**************************************

Form 6 Yearly Examination (2021 – 2022)

MATHEMATICS Compulsory Part

Paper 2
𝟏
(1 𝟒 hours)

INSTRUCTIONS

1. Read carefully the instructions on the Answer Sheet. After the announcement of the start
of the examination, you should first write your name, class and class number and insert
the information required in the spaces provided. No extra time will be given for writing
your name, class and class number after the ‘Time is up’ announcement.

2. When told to open this book, you should check that all the questions are there. Look for
the words ‘END OF PAPER’ after the last question.

3. All questions carry equal marks.

4. ANSWER ALL QUESTIONS. You are advised use an HB pencil to mark all your
answers on the Answer Sheet, so that wrong marks can be completely erased with a clean
rubber. You must mark the answer clearly; otherwise you will lose marks if the answers
cannot be captured.

5. You should mark only ONE answer for each question. If you mark more than one answer,
you will receive NO MARKS for that question.

6. No marks will be deducted for wrong answers.

Page 1
There are 30 questions in Section A and 15 questions in Section B.
The diagrams in this paper are not necessarily drawn to scale.
Choose the best answer for each question.

Section A

 
1. ( 4) 444  1222  =
2 

A.  2 666 .
B.  2 222 .
C. 2 222 .
D. 2666 .

2. (2a  b  3)(2a  b  3) 

A. 4a 2  b2  6b  9.
B. 4a 2  4ab  b2  9.
C. 4a 2  4ab  b2  9.
D. 4a2  12a  9  b2 .

a
3. If b  2  , then a =
2a

2b  4
A. .
1 b
4  2b
B. .
1 b
2b  4
C. .
1 b
4  2b
D. .
1 b

4. 0.089 695 =
A. 0.089 6 (correct to 4 decimal places).
B. 0.089 70 (correct to 5 significant figures).
C. 0.09 (correct to 2 significant figures).
D. 0.089 70 (correct to 4 significant figures).

Page 2
5. If ( x  1)( x  2)  ( x  2) 2  A( x 2  1)  Bx , find the values of A and B.

A. A  2, B  3
B. A  2, B  1
C. A  1, B  1
D. A  1, B  1

6. If F ( x)  (2 x  1)Q( x)  R , where F ( x ) and Q ( x ) are polynomials in x and R is a real constant,

find the remainder when F ( x ) is divided by 1  2x .

A. −𝑅
B. R
𝑅
C.
2
D. It cannot be determined.

x  4  0
7. The solutions of ‘  x or 3x  27 ’ are
 4
4

A. all real values of x.

B.  9  x  4 .
C. x  4 .
D. x  9 .

8. If the area of a square increases by 44%, then the diagonal of the square increases by

A. 11%.
B. 20%.
C. 31%.
D. 44%.

9. In the figure, the 1st pattern consists of 1 dot. For any positive integer n, the (n + 1)th pattern is
formed by adding (2n + 2) dots to the nth pattern. Find the number of dots in the 7th pattern.

A. 41
B. 55
C. 67
D. 71

Page 3
 10. If y varies directly as x and inversely as z , which of the following must be true?

x
I. is a constant.
y z
II. When x remains unchanged and z is halved, y is halved.
x2
III. z  2
y

A. I only
B. I and III only
C. II and III only
D. I, II and III

11. The weights of JoJo and Dio are measured as 69 kg and 85 kg respectively, correct to the nearest
0.5 kg. If the difference between their actual weights is x kg, find the possible range of x.

A. 15 < x < 17
B. 15.25 < x <16.75
C. 15.5 < x < 16.5
D. 15.75 < x < 16.25

12. The figure shows the graph of y = bx2 + cx + a. Which of the following must be true?
y

I. a>0
II. b 2  4ac  0
III. c < 0

A. I and II only
B. II and III only x
0
C. I and III only
D. I, II and III

13. Let a, b and c be non-zero numbers. If a : c = 2 : 1 and (3b  4c) : (4b  3c) = 1 : 2,
then (a + b) : (b + c) =

A. 1 : 1.
B. 3 : 7.
C. 6 : 7.
D. 9 : 7.

Page 4
14. The figure shows a sphere, a right circular cone and a cylinder.
2r
3r
3r

4r 5r

If their volumes are V1, V2 and V3 respectively, then

A. V1 > V3 > V2.
B. V3 > V2 > V1.
C. V1 > V2 > V3.
D. V3 > V1 > V2.

15. If f ( x)  2  2 x  x 2 , then  f ( x)  f (1  x) 

A. −1.
B. −2𝑥 + 1.
C. 2𝑥 2 + 2𝑥 + 3.
D. −2𝑥 2 − 6𝑥 + 1.

16. In the figure, the two straight lines intersect at a point on

the y-axis. Which of the following must be true?

I. r 0
II. q  s
III. pr  qs  0

A. I and II only
B. I and III only
C. II and III only
D. I, II and III

17. In the figure, ABCD is a parallelogram. E is a point lying on AB such that AE : EB = 7 : 3. F and
G are points lying on CD such that BFGE is a parallelogram and F is the mid-point of CD. EG and
BF cut AC at I and H respectively. If the area of BCH is 100cm2, then the area of AEI is
A E B
2
A. 98 cm .
B. 100 cm2.
I
C. 140 cm2.
D. 147 cm2. H

D G F C

Page 5
18. The bearing of town B from town A is N34°W and the bearing of town C from town A is S72°W.
If town B and town C have the same distances from town A, find the bearing of town C from
town B.

A. N3°E
B. N19°E
C. S3°W
D. S19°W

19. In the figure, BA  AC and DB  BC . BC = 3. The area of quadrilateral ACDB =

9
A. (tan 𝛼 + sin 𝛽 cos 𝛽).
2
9
B. (sin 𝛼 cos 𝛼 + tan 𝛽).
2
9
C. (tan 𝛼 + tan 𝛽).
2
9
D. sin(𝛼 + 𝛽).
2

︵ ︵
20. In the figure, AB : BC  3 : 2 . It is given that ∠BAD = 52° and
∠CBD = 24°. Find ∠ADB.

A. 28°
B. 36°
C. 38°
D. 42°

21. In the figure, ABE and DCE are straight lines. If AB = BE = 3 cm

and CD = 7 cm, find the length of CE.

A. 9 cm
7
B. 2 cm
7
C. cm
2
D. 7 cm

22. In the figure, PQRST is a regular pentagon. PR and PS intersect QT at the points X and Y
respectively. Which of the following are true?
P
I. PY = TY
II. PXY  PRS X Y
III. XYS = 3PQX Q T

A. I and II only
B. I and III only
C. II and III only
D. I, II and III R S
Page 6
23.

In the figure, OABC is a rectangle, where AB = 32 cm and BC = 24 cm. OCD is a straight
line and BED is an arc with centre O. F is a point on BC such that BC  EF. If
BF : FC = 1 : 5, find the area of the sector ODE correct to the nearest cm2.

A B
A. 419 cm2
B. 515 cm2 E
F
C. 628 cm2
D. 834 cm2

O C D

24. The rectangular coordinates of the point A are (√2, −√6). If A is rotated anticlockwise about the
origin through 210°, the the polar coordinates of its image are

A. (2, 90°).
B. (2√2, 90°).
C. (2√2, 150°).
D. (2√2, 180°)

25. Let the equation of the straight line L be 2x  3y + 6 = 0. P(x, y) is a point where the mid-point of
OP lies on L. Find the equation of the locus of P.

A. 2x  3y = 0
B. 2x  3y  6 = 0
C. 2x  3y  12 = 0
D. 2x  3y + 12 = 0

26. If M(1, 2) is the mid-point of a chord of the circle x2 + y2  6x + 4y  12 = 0, find the equation of
the chord.

A. x + 2y  6= 0
B. x  2y + 6 = 0
C. x + 2y  3 = 0
D. x  2y + 3 = 0

27. The coordinates of the points A, B and C are (1, √3), (7, 7√3) and (7, √3) respectively. Let
P be a point on BC such that AP is the angle bisector of BAC. The coordinates of point P are

A. (7, √3).
B. (7, 2√3).
C. (7, 3√3).
D. (7, 4√3).

Page 7
28. Two fair dice are thrown in a game. If the sum of the two numbers is greater than 10, $120 will
be gained; otherwise, $24 will be gained. Find the expected gain of the game.

A. $28
B. $30
C. $32
D. $34

29. The following figures show the cumulative frequency curves of the weight distributions of three
classes.

I. II. III.

Arrange the three distributions in descending order of standard deviations.

A. I, II, III
B. I, III, II
C. II, I, III
D. III, I, II

30. A class is split into two groups, A and B, to attend a Mathematics examination. The following
table shows the means and the standard deviations of the marks of the two groups of students in
the Mathematics examination.

Mean mark Standard deviation

Group A 55 6
Group B 65 6

Which of the following must be true?

I. The mean mark of the whole class is between 55 and 65.

II. The standard deviation of the marks of the whole class is 6.
III. The student who got the lowest mark belongs to group A.

A. I only
B. II only
C. I and II only
D. II and III only

Page 8
Section B

31. 13 × 248 − 249 + 14 × 165 + 6 × 220 =

A. A0000014000016.
B. B0000014000016.
C. A00000140000016.
D. B00000140000016.

2)
32. Find the sum of roots of the equation 2 − 10log(𝑥 = 𝑥.

A. 1 or −2
B. 1
C. −1
D. −2

33. The graph in the figure shows the linear relation between √𝑥 and 𝑦 5 . When 𝑦 = −2, then x =
𝑦5
A. 2601.
B. 51. 2
C. 36.
D. 51 .

√𝑥
0 3

34. Let y  f ( x) be a quadratic function. The figure below may represent the graph of y  f ( x) and
the graph of
y

A. y   f (4 x).
B. y  4 f ( x).
x
C. y  4 f ( x).
D. y  f (4 x).

35. For 0  x  360 , how many solutions does the equation sin x (cos2 x  2)  0 have?

A. 2
B. 3
C. 4
D. 6

Page 9
 1  2i 3  2i
36. Define w  and z  , where m is a real number. If w  z is a real number, then
mi mi
w z 

A. 1.
B. i.
C. 4  i.
D. 4  i.

37. If a, b, c, d are consecutive terms of an arithmetic sequence, which of the following must be
true?

I. 𝑑 − 𝑎 = 3(𝑐 − 𝑏)
II. 2𝑎 , 2𝑏 , 2𝑐 , 2𝑑 are consecutive terms of a geometric sequence.
III. 3𝑏 − 2𝑎, 4𝑐 − 3𝑏, 5𝑑 − 4𝑐 are consecutive terms of an arithmetic sequence.

A. I and II only
B. I and III only
C. II and III only
D. I, II and III

38. Consider the following system of inequalities:

3 x  4 y  12
 x  2 y  1


x  0
 y  0

Let (𝑥, 𝑦) be a solution to the above system of inequalities, where x and y are integers. Find the
greatest value of 𝑥 + 6𝑦 + 2.

A. 13
B. 10
C. 9
D. 6

39. In the figure, two circles intersect at B and C. PQ is the tangent

to the smaller circle at A. DCA is a straight line. If BAQ = 76°,
then BED =

A. 104°.
B. 114°.
C. 142°.
D. 152°.

Page 10
40. Find the number of intersection(s) between L: kx – y − 2 = 0 and S: x 2  y 2  4kx  4  0 ,
where k ≠ 0.

A. 0
B. 1
C. 2
D. Cannot be determined

41. In the figure, ABCDEFGH is a rectangular block, where AEF = 60 and CEH = 45. Find
cos AEC.

2
A.
6
3
B.
6
6
C.
4
D. 6
3

42. 3 teachers and 12 students play a game in the post examination period. 4 of them will be selected
for demonstration. If at least one of the teachers must be selected, find the number of possible
combinations.

A. 660
B. 870
C. 1365
D. 20 880

43. Marf, Day and six others are going to sit in two rows of 4. Find the probability that Marf and
Day sit in different rows if Marf must sit in the first row.

2
A.
7
3
B.
7
4
C.
7
5
D.
7

Page 11
44. If the mean and the standard deviation of the data a, b, c, d, e are c and s respectively, find the
standard deviation of the data a, b, d, e.

A. 4
s
5
B. s
C. 5
s
2
D. 5
s
4

45. Let x, y and z be the mean, inter-quartile range and variance of a group of numbers
{a, b, c, d, e, f} respectively, while k, m and n be the mean, inter-quartile range and variance of
another group of numbers {3a – 5, 3b – 5, 3c – 5, 3d – 5, 3e – 5, 3f – 5} respectively. Which of
the following must be true?

I. k = 3x – 5
II. m = 3y – 5
III. n = 9z

A. I and II only
B. I and III only
C. II and III only
D. I, II and III

END OF PAPER

Page 12