112
Ly 8g 3g e 12 0
Lyly Li 3cg 41 0
Cry 3 ly 41 0
y 32 andy 4
X I 2 42C I 12 32 1 8 7
2
sci 2 y 312 2C 7 y 4
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 18
21 OAB is a triangle.
*P66297A02628*26
23 OAB is a triangle.
A B
O
P
M
N Diagram NOT accurately drawn
OA→
= 2a and OB→
= 2b
M is the midpoint of AB. N is the point on OB such that ON : NB = 2 : 1
P is the point on AN such that OPM is a straight line.
Use a vector method to find OP : PM Show your working clearly.
OA ®
= 2a and OB ®
= 2b
M is the midpoint of AB. N is the point on OB such that ON : NB = 2 : 1
P is the point on AN such that OPM is a straight line.
Use a vector method to find OP : PM Show your working clearly.
b a b a27
za n
qq2b
zp 2gbON 2gx2b 4zbNB lz
AB 2b La Am b a MB
OM 2atb a at b OP d atb
AN 2at4gb AP k AN KC2atLzb
OP OA t AP
OP i 2 at KC 2at Ejb La Ika t 4zkb
so 2k a kb D atb
2 2k X 43kd
2 2k Iz k2 Ifk 2K
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 19
......................................................
(Total for Question 21 is 6 marks)
TOTAL FOR PAPER IS 80 MARKS
2 43k byK
2 togk
k 2,81 To 3
I 43 33 4g
OP 4g eb om e at b
Op i OM 4g Ig
4 I
4 I
Edexcel GCSE Mathematics (9–1) Practice Tests Set 16: Paper 1H – Spring 2021 (version 1.0) 20
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