Excel / Education
GCSE Mathematics
Paper 2A (Non-Calculator)
Higher Tier
Time: 2 hours
2A
Materials required for examination
Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser.
Tracing paper may be used.
Items included with question papers
Formulae sheet
Instructions to Candidates
Answer ALL the questions in the spaces provided in this question paper.
Supplementary answer sheets may be used.
Information for Candidates
The total mark for this paper is 100.
The marks for questions and parts of questions are shown in round brackets: e.g. (2).
Calculators must not be used.
Advice to Candidates
Show all your working.
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Higher 2A
GCSE Maths
1.
Work out
2 3
! . Simplify your answer as much as possible
5 4
……………………
(3)
2.
(a)
Expand
4(x – 3)
……………………
(2)
(b)
Factorise
12x + 15y
……………………
(2)
(c)
Solve
5x – 9 = 26
……………………
(2)
3.
A number sequence begins;
3, 7, 11, 15, 19, ………
(a)
Write down the next term
………………
(1)
(b)
Find, in terms of n, an expression for the n th term
………………
(3)
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4.
What percentage of this shape is shaded?
4 cm
10 cm
4 cm
10 cm
……………………%
(4)
5.
The table below gives the numbers of crabs found in each of 20 rock pools.
Crabs
0
1
2
3
4
(a)
Number of pools
3
6
5
4
2
Write down the mode.
………………..
(1)
(b)
Calculate the mean number of crabs in a pool
………………..
(3)
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(c)
Calculate the range of this data
……………………
(2)
6.
(a)
Simplify
y4 x y3
………………..
(1)
(b)
Simplify
8 p9
2 p3
………………..
(2)
7.
A recipe involves mixing flour and sugar in the ratio 3 : 2
(a)
How much flour is needed to make 1kg of the mixture?
(b)
………………g
(2)
Saeid has1200 g of flour. How much of the mixture can he make?
………………g
(2)
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8.
(a)
Calculate the length of the missing side, x, in this triangle.
10cm
6cm
x
………………..cm
(3)
(b)
The same triangle is the end of a triangular prism
6 cm
x
4 cm
Calculate the volume of the prism. State the units in your answer.
………………..
(3)
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9.
y
A
B
x
(a)
Describe fully the single transformation that takes triangle A to
triangle B.
(2)
(b)
Reflect triangle B in the y-axis. Label your answer “C”.
(2)
10.
The distance from the Earth to the moon is 4 x 105 km
Mars is 200 times further away than the moon.
(a)
Calculate the distance from the Earth to Mars. Give your answer in
standard form.
……………………
(3)
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(b)
A rocket takes 20 days to travel from Earth to the moon. How far does
it travel, on average, each day? Give your answer in standard form.
……………………
(3)
11.
In the diagram below, XY is the diameter of the circle.
PQ is a tangent to the circle at Y.
P
X
a
20o
b
(a)
Y
Q
Find angle a. Give a reason for your answer.
……………………
(2)
(b)
Find angle b. Give a reason for your answer.
……………………
(2)
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12.
In this question x = 3, y = - 4, z = 2
Work out
(a)
4x + 5y
……………………
(2)
(b)
2x 2 + y 2
z
……………………
(3)
13.
Solve;
(a)
2x + 3 = x + 10
x = …………
(3)
(b)
3(2x – 1) = 6
x = …………
(2)
(c)
(d)
x
!3=9
4
x = …………
(2)
4 x !1
=3
5
x = …………
(2)
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14.
The following table gives times taken in minutes for a group of students
(GROUP A) to complete a Maths task.
Time
0 – 10
10 – 15
15 – 20
20 – 30
30 – 50
50 – 60
(a)
Number of students
4
5
9
8
7
7
Cumulative frequency
Complete the cumulative frequency column of the table
(2)
(b)
On the grid (below), draw a cumulative frequency diagram to represent
the data.
cf
40
30
20
10
0
5
10
15
20
25
30
35
40
45
50
55
60
time
(min)
(4)
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(c)
Use your diagram to estimate;
(i)
The median
……………
(1)
(ii)
The lower quartile
……………
(1)
(iii)
The upper quartile
……………
(1)
(iv)
The inter-quartile range
……………
(1)
A different group of students (GROUP B) were also timed doing the same task and
the following were calculated (all in minutes)
median = 21
lower quartile = 10
upper quartile = 46
(d)
0
smallest = 5
largest = 68
On the grid below, draw a box and whisker plot to illustrate this data.
5
10
15
20
25
30
35
40
45
50
55
60
70
time
(min)
(3)
One of the se groups (GROUP A or GROUP B) had pupils from a wide variety of age
groups and abilities.
(e)
Which group do you think this was? Give a reason for your answer.
(2)
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15.
(a)
Write
3
as a decimal, giving the first 4 decimal places.
11
………………..
(2)
(b)
Write
. .
0.21 as a fraction in its simplest terms.
………………..
(3)
16.
Simplify;
(a)
(b)
√27
.....................
(1)
!5
!3
.....................
(2)
(c)
2
! 5 "1
.....................
(3)
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17.
Solve;
x(2x !1)
+1= 3
3
....................
(4)
18.
A right-angled triangle has sides x, x + 2 and x + 4.
(a)
Prove that x2 – 4x – 12 = 0
(3)
(b)
Hence find the value of x
………………..
(3)
End of Questions
(Total Marks: 100)
© Excel Education
Higher 2A
GCSE Maths