2HR Jan 2020
2HR Jan 2020
2HR Jan 2020
com
Please check the examination details below before entering your candidate information
Candidate surname Other names
Mathematics A
Paper 2HR
Higher Tier
Instructions
• Use black ink or ball-point pen.
• centre
Fill in the boxes at the top of this page with your name,
number and candidate number.
• Withoutallsufficient
Answer questions.
• Answer the questions working, correct answers may be awarded no marks.
• – there may be more spacein the spaces provided
than you need.
• You must NOT write anything on the formulae page.
Calculators may be used.
• Anything you write on the formulae page will gain NO credit.
Information
• The total mark for this paper is 100.
• 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.
• your answers if you have time at the end.
Check
Turn over
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P59817A
©2020 Pearson Education Ltd.
1/1/1/1/
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International GCSE Mathematics
−b ± b2 − 4ac
x=
2a b
1 2 Volume of prism
Volume of cone = πr h = area of cross section × length
3
Curved surface area of cone = πrl
l cross
h section
length
r
r
h
2
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(1)
(b) Write 800 as a product of its prime factors.
Show your working clearly.
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(2)
3
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2 The table gives information about the amount of money, in £, that Fiona spent in a
grocery store each week during 2019
0 x < 20 5
20 x < 40 11
40 x < 60 8
60 x < 80 19
80 x < 100 9
Work out an estimate for the total amount of money that Fiona spent in the grocery store
during 2019
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4 The diagram shows a rectangle and a diagonal of the rectangle.
8.5 cm
5 A plane takes 3 hours 36 minutes to fly from the Cayman Islands to New York.
The plane flies a distance of 2470 km.
Work out the average speed of the plane in km/h.
Give your answer correct to the nearest whole number.
....................................................... km/h
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6 Use ruler and compasses only to construct the perpendicular bisector of the line AB.
You must show all your construction lines.
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A
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B
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7 Solve the simultaneous equations
3x + 5y = 6
7x – 5y = –11
y = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
$. . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Diagram NOT
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accurately drawn
x cm
1.2 cm
force
pressure =
area
Work out the value of x.
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x = .......................................................
9
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10 The table shows information about the surface area of each of the world’s oceans.
Surface area in
Indian 6.86 × 107
Southern 2.03 × 107
Arctic 1.41 × 107
Atlantic 1.06 × 108
(a) Work out the difference, in square kilometres, between the surface area of the
Atlantic Ocean and the surface area of the Indian Ocean.
Give your answer in standard form.
k = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(1)
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11 (a) Write down the integer values of x that satisfy the inequality –2 < x 4
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(2)
The region R, shown shaded in the diagram, is bounded by three straight lines.
y
Diagram NOT
y=x–3 accurately drawn
y=6
R
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O x
x+y=5
(b) Write down the three inequalities that define the region R.
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(2)
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12 The diagram shows two congruent isosceles triangles and parts of two congruent regular
polygons, X and Y.
66° 66°
C F
Polygon Y
n = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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13
G F
Diagram NOT
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h cm H E
10 cm
A 12 cm D
The diagram shows a prism ABCDEFGH in which ABCD is a trapezium with BC parallel
to AD and CDEF is a rectangle.
BC = 7 cm AD = 12 cm DE = 10 cm
The height of trapezium ABCD is h cm
The volume of the prism is 608 cm3
Work out the value of h.
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h = .......................................................
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14 Max kept a record of the marks he scored in each of the 11 spelling tests he took one term.
Here are his marks.
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x
15 (a) Complete the table of values for y = x 2 − −3
2
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x –3 –2 –1 0 1 2 3
(2)
x
(b) On the grid, draw the graph of y = x 2 − − 3 for values of x from –3 to 3
2
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y
8
1
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–3 –2 –1 O 1 2 3 x
–1
–2
–3
–4
(2)
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16 Cody has two bags of counters, bag A and bag B.
Each of the counters has either an odd number or an even number written on it.
Bag A Bag B
Odd number
....................
Odd
number
7
10
....................
Odd number
....................
....................
Even
number
....................
Even number
(2)
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(b) Calculate the probability that the total of the numbers on the two counters will be an
odd number.
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(3)
Harriet also has a bag of counters.
Each of her counters also has either an odd number or an even number written on it.
Harriet is going to take at random a counter from her bag of counters.
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The probability that the number on each of Cody’s two counters and the number on
3
Harriet’s counter will all be even is
100
(c) Find the least number of counters that Harriet has in her bag.
Show your working clearly.
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(3)
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17 Some students in a school were asked the following question.
“ Do you have a dog (D), a cat (C) or a rabbit (R)?”
(3)
Given that a total of 50 students answered the question,
(b) work out the value of x.
x = . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(2)
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(1)
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A
Diagram NOT
accurately drawn
9 cm
C 8 cm
P
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D
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6 cm
....................................................... cm
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4 − 3x 3x − 5
19 (a) Solve − = −3
5 2
..................................................................................
(3)
20
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Diagram NOT
accurately drawn
13 cm
9 cm
A B
....................................................... cm2
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10 x 2 + 23 x + 12
21 (a) Simplify fully
4x2 − 9
5y
8 (3)
2 2 y × 23 y + 2 =
4n
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(4)
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23 Express 7 – 12x – 2x2 in the form a + b(x + c)2 where a, b and c are integers.
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24 L1 and L2 are two straight lines.
The origin of the coordinate axes is O.
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25 N is a multiple of 5
A=N+1
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B=N–1
Prove, using algebra, that A2 – B2 is always a multiple of 20
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26 The diagram shows trapezium OACB.
A 4b C
3a
O 6b B
→ → →
OA = 3a OB = 6b AC = 4b
N is the point on OC such that ANB is a straight line.
→
Find ON as a simplified expression in terms of a and b.
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