SEC 2 MID-YEAR MOCK EXAMINATION - Jimmy Maths - Math ...€¦ · SEC 2 MID-YEAR MOCK EXAMINATION...
Transcript of SEC 2 MID-YEAR MOCK EXAMINATION - Jimmy Maths - Math ...€¦ · SEC 2 MID-YEAR MOCK EXAMINATION...
www.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
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
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
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
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
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
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
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
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
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
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
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