1
ACS (INTERNATIONAL)
END OF YEAR EXAMINATIONS 2018 – YEAR 2
CANDIDATE
NAME
SUBJECT
GROUP NO.
FORM
CLASS
CAMBRIDGE INTERNATIONAL MATHEMATICS
Paper 1
26 October 2018
35 minutes
Candidates answer on the Question Paper.
READ THESE INSTRUCTIONS FIRST
Write in dark blue or black pen.
Do not use staples, paper clips, highlighters, glue or correction fluid.
You may use a pencil for any diagrams or graphs.
For Examiner’s Use
1
Answer all the questions.
2
CALCULATORS MUST NOT BE USED IN THIS PAPER.
3
4
All answers should be given in their simplest form.
5
You must show all the relevant working to gain full marks and you will be given
marks for correct methods, including sketches, even if your answer is incorrect.
6
The number of marks is given in brackets [ ] at the end of each question or part
question.
8
The total number of marks for this paper is
7
9
30.
Total
*Please circle your appropriate Tutor/Class
2Ma Tutor
2Ma Class
FYi
2MaV
OTH
2MaW
SSn
2MaX
DSe
2MaY
SSn
2MaZ
CCC
PGMa1
CCC
PGMa2
This question paper consists of 7 printed pages and 1 blank page.
2
Answer all questions.
1
Evaluate the following, leaving your answer in standard form.
(a)
4.7 104 1.2 103
Answer ………….….………….. [2]
(b)
1.8 10
4
2 102
Answer ………….….………….. [2]
___________________________________________________________________________
2
(a) Simplify.
x2 y
3
y2
Answer………………….. [2]
(b) Evaluate.
2
3
9
4
1
2
21
8
1
Answer ……….………….. [3]
___________________________________________________________________________
3
3
(a)
Simplify.
18
24
6
Answer …….…………..………….. [2]
(b)
Write
7
in its simplest form by rationalising the denominator.
5 1
Answer ……………..…….………….. [2]
___________________________________________________________________________
4
4
Express as a single fraction in its simplest form.
m 1
m 2m 3
2
Answer ……………………………….. [2]
___________________________________________________________________________
5
Solve.
4
2x 5
x
3
Answer
x =……………….… or x = ..…….…..…….. [3]
___________________________________________________________________________
5
6
(a) Factorise 2ap 6aq bp 3bq .
Answer ……………….…………………….. [2]
(b) (i) Factorise a 2 1
Answer ………………..…….….…………..
[1]
(ii) Hence find the 2 prime factors of 899.
Answer …....……. and ….……….. [1]
___________________________________________________________________________
7
(a)
State the number of lines of symmetry of this shape.
Answer
………….….………….. [1]
(b) Write down the order of rotational symmetry of this diagram.
Answer
………….….………….. [1]
__________________________________________________________________________
6
8
Make x the subject of the formula.
y
2x 5
3
Answer
x =………….….………….. [3]
___________________________________________________________________________
7
9
Solve the simultaneous equations.
5x 2 y
2
3 x 10
y
Answer
x = ….….…………..
y = ….….………….. [3]
___________________________________________________________________________
END OF PAPER
8
Key Answers:
1
2
3
(a)
4.58 104
(b)
9 10
(a)
x6 y
(b)
7
3
3
7
(a)
3 2
6 or
2 3
(b)
4
5
6
7 5 7
4
1
m 3
(a)
2a b
7
8
9
29, 31
(a)
1
(b)
2
x
3y2 5
2
x
2
y
4
5 1
4
x
p 3q
a 1 a 1
(b)(i)
7
or
3
or
2
x
(b)(ii)
3
4
1
ACS (INTERNATIONAL)
END OF YEAR EXAMINATIONS 2018 – YEAR 2
CANDIDATE
NAME
SUBJECT
GROUP NO.
FORM
CLASS
CAMBRIDGE INTERNATIONAL MATHEMATICS
Paper 2
26 October 2018
1 hour 25 minutes
Candidates answer on the Question Paper.
Additional Materials:
Graphics Calculator
READ THESE INSTRUCTIONS FIRST
Write in dark blue or black pen.
Do not use staples, paper clips, highlighters, glue or correction fluid.
You may use a pencil for any diagrams or graphs.
For Examiner’s Use
1
2
Answer all the questions.
3
Unless instructed otherwise, give your answers exactly or correct to three
significant figures as appropriate.
4
5
Answers in degrees should be given to one decimal place.
For
6
use your calculator value.
7
You must show all the relevant working to gain full marks and you will be given
marks for correct methods, including sketches, even if your answer is incorrect.
The number of marks is given in brackets [ ] at the end of each question or part
question.
The total number of marks for this paper is
70.
8
9
10
11
Total
*Please circle your appropriate Tutor/Class
2Ma Tutor
2Ma Class
FYi
2MaV
OTH
2MaW
SSn
2MaX
DSe
2MaY
SSn
2MaZ
CCC
PGMa1
CCC
PGMa2
This question paper consists of 15 printed pages and 1 blank page.
2
Formula List
Curved surface area, A, of cylinder of radius r, height h.
A 2 rh
Curved surface area, A, of cone of radius r, sloping edge l.
A
Curved surface area, A, of sphere of radius r.
A 4 r2
Volume, V, of pyramid, base area A, height h.
V
1
Ah
3
Volume, V, of cylinder of radius r, height h.
V
r 2h
Volume, V, of cone of radius r, height h.
V
1 2
r h
3
Volume, V, of sphere of radius r.
V
4 3
r
3
rl
3
Answer all questions.
1 (a)
The marks of 33 students in a test are shown in the table below.
Mark
1
2
3
4
5
6
Frequency
3
4
5
5
7
9
Find the mode, median and range of these marks.
Mode = …………………… [1]
Median = …………………… [1]
Range = …………………… [1]
(b)
The time, t seconds, taken for each of 50 students to eat an omelette is recorded.
Time
(t seconds)
Frequency
20 t
2
25
25 t 30
6
30 t
40
19
40 t 55
55 t 65
65 t 80
7
9
7
(i) Write down the modal time interval.
Answer …………………….. s
[1]
Answer …………………… s
[2]
(ii) Calculate an estimate of the mean time.
___________________________________________________________________________
4
2 (a)
The stem and leaf diagram shows the height of 14 plants.
0 7 8 8 9
1 1 3 6 7 9
2 0 1 2
3 2 4
Key
3 2 means 32 cm
(i) Find the median.
Answer ………………..….. cm
[2]
Answer …………………….. cm
[2]
(ii) Find the interquartile range.
(b)
The table shows the marks gained by some students in their Mathematics test.
Mark
52
75
91
Number of students
x
45
11
The mean mark for these students is 70.3.
Find the value of x.
Answer
x = ………………………… [3]
___________________________________________________________________________
5
3
A store serves coffee in paper cups of two sizes : regular and large.
The cups are geometrically similar and the capacity of the regular and large cups are
270 ml and 640 ml respectively.
NOT DRAWN TO SCALE
12 cm
Regular
Large
(a) The height of the regular cup is 12 cm.
Find the height of the large cup.
Answer …………………… cm
(b)
[2]
The cost of making a paper cup is dependent on its surface area.
A manufacturer charges 32 cents to make 1 large cup.
Find the cost of making 1 regular paper cup.
Answer …….………….. cents [2]
___________________________________________________________________________
6
4 (a) In the diagram, ADB and BFEG are straight lines. Angle BDF = 90º.
DF = DA = 3 cm and AC = FB.
D
A
B
25º
F
NOT DRAWN TO SCALE
E
G
(i) Name a pair of congruent triangles and state the reason.
Answer
Triangle…..…………is congruent to Triangle ……………… [1]
Reason : ….………………………………….........………… [1]
(ii) Calculate Angle DAC.
Answer ………………….º [1]
(b)
In the diagram, the radius of the two touching circles with centres X and Y are
6 cm and 4 cm respectively. XYZ and ABZ are straight lines.
Calculate the length of YZ.
NOT DRAWN TO SCALE
X
6 cm
A
Y
4 cm
B
Answer YZ = ………............................. cm
Z
[3]
___________________________________________________________________________
7
5
A map is drawn to a scale of 1 : 500 000.
(a)
The distance between two towns is 34 km.
Calculate in cm, their distance on the map.
Answer ………………..…….. cm
(b)
[2]
A field has an area of 1.8 cm2 on the map.
Calculate in km2, the actual area of the field.
Answer …………….…….. km2
[2]
___________________________________________________________________________
8
6 (a)
The perimeter of this sector of a circle is 30.2 cm.
Calculate the value of p.
pº
9 cm
NOT DRAWN TO SCALE
Answer
(b)
p = ……………….……………… [3]
The diagram below shows a sector of a circle with centre O and radius 25 cm.
Angle AOB = 62º.
O
Calculate the area of sector AOB.
A
B
NOT DRAWN TO SCALE
Answer ……………..…..……. cm2
[2]
___________________________________________________________________________
9
12 cm
7
14 cm
8 cm
7 cm
16 cm
(a)
Calculate the area of the cross section ABCDE.
Answer ………….………….……….. cm2
(b)
[3]
The prism is of length 7 cm.
Calculate the volume of the prism.
Answer ……………………………… cm3
[1]
___________________________________________________________________________
10
y
8
x
0
(a) On the diagram, sketch the graph of y
6 2 x 3x 2 .
[2]
(b) Write down the y-intercept.
Answer ………………………………….………. [1]
(c) Write down the x coordinates of the points where the graph crosses the x-axis.
Answer x = ……………. and x = …………….. [2]
(d) Find the coordinates of the maximum point.
Answer ( ………………… , ………..……….. ) [2]
(e) Write down the equation of the line of symmetry.
Answer ………………………..……..………….. [1]
(f) On the same diagram, sketch the graph of y
2x 4 .
[2]
(g) Find the coordinates of the points of intersection of the two graphs drawn above.
Answer ( …….….….. , …….….….. ) and ( ………….…. , …….………. ) [2]
___________________________________________________________________________
11
9
The graph shows a quadratic curve y
Ax 2
Bx , where A and B are natural numbers.
y
(-2 , 6) •
0
(a)
1
x
Find the values of A and B.
Answer
A = ………………….
B = ……………..…...
(b)
[3]
Write down the line of symmetry on the graph above.
Answer …………………………….. [1]
___________________________________________________________________________
12
10
An amusement park charges $x for an adult ticket and $ x 0.75 for a child ticket.
One day, the park receives
$ 168 from selling adult tickets
$ 207 from selling child tickets.
The total number of these tickets sold during this day is 100.
(a) Write an expression in terms of x for the number of adult tickets sold.
Answer …………………………….. [1]
(b) Write an expression in terms of x for the number of child tickets sold.
Answer …………………………….. [1]
(c)
Using your answers in part (a) and part (b), form an equation in terms of x and
show that it reduces to 50 x 2 225 x 63 0 .
[2]
13
(d)
Solve 50 x 2 225 x 63 0 by using a graphics calculator.
Answer
(e)
x = ……………….. or x = …………………… [2]
Find the price of a child ticket.
Answer
$ …………………….. [1]
___________________________________________________________________________
15
(c)
Calculate the volume of wood that was removed.
Give your answer correct to 3 significant figures.
Answer …………………… cm3
(d)
[3]
Calculate the total surface area of the pet feeding bowl.
Give your answer correct to 3 significant figures.
Answer …………………… cm2
[4]
___________________________________________________________________________
END OF PAPER
16
Key Answers:
1
2
3
(a)
Mode = 6
Median = 4
Range = 5
(b)(i)
30 t 40
(b)(ii)
45.1
8
(a),
(f)
(a)(i)
16.5
(a)(ii)
12
(b)
(b)
24
(c)
(a)
6
x
1.79, x 1.12
0.333, 6.33
16
(d)
(b)
4
(a)(i)
18
(e)
ACD, FBD
RHS or
ADC
(a)(ii)
(b)
AC
DF
65
20
(g)
FDB 90
FB( given)
DA 3cm
6
(a)
6.8
(b)
45
(a)
(b)
7
(a)
(b)
77.7 (3sf)
accept 77.66.....
338 (3sf)
accept 338.157.....
182 (3sf)
accept 181.85...
1270 (3 sf)
accept 1272.99...,
1273, 1274
0.333
1.72, 0.558
0.387, 4.77
9 (a)
A 1
B
1
(b)
x 0.5
10 (a)
5
x
(b)
168
x
207
x 0.75
(d)
x 0.3, x 4.2
(e)
3.45
11 (b)
28.7
(c)
1690
(d)
1100