www.jimmymaths.com

jimmyling@jimmymaths.com

1 | P a g e

SEC 2 MID-YEAR MOCK EXAMINATION

SOLUTIONS

1 Janice jogs 1260m in 6 minutes. Express his average speed in kilometres per hour. [2]

Avg. speed = 1260 m ÷ 6 min

6 = 1.26km ÷ h

60

= 12.6km / h

2 The formula used in an experiment is given by E =w

w x.

a) Find the value of E when w = 30 and x = 18. [1]

b) Express w in terms of E and x. [1]

a)

b)

E =

30E =

30 18

30E =

48

5E =

8

w

w x

E =

E =

E E =

E = E

E = E

1 E = E

E

1 E

w

w x

w x w

w x w

w w x

w w x

w x

xw

www.jimmymaths.com

jimmyling@jimmymaths.com

2 | P a g e

3 Expand and simplify the following.

a) -6 2 +3 +6x y x y xy [2]

b) 9 2 1 4 5x x x [2]

a)

b)

4 Solve the following equations.

a) 11 7

7 11

x

x

[2]

b) 229

3n n [2]

a)

b)

2 2

2 2

- 6 2 + 3 + 6 2 3 12 18 6

2 3 18

x y x y xy x xy xy y xy

x xy y

2

2

2

9 2 1 4 5 9 8 10 4 5

9 8 10 4 5

5 3 8

x x x x x x x

x x x x

x x

2

2

11 7

7 11

7 7 121

14 49 121

14 72 0

18 4 0

18 4

x

x

x x

x x

x x

x x

x or x

2

2

2

2 9

3

3 2 27

27 3 2 0

3 1 9 2 0

1 2

3 9

n n

n n

n n

n n

n or n

www.jimmymaths.com

jimmyling@jimmymaths.com

3 | P a g e

5 Using the elimination method, solve the simultaneous equations [3]

3 13,

1.3 4

x y

x y

3 13 3 13 1

1 4 3 12 23 4

x y y x

x yx y

1 3:

3 9 39 3

3 2 :

3 3 9 4 39 12

0 5 27

5 27

2 5

5

2. 5 into 1 ,

5

23 5 13

5

13

5

2 1 5 , 3

5 5

y x

y y x x

x

x

x

Sub x

y

y

When x y

www.jimmymaths.com

jimmyling@jimmymaths.com

4 | P a g e

6 Factorise each of the following completely.

a) 2

7 81m [2]

b) 2 2ac bc bd ad [2]

a)

b)

7 Express 2

1 1a

a a

as a fraction in its simplest form. [2]

2 2 2

2

2

1 1 1

1

1

a a a

a a a a

a a

a

a

8 Without using a calculator, evaluate the following.

a) 2108 . [1]

b) 896 904 [1]

a)

b)

27 81 7 9 7 9

2 16

m m m

m m

2 2 2

2

2

ac bc bd ad c a b d b a

c a b d a b

a b c d

22

2 2

108 100 8

100 2 100 8 8

10000 1600 64

11664

2 2

896 904 900 4 900 4

900 4

810000 16

809984

www.jimmymaths.com

jimmyling@jimmymaths.com

5 | P a g e

9 Given that 2 1

2 1

ax

a

and

1

3 2y

a

, express x in terms of y. [4]

2 1

2 1

2 1 2 1

2 2 1

2 2 1

2 2 1

1

2 2

ax

a

x a a

ax x a

ax a x

a x x

xa

x

1

3 2

3 2 1

3 2 1

3 1 2

1 2

3

ya

y a

ay y

ay y

ya

y

1 1 2

2 2 3

3 1 1 2 2 2

3 3 2 2 4 4

3 2 4 2 4 3

3 2 4 2 4 3

2 4 3

3 2 4

2 7

2

2 7

2

x y

x y

y x y x

y xy x xy y

xy x xy y y

x y y y y

y yx

y y

yx

y

yx

y

www.jimmymaths.com

jimmyling@jimmymaths.com

6 | P a g e

10 The resistance of a wire of constant length is inversely proportional to the square of its

diameter. If a copper wire of radius 1 mm and length 1 km has a resistance of 23 ohms, find

the resistance of another copper wire of diameter 2.3 mm and length 1 km. [2]

Let R be the resistance of the wire

Let d be the diameter of the wire

2

2

2

2 , 23 ,

232

92

92

kR

d

When d mm R ohms

k

k

Rd

2

2

92

2.3 ,

92

2.3

17.4 3 .

Rd

When d mm

R

ohms s f

www.jimmymaths.com

jimmyling@jimmymaths.com

7 | P a g e

11 Map A is drawn to a scale of 1 cm to 2.5 km while map B is drawn to a scale of 3 cm to 4

km. A forest is represented by an area of 72 cm2 on map A. Find the exact area of the forest

represented on map B. [3]

2 2

2 2

( )

1 : 2.5

( )

1 : 2.5

1 : 6.25

Map Scale A

cm km

Area Scale A

cm km

cm km

22

2

2

( )

72 6.25

1

450

Actual area of the forest Map A

cmkm

cm

km

2 2

2 2

( )

3 : 4

( )

3 : 4

9 :16

Map Scale B

cm km

Area Scale B

cm km

cm km

22

2

2

( )

450 9

16

253.125

Map area of the forest Map B

kmcm

km

cm

www.jimmymaths.com

jimmyling@jimmymaths.com

8 | P a g e

12 The diagram is the speed-time graph of a car. The car retarded uniformly from a speed of

36 m/s to a speed of 24 m/s in a time of 40 seconds. It is then brought uniformly to rest

after a further 10 seconds. Calculate

(a) the retardation of the car during the first 40 seconds. [1]

(b) the total distance traveled by the car for the whole journey. [2]

(c) the speed of the car when the time is 18 seconds. [2]

(a) 24 36

40

20.3 /m s

Retardation = 0.3 m/s2

(b) 1 1

(36 24)(40) (10)(24)2 2

= 1320 m

(c) Let the speed be x

360.3

18

36 5.4

30.6 m/s

x

x

x

40 50 Time(s)

Speed(m/s)

www.jimmymaths.com

jimmyling@jimmymaths.com

9 | P a g e

13 The exchange rate between the sterling pound (£) and the Swiss franc (₣) on a particular day

is £1 = ₣1.4425. Find

i) the number of complete Swiss francs that can be exchanged for £825. [1]

£825

£1₣1.4425 = ₣1190

ii) the number of complete sterling pounds that can be exchanged for ₣1600. [1]

1600

1.4425£1 £1109

14 A car travels the first 20 km of its journey in 24 minutes, the next 40 km at an average speed

of 60 km/h and the remaining 1

272

km at an average speed of 66 km/h. Find the average

speed of the car for its entire journey. [3]

Time taken for the 2nd part of journey

40 60 /

2

3

km km h

h

Time taken for the last part of journey

127 66 /

2

5

12

km km h

h

Average speed of the entire journey

120 40 27

224 2 5

60 3 12

8858 / 59.0 /

89

km km km

h h h

km h or km h

www.jimmymaths.com

jimmyling@jimmymaths.com

10 | P a g e

15 Tap A takes 5 minutes to fill a bathtub and Tap B takes 10 minutes to fill the same bathtub.

Pipe C can empty the bathtub in 12 minutes 30 seconds. Find the difference between the

time taken to fill up the bathtub if Pipe C is in use when Tap A is turned on, and the time

taken to fill up the bathtub if Pipe C is in use when Tap B is turned on. Leave your answer

in min and sec. [3]

In 1 min,

11 5

5

of ba

T

thtub

ap A

1

1 10 10

Ta

of bat u

B

b

p

ht

1 21 12

2 25

of b

P

a

ipe C

thtub

1 2

5 25

3

25

31

25

18 m

3

i

n

Time taken

Pipe C with Tap A

1 2

10 25

1

50

11

50

50min

P

Timetaken

ipe C with Tap B

150min 8 min

3

241 min

3

41 min 40 sec

Difference

www.jimmymaths.com

jimmyling@jimmymaths.com

11 | P a g e

16 Andrew deposits $150 000 in a bank that pays simple interest at a rate of 0.25 % per annum.

If the interest rate increases by x% every 6 months, she will receive $150 more every year.

Find the value of x. [2]

$150000 0.25 1

100

$375

0.25% % 2

0.25 2 %

$150000 0.25 2 1

100

Simple Interest

New Interest Rate x

x

xNew Simple Interest

$ 375 3000

$ 375 3000 $375 $150

3000 150

0.05

x

x

x

x

www.jimmymaths.com

jimmyling@jimmymaths.com

12 | P a g e

17 The diagram shows the curve y x p x q , where p q . The curve cuts the x-axis

at the points A (-4, 0) and B (3, 0) and the y-axis at point C.

a) Write down the value of p and of q. [2]

. ( 4,0),

4

4 0

At pt A

x

x

. (3,0),

3

3 0

At pt B

x

x

( 3)( 4)y x x

Since p < q,

3 4p and q

b) Find the area of triangle ABC. [1]

, 0

(0 3)(0 4)

12

. (0,12)

On y axis x

y

y

pt C

2

1 7 12

2

42

Area of triange ABC

units