St. Anthony’s Girls’ Catholic Academy
Easter 2017
The idea of ‘5 A Day’ is for you to spend 30mins each day
for 11 days revising your GCSE 9-1 Mathematics. There are
5 questions to complete each day in the five categories of
Number, Algebra, Ratio, Proportion and Rates of Change,
Geometry and Probability & Statistics. You can use your
calculator on alternate days. You could also use your maths
revision guide, CGP online textbook or online support such as
Corbettmaths.
The answers to ‘5 A Day’ will be available on the academy
website so that you can mark your work at home. Remember
to make a list of the questions that you are still finding
difficult to ask your maths teacher about after the Easter
holidays.
Please bring in the completed booklet on Monday 24thApril
so your teacher can check to see it has been completed and
marked to the best of your ability.
Good Luck!
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 1 Number & Calculation ( Non Calculator )
1.
(a)
Write these numbers in standard form
(i)
9 170 000
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Answer ……………………………………………
(1)
(ii)
0.000 048
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Answer ……………………………………………
(1)
(b)
Find the value of (1.8 × 1012) ÷ (2 × 108)
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Answer ……………………………………………
(2)
(Total 4 marks)
2.
(a)

Express 0.51 as a fraction in its simplest form.
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Answer .............................................................
(2)
(b)

Express 0.451 as a fraction in its simplest form.
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St. Anthony’s Girls’ Catholic Academy
Easter 2017
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Answer .............................................................
(3)
(Total 5 marks)
3.
(a)
1
49 2 × 5–3
Work out
Give your answer as a fraction.
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Answer .........................................................................
(2)
7
(b)
4
4 – 2 giving your answer in the form 2n.
Calculate
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Answer .........................................................................
(2)
(c)
Work out the value of
– 34
81
Give your answer as a fraction.
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Answer .........................................................................
(3)
(Total 7 marks)
4.
(a)
Simplify
(i)
3 3
Answer ................................................................
(1)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
(ii)
3 3
Answer ................................................................
(1)
(b)
Show that
75  12
75  12
3
7
simplifies to
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(3)
(Total 5 marks)
5.
Use approximations to estimate the value of
37.48  6.13
(1.95) 2
You must show your working.
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Answer ................................................................
(Total 3 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 2 (Calculator allowed)
6.
A lift cable can safely carry a total load 1200 kg.
The lift weighs 280 kg.
Both numbers are given to two significant figures.
The total load is made up of the weight of the lift and its contents.
The lift carries boxes weighing 65 kg each, correct to the nearest kg.
How many boxes can safely be carried?
You must show all your working.
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Answer .....................................................
(Total 4 marks)
7.
(a)
(i)
2
2
Use your calculator to find 28.9 – 9.24 .
Give all the figures in your calculator display.
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Answer ......................................................
(1)
(ii)
Write your Answer to 3 significant figures.
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Answer ......................................................
(1)
(b)
Find the value of (3.18 × 105) × (4.25 × 103).
Give your answer in standard form.
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St. Anthony’s Girls’ Catholic Academy
Easter 2017
Answer ......................................................
(2)
(Total 4 marks)
8.
On Tuesday, Matthew picked 48 strawberries for tea.
This was 20% more than the number he picked on Monday.
How many strawberries did Matthew pick on Monday?
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Answer ............................................
(Total 3 marks)
9.
A coffee machine dispenses 130 millilitres of black coffee into cups with a capacity of
175 millilitres.
These values are accurate to 3 significant figures.
Milk is supplied in small cartons which contain 21 millilitres, accurate to the nearest
millilitre.
Beryl likes milky coffee and always puts 2 cartons of milk in her coffee.
Will Beryl’s cup ever overflow?
You must show all your working.
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St. Anthony’s Girls’ Catholic Academy
Easter 2017
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(Total 4 marks)
10. Use your calculator to find the values of
(a)
10 – π
(i)
Write down all the figures on your calculator.
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Answer ....................................................
(1)
(ii)
Give your answer to 3 significant figures.
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Answer ....................................................
(1)
(b)
Work out (3.24 x 10–2) ÷ (2.4 x 103)
Give your answer in standard form.
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Answer ....................................................
(2)
(Total 4 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 3 (Non Calculator)
1.
(a)
Simplify fully the expression
8 x 2  24x
2 x 2  5x  3
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Answer ....................................................
(3)
(b)
You are given that
(x + a)2 + b = x2 – 6x + 13.
Find the values of a and b.
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Answer ....................................................
(3)
(Total 6 marks)
2.
Solve the equation
x
2
–
1
x 1 x –1
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St. Anthony’s Girls’ Catholic Academy
Easter 2017
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Answer .............................................................
(Total 5 marks)
3.
y is inversely proportional to the square of x.
When y = 3, x = 2
Find the value of y when x = 4
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Answer y = ..........................................................
(Total 3 marks)
4.
Solve the equations.
(a)
5y + 11 = 3(y + 7)
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Answer y = ……………………………..
(b)
x 1  x  2 1
3
5
You must show your working.
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St. Anthony’s Girls’ Catholic Academy
Easter 2017
(3)
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Answer x = …………………………………
(4)
(Total 7 marks)
5.
(a)
Solve the equation
4(x + 3) = 9(x – 2)
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Answer x = ................................................................
(3)
(b)
Solve these simultaneous equations
5x + 3y = 6
3x – 7y = 19
You must show your working.
Do not use trial and improvement.
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Answer x = ......................... , y = ...........................
(4)
(Total 7 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 4 (Calculator allowed)
6.
(a)
Find the values of a and b such that
x2 + 8x – 5 ≡ (x + a)2 + b
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Answer a = ......................... b = ...........................
(2)
(b)
Hence, or otherwise, solve the equation
x2 + 8x – 5 = 0
Give your answers to 2 decimal places.
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Answer .......................................................................
(2)
(Total 4 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
7.
Solve the equation x2 + 4x – 10 = 0
Give your answers to 2 decimal places.
You must show your working.
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Answer .................................................................
(Total 3 marks)
8.
Cheese is sold in different sizes. The weight of each cheese, W kilograms, is
proportional to the cube of its height, h centimetres. A cheese of weight 10 kg has a
height of 12 cm.
(a)
Find an equation connecting W and h.
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Answer ...................................................................................................
(3)
(b)
Another cheese has a height of 6 cm. Find its weight.
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Answer ................................................................................................ kg
(1)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
(c)
Find the height of a cheese that has a weight of 20 kg.
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Answer ................................................................................................ cm
(3)
(Total 7 marks)
9.
A shape is made from two trapezia.
a
b
a
h
h
The area of this shape is given by
h
b
A = 2 (a + b) + 2 (a + h)
Rearrange the formula to make a the subject.
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Answer a .......................................................
(Total 4 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
10. Solve the simultaneous equations.
y=x+7
x2 + y2 = 25
YOU must show your working.
Do not use trial and improvement.
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Answer ..................................................................
(Total 7 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 5 (Non Calculator)
1.
(a)
Not drawn accurately
40º
xº
yº
(i)
Write down the value of x.
Answer ............................................................ degrees
(1)
(ii)
Calculate the value of y.
...........................................................................................................................
Answer ............................................................ degrees
(1)
(b)
A and C are points on the circumference of a circle centre B.
AD and CD are tangents.
Angle ADB = 40°.
A
Not drawn accurately
40º
B
D
C
Explain why angle ABC is 100°.
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(2)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
(c)
ABCD is a cyclic quadrilateral.
PAQ is a tangent to the circle at A.
BC = CD.
AD is parallel to BC.
Angle BAQ = 32°.
C
Not drawn accurately
D
B
32º
P
A
Q
Find the size of angle BAD.
You must show all your working.
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Answer Angle BAD = ............................... degrees
(5)
(Total 9 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
2.
B
Not drawn accurately
b
Q
M
P
b
A
O
a
OAB is a triangle where M is the mid-point of OB.
P and Q are points on AB such that AP = PQ = QB.
OA = a and OB = 2b
(a)
Find, in terms of a and b, expressions for
(i)
BA
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Answer ..........................................................
(1)
(ii)
MQ
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Answer ..........................................................
(2)
(iii)
OP
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Answer ..........................................................
(2)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
(b)
What can you deduce about quadrilateral OMQP?
Give a reason for your answer.
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(2)
(Total 7 marks)
3.
Triangle P is an enlargement of the shaded triangle.
y
6
5
4
3
2
1
P
–5
–4
–3
–2
–1 O
1
2
3
4
5 x
–1
–2
–3
–4
(a)
What is the scale factor of the enlargement?
Answer ......................................................
(b)
(1)
What is the centre of enlargement?
Answer (........................, ........................)
(1)
(Total 2 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
4.
(a)
The diagram shows a right-angled triangle ABC.
AB = 10 cm and AC = 15 cm
C
15 cm
A
Not drawn
accurately
B
10 cm
Calculate the length of BC.
Leave your answer as a square root.
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Answer .................................................................. cm
(3)
(b)
Triangle PQR is similar to triangle ABC.
Angle CAB = angle RPQ.
PQ = 25 cm
R
Not to scale
P
Q
25 cm
Work out the length of PR.
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Answer .................................................................. cm
(3)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
(c)
The diagram shows a right-angled triangle DEF.
EF = 10 cm
Angle F = 50°
D
Not drawn
accurately
E
50º
10 cm
Angle
Sine
Cosine
Tangent
40°
0.643
0.766
0.839
50°
0.766
0.643
1.192
F
Use the table of data to work out the length of DE.
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Answer .................................................................. cm
(3)
(Total 9 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
5.
The first diagram shows a cylindrical block of wood of diameter 24 cm and height 10
cm.
It is cut into six equal prisms as shown.
One of the prisms is shown in the second diagram.
F
B
E
E
C
D
10 cm
A
10 cm
A
24 cm
C
F
B
D
Not to scale
(a)
Calculate the area of sector BEC, the cross-section of the prism.
Give your answer in terms of π.
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Answer ..................................................................cm2
(2)
(b)
Calculate the area of CDFE, the curved surface of the prism.
Give your answer in terms of π.
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Answer ..................................................................cm2
(c)
(3)
Calculate the volume of the prism.
Give your answer in terms of π.
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Answer ..................................................................
(3)
(Total 8 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 6 Calculator allowed
6.
(a)
Sketch the graph of y = cos x for 0° ≤ x ≤ 360° on the axes below.
y
1
0
90
180
270
360
x
–1
(1)
(b)
You are given that cos 27° = 0.891
(i)
Solve the equation cos x = 0.891 for 180° ≤ x ≤ 360°
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Answer x = ...................................................degrees
(1)
(ii)
Solve the equation cos x = –0.891 for 0° ≤ x ≤ 360°
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Answer x = ...................................................degrees
(2)
(iii)
State a solution of the equation cos (x – 90°) = 0.891 for 0° ≤ x ≤ 360°
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Answer x = ...................................................degrees
(1)
(iv)
State a solution of the equation sin x = 0.891 for 0° ≤ x ≤ 360°
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Answer x = ...................................................degrees
(1)
(Total 6 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
7.
(a)
ABC is a triangle.
AC = 19 cm, BC = 17 cm and angle BAC = 60°
B
17 cm
A
60°
19 cm
C
Not to scale
Calculate the size of angle ABC.
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Answer ........................................................... degrees
(3)
(b)
PQR is a triangle.
PR = 23 cm, PQ = 22 cm and angle QPR = 48°
Q
22 cm
P
48°
23 cm
R
Not to scale
Calculate the length of QR.
Give your answer to an appropriate degree of accuracy.
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Answer ........................................................... cm
(4)
(Total 7 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
8.
VABCD is a right pyramid on a square base.
V is vertically above the centre of the square.
VA = VB = VC = VD = 20 cm
AB = 15 cm
V
Not drawn accurately
20 cm
D
C
A
B
15 cm
Calculate the angle between the edge VA and the base ABCD.
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Answer ......................................................... degrees
(Total 5 marks)
9.
AB is an arc of a circle, centre O,with radius 9.7cm.
Angle AOB = 110°
O
110°
A
not drawn accurately
9.7 cm
B
Calculate the area of the sector OAB.
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St. Anthony’s Girls’ Catholic Academy
Easter 2017
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Answer.............................................................................................................................cm2
(Total 3 marks)
10. A ruined tower is fenced off for safety reasons.
To find the height of the tower Rashid stands at a point A and measures the angle of
elevation as 18°.
He then walks 20 metres directly towards the base of the tower to point B where the
angle of elevation is 31°.
Calculate the height, h, of the tower.
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Answer .....................................................................m
(Total 6 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 7 (Non Calculator)
1.
A weather forecast says
The probability that it will rain on Monday is 0.6
The probability that it will rain on Tuesday is 0.8
(a)
Complete the tree diagram showing the possible outcomes
Monday
Tuesday
0.8
rain
rain
0.6
......
......
not
rain
......
rain
......
not
rain
not
rain
(1)
(b)
Calculate the probability that it rains on just one of the two days.
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Answer ....................................................
(3)
(Total 4 marks)
2.
50 customers leaving a shop were asked how much money they had spent.
The table shows the results.
Amount A (£)
Number of
customers
0 < A ≤ 10
4
10< A ≤ 40
24
40< A ≤ 60
12
60< A ≤ 100
10
Draw a histogram to show this information.
St. Anthony’s Girls’ Catholic Academy
Easter 2017
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Frequency
density
0
10
20
30
40
70
50
60
Amount, A(£)
80
90
100
110
120
(Total 3 marks)
3.
Sue has ten one pound coins.
Four have a thistle design and six have a leek design.
Sue chooses a one pound coin at random.
If the first coin chosen has a thistle design she replaces it, and chooses again.
If the first coin has a leek design she does not replace it, but chooses again.
What is the probability that the second coin has a leek design?
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St. Anthony’s Girls’ Catholic Academy
Easter 2017
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Answer ....................................................
(Total 4 marks)
4.
Brian and George played 40 games of golf.
The cumulative frequency diagram shows information about Brian’s scores.
The box plot shows information about George’s scores.
40
Brian
30
Cumulative
frequency
20
10
0
0
60
70
80
90
100
110
120
90
100
110
120
Scores
George
Box plot
0
60
70
80
Scores
(a)
Showing your method clearly, find
(i)
Brian’s median score
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Answer ............................................
(1)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
(ii)
Brian’s inter-quartile range.
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Answer ............................................
(2)
(b)
Use the cumulative frequency diagram and the box plot to answer the following.
(i)
Which player is the more consistent in his scoring?
Give a reason for your choice.
.....……………………………………………………………………………..
(1)
(ii)
The winner of a game of golf is the player who has the lowest score.
Who do you think is the better player?
Give a reason for your choice.
.....……………………………………………………………………………..
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(1)
(Total 5 marks)
5.
The histogram shows the test scores of 320 children in a school.
6
5
Frequency
density
4
3
2
1
0
70
80
90
100
110
Score
(a)
Find the median score.
St. Anthony’s Girls’ Catholic Academy
Easter 2017
120
130
140
150
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Answer ………………….……………..
(2)
(b)
Find the interquartile range of the scores.
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Answer ………………….……………..
(2)
(Total 4 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 8 (Calculator allowed)
6.
There are 250 workers in a factory.
The table shows the number of each type of worker in the factory.
Managers
Craftsmen
Labourers
Administrator
s
25
130
54
41
(a)
A stratified sample of size 40 is required.
Calculate the number of each type of worker that should be chosen.
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Answer Managers ....................................................
Craftsmen ...................................................
Labourers ...................................................
Administrators ...........................................
(3)
(b)
Describe a method to obtain a stratified sample of size 40 from the workers in
the factory.
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(2)
(Total 5 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
7.
Kali has a spinner with coloured sections of equal size.
She wants to know the probability that her spinner lands on pink.
She spins it 100 times and calculates the relative frequency of pink after every 10
spins.
Her results are shown on the graph.
0.7
0.6
0.5
Relative
frequency
of pink
0.4
0.3
0
0
(a)
10
20
30
40
70
50
60
Number of spins
80
90
100
Use the graph to calculate the number of times that the spinner landed on pink
(i)
after the first 10 spins,
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Answer ………………………………………
(2)
(ii)
after the first 50 spins.
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Answer ………………………………………
(2)
(b)
From the graph, estimate the probability of the spinner landing on pink.
Answer ………………………………………
(1)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
(c)
Kali’s results confirm that her spinner is fair.
The spinner has five equal sections.
(i)
How many sections are pink?
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Answer ………………………………………
(1)
(ii)
Kali spins the spinner two more times.
What is the theoretical probability that the spinner lands on pink both
times?
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Answer ………………………………………
(2)
(Total 8 marks)
8.
A group of 80 trainee secretaries have their typing speeds tested. The table shows
their results in words per minute (wpm).
Speed, s
(wpm)
Number of
typists
Speed, s
(wpm)
8
< 30
30 ≤ s < 40
30
< 40
40 ≤ s < 50
24
< 50
50 ≤ s < 60
13
< 60
60≤s < 70
5
< 70
20
(a)
(i)
s < 30
Cumulative frequency
Complete the cumulative frequency column in the table.
(1)
(ii)
Draw a cumulative frequency diagram on the grid below.
St. Anthony’s Girls’ Catholic Academy
Easter 2017
80
70
60
Cumulative
frequency
50
40
30
20
10
0
0
10
20
30
40
Speed, s (wpm)
50
70
60
(3)
(b)
Use your diagram to estimate the interquartile range.
......................................................................................................................................
Answer ........................................................ wpm
(2)
(c)
Typists achieving less than 45 words per minute have to resit the test.
Estimate the number of typists who have to resit the test.
......................................................................................................................................
Answer ..................................................... typists
(1)
(Total 7 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
9.
120 men took part in a fitness test.
The times taken to complete the test are shown in the table.
(a)
Time, t
(minutes)
Frequency
10 < t ≤ 12
21
12 < t ≤ 14
49
14 < t ≤ 16
37
16 < t ≤ 18
13
Total
120
Which class interval contains the median time taken by these men to complete the
test?
You must show your working.
......................................................................................................................................
......................................................................................................................................
Answer …………………… < t ≤ ……………………………
(b)
(2)
Calculate an estimate of the mean time taken by these 120 men to complete the
test.
......................................................................................................................................
......................................................................................................................................
Answer ………………………………......... minutes
(c)
(4)
90 women also took part in this fitness test.
An estimate of the mean time taken by these 90 women was calculated.
It was found to be 15.8 minutes.
Calculate an estimate of the mean time taken by all the 210 people to complete
this test.
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
......................................................................................................................................
Answer ………………………………......... minutes
(3)
(Total 9 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
10. There are 60 students at a college.
20 students study both French and Spanish.
13 students study French but not Spanish.
A total of 43 students study Spanish.
(a)Complete the Venn diagram for this information.
(3)
One of the students at the college is to be selected at random.
(b) Write down the probability that this student studies neither French nor Spanish.
.......................................................
(1)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 9 (Non Calculator)
1.
Simplify fully
150  6
12
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
Answer ………………………………….........
(Total 4 marks)
2.
Work out
13  1 4
4
11
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer ..............................................................
(Total 3 marks)
3.
Mr Smith leaves the home at 10 am to go to the shopping mall.
He walks to the station where he catches a train.
He gets off the train at the mall.
The travel graph shows his journey.
15
10
Distance
from home
(km)
5
0
10 am
11 am
12 am
Time
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Easter 2017
1pm
2 pm
After shopping Mr Smith goes home by taxi.
The taxi leaves the mall at 1 pm and arrives at his home at 1.45 pm.
(a)
Complete the travel graph.
(2)
(b)
Calculate the average speed of the taxi.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer .......................................................km per hour
(2)
(Total 4 marks)
4.
The diagram shows a scale drawing of two points, A and B.
N
A
B
(a)
Measure and write down the bearing of B from A.
Answer .......................................................
(1)
(b)
The point C is South-East of A and on a bearing of 100° from B. Draw the position
of C on the diagram.
(2)
(Total 3 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
5.
(a)
On the grid draw the graph y = 2x + 3 for values of x from 0 to 4.
.....................................................................................................................................
.....................................................................................................................................
y
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0
1
2
3
4
x
(3)
(b)
Solve
2x + 3 = 7.5
.....................................................................................................................................
.....................................................................................................................................
Answer x = .......................................................
(2)
(Total 5 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 10 Calculator allowed
6.
Nick invests £10 000 for 3 years at 4% per year compound interest.
How much interest does he earn?
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer £.....................................................
(Total 3 marks)
7.
58  7.412
Find the value of
(a)
(i)
Write down your full calculator display.
...........................................................................................................................
Answer ………………………………….........
(1)
(ii)
Write your answer to 3 significant figures.
...........................................................................................................................
Answer ………………………………….........
(1)
(b)
Evaluate
58
Write your answer in standard form.
.....................................................................................................................................
.....................................................................................................................................
Answer ………………………………….........
(2)
(Total 4 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
8.
A child’s toy is in the shape of a cone on top of a hemisphere.
The diameter of the hemisphere is 15 cm and the overall height of the toy is 26 cm.
Not to scale
26 cm
15 cm
Calculate the volume of this toy.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer ................................................................. cm3
(Total 5 marks)
9.
(a)
ABC is a right-angled triangle.
AC = 19 cm and AB = 9 cm.
A
Not to scale
9 cm
B
Calculate the length of BC.
St. Anthony’s Girls’ Catholic Academy
Easter 2017
19 cm
C
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer ................................................................... cm
(3)
(b)
PQR is a right-angled triangle.
PQ = 11 cm and QR = 24 cm.
P
Not to scale
11 cm
Q
R
24 cm
Calculate the size of angle PRQ.
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
.....................................................................................................................................
Answer ........................................................... degrees
(3)
(Total 6 marks)
10. (a)
Complete the table of values for the graph of y = x3 + 2x
x
y
–3
–2
–1
–12
–3
0
1
2
3
12
33
......................................................................................................................................
(2)
(b)
On the grid, draw the graph of y = x3 + 2x for values of x from –3 to +3.
St. Anthony’s Girls’ Catholic Academy
Easter 2017
y
35
30
25
20
15
10
5
–3
–2
–1
O
1
2
3
x
–5
–10
–15
–20
–25
–30
–35
(c)
(3)
3
Use your graph to write down the value of x + 2x when x = –1.5
Answer …………………………………………….
(1)
(d)
Use the graph to solve
x3 + 2x = 20
Answer …………………………………………….
(1)
(Total 7 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
Day 11: New 9-1 GCSE Higher questions
1. Here are the first four terms of a quadratic sequence.
3
8
15
24
(a) Find an expression, in terms of n, for the nth term of this sequence.
.......................................................
(3)
2. Alex wants to find out how many ducks there are in a park.
One day he puts a tag on each of 30 of the ducks.
The next day he catches 40 ducks.
8 of these ducks have tags on them.
(i) Work out an estimate for the number of ducks in the park.
.......................................................
Alex assumed that none of the tags fell off during the night.
(ii) If Alex’s assumption is wrong, explain how this could affect your answer to part (i).
......................................................................................................................................................
......................................................................................................................................................
(Total for Question 13 is 4 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
3. There are 95 girls and 87 boys in Year 13 at a school.
One girl is going to be chosen for the role of Head Girl.
A different girl is going to be chosen for the role of Deputy Head Girl.
One boy is going to be chosen for the role of Head Boy.
A different boy is going to be chosen for the role of Deputy Head Boy.
Work out how many different ways this can be done.
4. Here is a sketch of part of the graph of y = pqx where q > 0
The points (0, 5), (2, k) and (4, 405) are all on the graph of y = pqx
Find the value of k.
5. Kim, Laura and Molly share £385.
The ratio of the amount of money Kim gets to the amount of money Molly gets is 2 : 5
Kim gets £105 less than Molly gets.
What percentage of the £385 does Laura get?
St. Anthony’s Girls’ Catholic Academy
Easter 2017
6. The diagram shows a piece of wood in the shape of a cuboid.
The piece of wood is 3 cm by 20 cm by 1.2 m.
The mass of the piece of wood is 8 kg.
The piece of wood will float in sea water if the density of the wood is less than the
density of the sea water.
In a large pool, 1 litre of sea water has a mass of 1030 g.
Will the piece of wood float in this pool?
You must show how you get your answer.
(Total for Question 12 is 4 marks)
7
(a) Show that the equation x3 + 5x – 4 = 0 has a solution between x = 0 and x = 1
(2)
4
x 2
x 5
(b) Show that the equation x3 + 5x – 4 = 0 can be arranged to give
(c) Starting with
x0 = 0,
use the iteration formula
to find an estimate for the solution of
4
2
xn + 1 = xn  5
(2)
twice,
x3 + 5x – 4 = 0
.......................................................
(3)
(Total for Question 13 is 7 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
8
The number of fish in a lake decreases by x % each year.
Given that the number of fish halves in 8 years, work out the value of x.
Give your answer correct to 1 decimal place.
.......................................................
(Total for Question 14 is 3 marks)
9.
For all values of x
f(x) = 2x – 3
(a) Find
and
g(x) = x2 + 2
g(−4)
.......................................................
(1)
(b)
Show that
gf(x) = 4x2 − 12x + 11
(2)
(c) Solve
fg(x) = gf(x)
.......................................................
(4)
(Total for Question 20 is 7 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
10. A parachutist jumps out of a plane.
This graph shows information about the velocity, v m/s, of the parachutist t seconds after he jumped.
(a) Work out an estimate for the acceleration of the parachutist when t = 8
.............................................................. m/s2
(3)
(b) Work out an estimate for the distance the parachutist falls in the first 6 seconds.
.............................................................. m
(3)
(Total 6 marks)
St. Anthony’s Girls’ Catholic Academy
Easter 2017
11. A company orders a number of bottles from a factory.
The 8 machines in the factory could make all the bottles in 5 days.
All the machines work at the same rate.
For 2 days, only 4 machines are used to make the bottles.
From the 3rd day, all 8 machines are used to make the bottles.
Work out the total number of days taken to make all the bottles.
3 marks
12. Martin expands
He gets
(2x + 1)(2x − 3)(3x + 2)
12x3 − 4x2 − 17x + 6
(b) Explain why Martin’s solution cannot be correct.
......................................................................................................................................................
......................................................................................................................................................
(1)
St. Anthony’s Girls’ Catholic Academy
Easter 2017