Sing Yin Secondary School
First Term Examination, 2013 – 2014
Mathematics 1
Form 3
Full marks: 100
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Time allowed: 1.5 hours
Answer ALL questions.
Unless otherwise specified, all working must be clearly shown.
The diagrams in this paper are not necessarily drawn to scale.
Unless otherwise specified, numerical answers should either be exact or correct to 3 significant figures.
1.
Convert 2 846 into a hexadecimal number. Show your steps.
2.
Rationalize
3.
Simplify
2
3 1
xy 2
xy  2
(3 marks)
.
(3 marks)
3
4. Simplify

and express the answer with positive indices.
(4 marks)

15 12  3 .
(4 marks)
5.
a
Express 1.083 in the form of
where a and b are positive integers.
b
6.
Simplify
7.
The mode and the median of five integers a, b, c, d and e are 4 and 7 respectively,
where a  b  c  d  e.
(a) Write down the values of a, b and c.
(b) Given that the mean of a, b, c, d and e is 6.6. Find the values of d and e.
5  1010
2.54  10  2014  1.35  10  2012
(4 marks)
and express the answer in scientific notation.
(5 marks)
(6 marks)
U
8.
In the figure, PQRS is a parallelogram and QT is the angle
bisector of PQR. QTU and USR are straight lines.
TUS = 55. Find UTS.
(4 marks)
o
55
P
T
Q
9.
S
R
S3X Class was asked how many times they visited the museum last year. The mean of the number of
visits is 2.6 and the results are shown in the table below:
Number of visits
Number of people
(a)
(b)
(c)
(d)
1
7
2
10
3
8
4
n
Find n.
Write down the median number of visits.
Write down the mode(s) number of visits.
If another class S3Y of 40 students was asked the same question and the overall mean
number of visits for two classes was 2.48, find the mean number of visits for S3Y.
(6 marks)
10. Solve
x 5
 1  2x
3
or  x  1 0 and represent the solution graphically.
11. Solve 5 x  5 x1  750 .
(6 marks)
(4 marks)
F.3 First Term Exam, 2013-2014
Mathematics 1
P.2 of 3
A
12. In the figure, ABCD is a rectangle. AC and BD intersect at E.
If DEC = 40 and AC = 10 cm, find the area of ABCD.
(5 marks)
D
o
E
40
C
B
13. A rectangular flower bed has length (2x + 1) m and breadth 5 m. Its perimeter is greater than 14 m and
its area is not greater than 65 m2.
(a) Find the range of the values of x.
(b) If the cost of fencing the flower bed is $320/m, what is the maximum cost for the fence?
(6 marks)
o
14. In the figure, ABCD is a rhombus and∠ABC = 65 .
BC is produced to E such that CD = DE.
AE and CD intersect at F.
(a) Find ∠CDE.
A
65
F
o
B
(b) Find ∠DAE.
(c) Is AE a perpendicular bisector of CD?
15. Evaluate
D
E
C
Explain your answer.
(7 marks)
4n  4n1
.
4 n 2
(4 marks)
16. (a) Factorize x 3  8 .
(b) Hence, or otherwise, factorize x 3  3x  2 .
(5 marks)
17. The bacteria in a sample grows at a rate of r% per hour. At the beginning of the experiment, the
number of bacteria in the sample was 20 000. Assuming that the bacteria did not die during the
experiment.
(a) Express the number of bacteria in terms of r after 2 hours.
(b) Accidentally, 8 000 bacteria were added in the sample after 1 hour. As a result, there were
64 000 bacteria after two hours. Find the value of r.
(7 marks)
18. In the figure, ABC is a triangle with AC = 15 and BC = 9. AB
is produced to D such that and CD is an altitude. AD = a and
BD = b.
(a) Find the value of a2 – b2.
(b) Given that AB = 8.
(i) Find the value of a + b.
(ii) Find the value of a.
(8 marks)
(b)
15
9
B
A
Prove that SBP  QPC.
S
If SB = SR and RQ = QC, prove that PQRS is a
rectangle.
(9 marks)
END OF PAPER
****
Q
30
D
A
30
60
B
****
D
R
19. In the figure, ABCD is a rectangle. AC cuts BD at P.
SAB and BDQ are straight lines. BSP = DCQ = 30
and ABD = 60.
(a)
C
P
C
F.3 First Term Exam, 2013-2014
Answers:
1.
B1E(16)
2.
3 1
3.
8
y3
2
x3
4.
5.
9 5
13
1.08 3 
12
 3.77  10 2022
7a) a = b = 4, c = 7
7b) d = 8 and e = 10.
8.
UTS = 55
9a) n = 10
9b) median = 3
9c) mode = 2 and 4
9d) m  2.375
10. x  1
6.
1
x3
11.
12. 32.1 (cm2)
13a) 1
<x≤6
2
13b) $11 520
14a) ∠CDE = 50o
14b) 32 .5
14c) AE is not a perpendicular bisector.
15. 12
16a) x 3  8  ( x  2)( x 2  2 x  4)
x 3  3x  2  ( x  2)( x  1)2
17a) 20000 (1+ r%)2
b) r = 60.
18a) a 2  b2  144
16b)
bi) a + b = 18
bii)
a = 13
Mathematics 1
P.3 of 3