AlsttAAAlsllkmel GCSE Mathematics Practice Tests: Set 16

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


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)


2 84 109

0.00025

L C5 3 5 4

5y3 3ye Liu

16 122C 5 8

11 x

x I4

14


3 (a) Simplify (2x3y5)4

...................................................... (2)

(b) (i) Factorise x2 + 5x – 36

...................................................... (2)

(ii) Hence, solve x2 + 5x – 36 = 0

...................................................... (1)


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


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)


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


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)


(1)


8 2 202C 622 t 92C

2 2 29 x

Eth

ysxy y

n 1414

St 8C 7

St C 15t C 3

O


6 Expand and simplify 2x(x – 5)(x – 3)

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


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)


(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)


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


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)


A 2L 23 25 27 29

B 21 24 27

21,27

21,23 24,25 27,29


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.

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


8 S 3

3 7 8 8

9could be

45OR

6

34788 OR 35788 or 36788


10 Make c the subject of the formula p =

ac + 83 + c

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


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)


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


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.

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


Ucf 23 3 52

LCM 23 2 3 3 x 52 52 11 13

24 32 5 4 11 13

24 3454 11 13


13 Express

4x - 2

-3

x + 1 as a single fraction.

Give your answer in its simplest form.

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


46cal 3 x 2

x 2 act l

42C 14 32C16x 2Cacti

10

Go 2 Xtc2C 110Go 2 Rtl


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)


(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)


Loc b

42 9

911

I 32C 80 Russian 26 6 14 2 38320 39 382C 13


15 Simplify fully

9t4w9

18t6w10

æ

èçö

ø÷

-2

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


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


18 tbwaatt they

t4w2

t4w2

x x x D x x x D a a D x x x

IQR 13 4

9


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.


2

G 3ozGt3b t352

2Cb t 352

36 1852 4852 18

124152183

231 as required


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 = ......................................................


racks TE

40 8Fa 5rad sa

40 t 3 Be a y TE t 21

1 40 2C 21

see 19

y 3 193


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)


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


20 Solve the simultaneous equations

x2 – 9y – x = 2y2 – 12

x + 2y – 1 = 0

Show clear algebraic working.

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


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


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


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


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


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AlsttAAAlsllkmel GCSE Mathematics Practice Tests: Set 16