DEPARTMENT OF MATHEMATICS
FYE Mock Test for Secondary 1 Accelerated
Academic Year 2024-2025
Marking scheme
Thursday
15 May 2025
13:15 – 14:45 (1 hr 30 min)
75.
25
50
75
8
⑪
2
SECTION A ( 25 marks)
1 The numbers 168 and 324, written as products of their prime factors are
168 = 23 × 3 × 7
324 = 2! × 3" .
(a) Find the √324 , expressing your answer in index notation.
2xz3
…......................................... [1]
(b) Determine the smallest integer that must be multiplied to 168 to make it a perfect square.
2x3X7
42
…......................................... [1]
(c) Write down the HCF of 168 and 324.
12
…......................................... [1]
22x3
2 A rectangular table is 34.5 m by 21.8 m rounded to 1 decimal place.
Find its minimum perimeter.
34, 45 + 34 45 + 21 75
.
,
+ 21 75
.
112 4
.
…........................................ m [3]
3 Estimate 386.71 × 0.02049 by rounding off each given value to one significant figure.
400X0
,
02
8
…......................................... [2]
4 A restaurant offers a 20% discount and charges 10% service charge and 7% of GST on the total
order. Calculate the total marked price of a customer’s order if the final bill was $272.50.
2)2 50
.
+
80
289 40
$ .......................................... [3]
.
2425_FYE_MOCKTEST_S1A_MATH_QP
11
3
5 (a)
Factorise.
$! % ! "#! ! !
3a
a
-4
?
3
-
12a
2
2a
-
8
(3a + 2)(a
-
4)
….......................................... [2]
(b)
Expand and simplify.
#!(! ! "" ) ! !(!" + ! )
5a2-30ab-gab- a?
4a2
39ab
…..........................................
[3]
-
6 Solve.
"! ! # "
=
!+! !
3(2x
6x
6x
-
-
-
5)
=
15
=
2x
=
4X
=
2(x + 3)
2x + 6
15 + 6
21
x = 5 255 25
x = ....................................... [3]
.
z
.
2425_FYE_MOCKTEST_S1A_MATH_QP
4
7 In an n-sided regular polygon, the size of an interior angle is seven times that of the size of an
exterior angle. Find the value of n.
X + 1x
n=
360 +
n=
16
180
=
8X =
180
X
22 5
=
.
(exterior 4)
22 5
.
16
n = ........................................ [3]
8 A swimming pool is 65 m long and 30 m wide.
It is 2.5 m deep at the shallow end and 7 m deep at the other end, as shown.
Find the volume of water in the pool when it is full.
65 m
30 m
2 51
.
7m
Base area (trapezium)
Volume
=
v
=
308
.
25
9262
2x65
=
.
x
30
5
m
NOT TO
SCALE
2.5
65
x
m
(7 + 2 5)
.
=
308
.
75
9262 5
,
...................................... m³ [3]
6
2425_FYE_MOCKTEST_S1A_MATH_QP
5
SECTION B ( 50 marks)
1 t is inversely proportional to the square of d.
The difference in the values of t when d = 16 and when d = 24 is 10.
Write down an equation connecting t and d.
t
t
t
k
=
-
Je
=
t
2
t
=
=k
=
1
-
256
=
10
2304
k
=
10
=
=
4608
546
=
4608
+d
..….......................................
[3]
=
2 In the figure, ABC, DBE, and CEF are straight lines.
∠ABD = 92°, ∠ACE = 50°, ∠CDE = 42° and ∠AED = ∠AEF,
L
NOT TO SCALE
88
↓
920
-XX
S
·
30
Find,
(a) ∠AED,
180
-
50
142 : 2
-
=
92
=
142
71
7)
..…....................................... ° [2]
(b) ∠CAE.
100
-
88
-
71
=
21
2
..…....................................... ° [1]
T
2425_FYE_MOCKTEST_S1A_MATH_QP
6
3 John deposited some amount of money to his bank account that gives a simple interest of 5% per year.
If he earned $360 in 3 years, calculate the total amount of money in his bank account after 3 years.
360 = 3 =
120 +
120
70
=
2400
+ 360
=
$2760
2400
2760
$ ..…....................................... [3]
4 The number of male workers in factory ABC from year 2000 to 2003 is shown in the table below.
(a) Calculate the percentage increase in the number of workers in the factory from year 2000 to year
2003.
8 700
-
7500
X
100
7500
16
..…....................................... % [2]
(b) The ratio of the number of male workers to the number of female workers in the factory in year
2003 was 15:11. Find the number of female workers in the factory in 2003.
154
=
In
=
560
8700
x
11
580
6380
..…....................................... [2]
5 The diagram on the right shows a semi-circle ABCO with center at O and radius of 6.5 cm, AB = 5
cm and
BC = 12 cm. If the right-angle triangle is cut-out and discarded, find the area of the remaining shape.
Give your answer to 2 significant figures.
Triangle 5x12xt
=
semi-circle
21
.
=
ExX 6 52
.
125π
-
NOT TO
SCALE
30
=
30 =
=
21 125 i
.
36 3661
.
...
36
Area = ..…....................................... cm2 [3]
To
2425_FYE_MOCKTEST_S1A_MATH_QP
7
6 A composite solid is formed by joining two right circular cones, A and B, of the same radius 10 cm,
at their bases as shown. The length of the composite solid is 72 cm.
NOT TO SCALE
10 cm
cone B
cone A
72 cm
(a) Given that the ratio of the height of cone A to the height of cone B is 3 : 5, find the slant height
of cone A and cone B.
3u + zu
slantheight A
72
=
zu 72
=
In
height A
height B
=
=
=
=
=
9
Start height B
=
27
=
45
+ 272
5829
N02
=
28 792
...
,
102 + 452
46
.
=
25
0977...
28 , 8
slant height of cone A = ……..... cm
1
46 cm [4]
slant height of cone B = .............
.
(b) Calculate the total surface area of the composite solid.
#
(10)(29) + # (10) (5)
=
2352 741
,
...
2350
(35f)
….................................. cm² [3]
7
2425_FYE_MOCKTEST_S1A_MATH_QP
1500 m
8
7 A construction company was awarded a contract to build a 1.5 km tunnel in 50 working days.
#
The company hired 48 workers who worked 7! hours a day.
After working for 24 days, 540 m of the tunnel was completed.
The company decided to employ 16 more workers to speed up the job by 6 days.
Find the number of hours per day that each of the workers must work to complete the job.
24 X 7 5
=
.
~
1500
-
540
50-6
-
~
=
44-24
48 + 16
=
=
180 hrs
WH
960 m
48(180)
=
44 days
k
days
20
=
=
64H
RK
540K
=
H
16
=
=
960(16)
240
240 +
20
=
12
64 workers
12
..…….................................... hr [4]
8 In the diagram, ABCD is a rectangle.
=
1 + 4 + 16
2
-
3+ 1
=
NOT TO SCALE
4+3 +5
⑫
14 3 +
=
10
(a) Form a pair of simultaneous equations and solve for the values of x and y.
y
+ 2x + 16
2x +
by +5
-x
4y
-
5x +
-
=
30y
34y
y
-
=
(x
=
x
-
-
6
=
=
=
D5X
3y + 10
-
-
4y
b 5(x + by
3y + 13
-
=
=
6
8)
X + G() = 8
40
X
34
X= 2
=
8
-
6
1
I
2
x =……………… y =………………… [4]
(b) Calculate the area of rectangle ABCD.
21x12
252
…………………………………… cm2 [2]
2425_FYE_MOCKTEST_S1A_MATH_QP
To
9
9 The diagram shows three lines, Line 1, Line 2 and Line 3, on a grid.
q units
6 units
o-----------
O
1
(a)
·
-
(2 , 1)
Write down the gradient and the equation of Line 1.
undefined
gradient = ............................ [1]
X
=
2
….......................................... [1]
(b)
Work out the equation of Line 2.
m
y
(c)
==
=
EX
y
….......................................... [2]
-
=
2
+ 2
Find the coordinates of the intersection point of Line 1 and Line 2.
21
(…............... , …................ ) [1]
(d)
Calculate the area of the triangle bounded by Line 1, Line 2 and Line 3.
* x9X6
27
…................................ units² [3]
T
2425_FYE_MOCKTEST_S1A_MATH_QP
10
10 Ezra made a series of diagram using dots and lines. The first three figures he made are as shown.
(a) The number of dots and the number of smallest right-angle triangles formed to make each figure is
shown in the table below. Complete the table for the row of Figure 4.
1
,
40
32)14
25
[1]
(b) The formula for the nth term of the number of dots is, Dn = (n+ 1)2. Find the number of dots for
Figure 35.
(35 + 1)2
1296
…................................ dots [2]
(c) Find, in terms of n , a formula for the nth term of the number of smallest right-angle triangles, Tn.
2
,
8
,
18
,
32
Yo Yt
In 2
=
v
44
?
zn
Tn = …................................ [2]
5
2425_FYE_MOCKTEST_S1A_MATH_QP
11
11 The figure shows a rectangle ABCD. Given that AB = (8x – 2) cm and AD = (4x – 2) cm.
8X
-
2(3x 2)
-
2
F
4x
4X- 2
4x 2
-
8x
-
2
(a) Given that the triangle AEB is an isosceles triangle where the sides AE = 2(3x – 2) cm and BE =
(4x + 7) cm. Form an equation with the given information to find the value of x.
2(3X 2) = 4X + 7
-
(x
-
4
=
4X + 7
2x =
11
X= 5 5
.
5 5
.
x = …................................ cm [2]
(b) Using the value of x in (a), calculate the area of the shaded region of the figure, giving your answer
to 2 significant figures.
4(5 5)
-
.
8 (5 5)
.
-
2 = 20
2
=
42
20x42
=
& x20x42
840
-
240
=
220
420
=
(rectangle)
(triangle)
420
420
Area = …................................ cm2 [2]
END OF PAPER
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2425_FYE_MOCKTEST_S1A_MATH_QP