SMK (P) Treacher
Methodist, Taiping
Set 2 -- use on March of the year
Mathematics Paper 2
Form 5
2 hours 30
minutes
Instruction :
This question paper consists of 2
sections. Section A and Section B. Answer all questions in
Section
A and Section B. Write all your
answers clearly in the spaces provided, Incomplete working may
cause you loosing marks. The diagrams in
the questions are not drawn to scale unless stated otherwise.
Section A (52 marks): Answer all question in this section.
|
1.
|
The diagram shows a rectangle with a perimeter of 124 cm.
|
(a)
|
Form an equation relating x and y.
|
|
|
(b)
|
Find the value of x when y = 6.
|
[5 marks]
|
|
|
|
|
|
|
2.
|
|
Factorise and solve the quadratic equation x2
-7x +12 = 0.
|
[4 marks]
|
|
|
3.
|
|
A right pyramid with height 26 cm and a rectangular base
is cut into two parts as shown
|
|
above. Calculate the volume of the bottom portion if its
height is 13 cm.
|
[6 marks]
|
|
|
|
|
|
4.
|
|
In the above diagram, PQRS is a trapezium and RTS is a
semicircle.
Find the area of the shaded region in cm2.
|
[Take p =
|
22
|
]
|
[5 marks]
|
|
7
|
|
|
|
|
|
5.
|
The Venn diagram shows the number of students in a class. It is given that
x = { all students in the class },
A = { students who like swimming },
B = { students who like reading }.
Find the number of students
(a) who like swimming or reading or both.
|
(b) who like neither swimming nor reading.
|
[4 marks]
|
|
|
6.
|
In the diagram, O is the origin and OPQR is a parallelogram.
Find
|
(a) the y-intercept of line PQ,
(b) the x-intercept of line QR.
|
[6 marks]
|
|
|
7.
|
|
The probability that a faulty radio is produced by a
factory is 0.01. 2400 radio are
|
checked during an
inspection. How many radios are expected to be faulty?
|
[4 marks]
|
|
|
|
8.
|
Solve the simultaneous
equations 2x + y = 29 and 5x - 3y = 12.
|
[5 marks]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
9.
|
|
(a)
|
Complete the following statement with suitable
quantifier to form a false statement.
|
|
|
"________ odd numbers are prime numbers.."
|
|
(b)
|
Form a combined statement by using 'and' or 'or', in
which the truth-value of the combined statement is false.
|
|
|
Statement 1:
|
Equilateral triangles have three sides of the same
length.
|
|
|
Statement 2:
|
Heptagons has 6 sides.
|
|
|
[4 marks]
|
|
|
10.
|
|
In the graph above, shade the region which satisfies the
inequalities
|
|
y £ 2x,
y ³ 6 - 2x and x < 3.
|
[4 marks]
|
|
|
|
|
|
11.
|
|
In the diagram above, ABC
is a straight line. Given that sin x =
|
7
|
, find the value of
|
|
11
|
|
Section B (48
marks) Answer all questions
|
12.
|
|
(a)
|
The table below shows the values of x and y
which satisfy the equation
y = 2x2 - 2x
- 20. Calculate the two missing
values.
|
x
|
-4
|
-3
|
-2.2
|
-1
|
0
|
1
|
2
|
2.5
|
4
|
|
y
|
20
|
4
|
|
-16
|
-20
|
-20
|
|
-12.5
|
4
|
|
|
(b)
|
By using a scale of 2 cm to 1 unit on the x-axis
and 2 cm to 5 units on the y-axis,
draw the graph of y = 2x2 - 2x - 20 for -4 £ x £
4.
|
|
(c)
|
From your graph, find
(i) the value of y when x = 0.6,
(ii) the value of x when y = -11.
|
|
(d)
|
Draw a suitable straight line on your graph to find a
values of x which satisfy the
|
|
|
equation 2x2 + x - 22 = 0 for -4 £
x £ 4.
|
|
|
State the values of x.
Answer :
(b) Use your own graph paper
(c) (i)
(ii)
(d)
|
[12 marks]
|
|
|
13.
|
36 37 61 41
57 44 68 76 70 95
93 78 72 91 97 87 52
79 82 74 92 78
The data above shows the marks of 22 students in a Mathematics
test.
|
(a) Construct a frequency table with intervals
class of 10 marks, that is 30 - 39,
40 - 49,
and so on.
(b) Based on the table in (a),
|
|
|
(i)
(ii)
(iii)
|
determine the midpoint and frequency of each of the
class interval in the table,
state the modal class,
calculate the mean mark for the test and give your answer correct to two
decimal places.
|
|
(c)
|
By using a scale of 2 cm to 10 marks on the x-axis
and 2 cm to 1 students on the
|
|
y-axis, draw a frequency polygon for the data.
Answer:
|
[12 marks]
|
|
|
|
14.
|
|
(a)
|
Complete the table in the answer space for the equation y
= 7 – x3 by writing down the values of y
when x = –1 and x = 2.
|
|
|
[2 marks]
|
|
|
|
|
(b)
|
By using a scale of 2 cm to 1 unit on the x-axis
and 4 cm to 10 units on the y-axis, draw the graph of y = 7
– x3 for –3 ≤ x ≤ 2.5.
|
|
|
[4 marks]
|
|
|
|
|
(c)
|
From your graph, find
(i) the value of y when x = 1.2,
(ii) the value of x when y = 20.
|
|
|
[2 marks]
|
|
|
|
|
(d)
|
Draw a suitable straight line on your graph to find the
values of x which satisfy the equation x3 – 8x
– 7 = 0 for –3 ≤ x ≤ 2.5. State these values of x.
|
|
|
[4 marks]
|
|
Answer:
|
(a)
|
|
x
|
–3
|
–2.5
|
–2
|
–1
|
0
|
1
|
2
|
2.5
|
|
y
|
34
|
22.63
|
15
|
|
7
|
6
|
|
-8.63
|
|
|
|
|
|
(b)
|
Use your own
graph paper
|
|
|
|
|
(c)
|
(i) y = __________
|
|
|
|
|
|
(ii) x = __________
|
|
|
|
|
(d)
|
x = __________, __________
|
|
|
|
|
|
|
15.
|
|
The table shows the frequency distribution of the mass,
in kg, of a group of 80 students.
|
|
Mass (kg)
|
Frequency
|
|
|
30 - 34
|
4
|
|
|
35 - 39
|
12
|
|
|
40 - 44
|
24
|
|
|
45 - 49
|
18
|
|
|
50 - 54
|
12
|
|
|
55 - 59
|
7
|
|
|
60 - 64
|
3
|
|
|
|
|
|
|
(a)
|
(i)
|
State the modal class.
|
|
|
|
|
|
|
(ii)
|
Calculate the estimated mean of the mass of the group of
students.
|
|
|
[4 marks]
|
|
|
|
|
(b)
|
Based on the table above, complete the table in the
answer space to show the cumulative frequency distribution of the masses.
|
|
|
|
[3 marks]
|
|
|
|
|
|
(c)
|
By using the scale of 2 cm to 5 kg on the horizontal
axis and 2 cm to 10 students on the vertical axis, draw an ogive for the
data.
|
|
|
|
[4 marks]
|
|
|
|
|
|
(d)
|
50% of all the students in the group have a mass of less
than m kg. These students will be supplied with nutritional food.
Using the ogive you had drawn in (c), find the value of m.
|
|
|
|
[1 mark]
|
|
|
|
|
|
Answer : Part B
12. (a) k = -5.92, m = -16
(b)
(c) (i) y = -20.5, (ii) x = -1.7, 2.7
(d) y = -3x +
2, x = -3.6, 3.1
13. (a)
|
|
Marks
|
Midpoint
|
Frequency
|
|
30 - 39
|
34.5
|
2
|
|
40 - 49
|
44.5
|
2
|
|
50 - 59
|
54.5
|
2
|
|
60 - 69
|
64.5
|
2
|
|
70 - 79
|
74.5
|
7
|
|
80 - 89
|
84.5
|
2
|
|
90 - 99
|
94.5
|
5
|
(b) (i) refer (a)
(ii) 70 - 79
(iii) 70.86
(c)
|
|
|
14
(a) |
x
|
–3
|
–2.5
|
–2
|
–1
|
0
|
1
|
2
|
2.5
|
|
y
|
34
|
22.63
|
15
|
8
|
7
|
6
|
-1
|
-8.63
|
|
|
|
|
x
|
=
|
–1,
|
y
|
=
|
7 – (–1)3
|
|
|
|
|
|
=
|
8
|
|
|
|
|
|
|
|
|
x
|
=
|
2,
|
y
|
=
|
7 – (2)3
|
|
|
|
|
|
=
|
-1
|
|
|
|
|
|
(b)
|
|
|
|
|
|
(c)
|
|
(i)
|
When
|
x
|
=
|
1.2,
|
|
|
|
y
|
=
|
5.27
|
|
(ii)
|
When
|
y
|
=
|
20,
|
|
|
|
x
|
=
|
–2.35
|
|
|
|
|
|
(d)
|
|
y
|
=
|
7 – x3
|
....... (1)
|
|
x3 – 8x – 7 = 0
|
....... (2)
|
|
|
|
Equation (1) + Equation (2)
|
|
y
|
=
|
–8x
|
|
|
|
|
From the graph,
|
|
x
|
=
|
–1, –2.2
|
|
|
|
|
|
|
|
|
|
15
(a)
|
(i) |
Modal class is (40 - 44) kg.
|
|
|
|
|
|
|
(ii)
|
|
Mean
|
=
|
(32 × 4) + (37 × 12) + (42 × 24) + (47 × 18) + (52 ×
12) + (57 × 7)
+ (62 × 3)
|
|
80
|
|
|
=
|
3635
|
|
|
80
|
|
|
=
|
45.44 kg
|
|
|
|
|
|
|
(b)
|
|
Upper
Boundary (kg)
|
Cumulative
Frequency
|
|
29.5
|
0
|
|
34.5
|
0 + 4 = 4
|
|
39.5
|
4 + 12 = 16
|
|
44.5
|
16 + 24 = 40
|
|
49.5
|
40 + 18 = 58
|
|
54.5
|
58 + 12 = 70
|
|
59.5
|
70 + 7 = 77
|
|
64.4
|
77 + 3 = 80
|
|
|
|
|
|
|
(c)
|
|
|
|
|
|
|
(d)
|
|
50
|
× 80
|
=
|
40
|
|
100
|
|
Therefore, p = 44.5 kg.
|
|
|
|
|
|
|
|