2024年新加坡入学考试英语数学.doc

Name: ___________________________________
Identity no: _________________________ Date: __________________ Seat No: _________

BCA ACADEMY
SCHOOL OF BUILDING & DEVELOPMENT
SINGAPORE
MATHEMATICS SCREENING TEST
Set A
1.5 HOURS

Instructions to candidates
1. Do not turn over this page until you are told to do so.
2. Check that you have the correct exam paper, number of pages and questions.
3. This paper consists of TEN (10) questions (100 marks). Answer ALL questions
4. Write your Name, IC NO. and Seat No. on this cover page.
5. All answers are to be written in THIS booklet.
6. Do NOT tear out any page. This booklet is the property of BCA Academy and must not be removed from the test centre.
7. Mobile phones are to be switched off and electronic equipments are not allowed to be used.
8. Candidates are to bring their own non-programmable scientific calculator.
· Unless otherwise stated, leave your answers in 3 significant figures.
· Unless the questions require the answers in term of, the calculator value for should be used.
· If working is needed for any question, it must be shown with the answer. Omission of essential working will result in loss of marks.

For Official Use:
Test Centre:
Test Date:
Marks ( /100):
Marker:
Checker:

1. Simplify the following expressions using fractions only. Show your working clearly .
(a) (5 marks)

(b) (12.96) (5 marks)

(a) =
(b) (12.96)=

2. (a) Given if 27= 81 and 3= 27, find 9. (5 marks)

(b) , find z. (5 marks)

(a) 9=6561

(b) z=

3. (a) The following figure shows a right-angled triangle and its dimensions. Find x. (4 marks)

(x+3) cm

(3x-2) cm

(2x-1) cm

+

X=

3. (b) A pencil case contains 2 green, 6 red and 12 orange pens. A pen is picked out at random and replaced. A second pen is then picked out at random and not replaced. A third pen is finally picked out at random. Find the probability that all three pens picked are of different colours. (6 marks)

P=

North
4. (a) The diagram shows four points, A, B, C, D, on level ground. It is given that D is due North of C, ABC=52°, ACD=120° and ACB=90° .
D

120°

C

A

52°
B

Find:
(i) BCD, and
(ii) Bearing of B from A
(5 marks)
(i) BCD=150°
(ii) east by north 18°

4 (b) Given that AD = BE = 12 m. BEC = 55° and ADC = 68°. Find length AB.
(5 marks)
A

B

C
E
55°
68°

D

AB=

5. In the diagram, PST is a straight line, QR = 21 m and RS = 62 m. The angle of depression of R from Q is 23°. The angle of depression of T from R is 66°.
(a) How much higher is Q than R?
(b) Calculate RST.
(c) Calculate the length of ST.
(10 marks)
21m
62m
66°
23°
S
R
Q
P
T

H= ()m
RST=
L=()m

6. OAB and ORS are two sectors with common centre O and radii OA and OR respectively. PQRS a rectangle in which PQ = 18 cm and QR = r cm. RS is tangent to the arc ANB at N, PO = OQ and MN = 4 cm.
Calculate
(a) ROS in radians,
(b) the perimeter of the shaded region, and
(c) the shaded area.
Hint:
Length of arc, S = rθ
Area of sector =
where, r = radius
θ = angle of the arc (in radian)

(10 marks)

ROS=-arcsin
L=
S=

7. In the diagram, the points A, B, C and D lie on a circle. O is the centre of the circle. AOC is a diameter and ED is a tangent of the circle.ADO = 34° and BAC = 28°. Calculate
(a) CDE
(b) ABD
(c) BDO
(d) BCD
(10 marks)

BB
C
E
D
A

CDE=
ABD=
BDO=
BCD=

8. (a) Find the values of x, y and z equation of the following. (5 marks)

=

X=
Y=
Z=1

8. (b) Given that=, find the values of and . (5 marks)

M=-5
N=5
In the diagram, = a, =b and =. E and F are points on CB such that CE:EB=1:2 and CF:FB=3:1.

Express, as simply as possible, in terms of a and b,

9. A
B
C
F
E
D
a
b

(a) ,
(b) ,
(c) ,
(d) ,
(e) .
(10 marks)

=
=()
=()
=
=

10. (a) Simplify
log 125 • log 121• log 3. (5 marks)
log 125 • log 121• log 3=6
(b) Given that sin 40° = a, express the following in terms of a.
(i) tan 40°
(ii) cos 40°
(5 marks)

tan 40°=

cos 40°=

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