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Form 4 Mathematics Paper 2 Holiday Revision Questions and Answers
Given that a = 5i +4j, b=3i -2j and c = 7i +10j.Find the parameters
λ
and µ such that µa +
λ
b = c
(4m 5s)
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1.
Three horses Daisy, Everest and Fiona are competing for this year’s grand prix race. The probability that they will qualify for the grand prix is
2
3
,
2
5
and
5
6
respectively. Using a tree diagram, find the probability that only one horse qualify for the Grand prix.
2.
a).Expand and simplify
(
1
-
3
x
)
4
up to the term in
x
4
. b).Use the above result to calculate to 5 decimal places the value of
(
0.97
)
4
.
3.
High grade tea costs sh 240 per kg while low grade tea costs sh 144 per kg. A trader mixed the two grades to make a blend which he sold at sh 252 per kg. In so doing he made a profit of 40%.Find the ratio in which the trader mixed the two grades of tea.
4.
Wanja bought 240kg of rice from a wholesaler. She later sold 200kg of the rice and received as much as she had spent in buying all the rice. If she sold all the rice at the same price, calculate her percentage profit.
5.
The sum of the first two terms of a geometric progression is 30.Given that the common ratio is
1
2
, determine the first term of the progression.
6.
Use matrix method to solve the simultaneous equations 2s -3t = 7 3s- 2t = 8
7.
A quantity F is partly constant and partly varies as the cube of E. When E =1,F= 23 and when E =2,F= 44.Find the value of F when E =5
8.
Solve the equation
3
-
x
x
+
2
=
2
3
x
9.
The expression
36
x
2
-
84
x
+
k
is a perfect. Find the value of k.
10.
A large estate is represented by a rectangle 8mm long and 6mm wide on a map whose scale is1:200000.Determine the actual area of the estate in hectares.
11.
The cash price of the radio is sh 2800.The radio can be bought by hire purchase which requires a deposit of sh.1020, followed by 5 equal monthly installments of sh.440 each. Calculate the percentage increase in the hire purchase value over the cash price.
12.
The gradient function of a curve is given by
d
y
d
x
=
3
x
-
6
.Determine a).The equation of the curve given that it passes through the point (0,7). b).The coordinates of the turning point of the curve.
13.
Without using mathematical tables or a calculator. evaluate
3
log
10
5
+
log
10
64
–
log
10
8
14.
Make T the subject of the formula
F
=
L
2
+
P
T
Q
-
4
T
15.
Use matrix method to solve the simultaneous equations. 3p – 4q =2 5p +3q =13
16.
The equation of a curve is
y
=
3
x
2
-
12
x
+
7
.Detremine the coordinates of the turning point of the curve.
17.
Given the column vectors p =
(
-
1
2
1
)
,
q
=
(
2
-
4
8
)
,
r
=
(
5
-
10
-
5
)
and that vector a =#3p - 1/2 q + 2/5 r, express a as a column vector and hence find its magnitude to 3 significant figures.
18.
A stationary observer on a platform notices that a train completely passes him in 10.8 seconds. If the speed of the train is 25 km/h, find the length of the train in meters.
19.
Quantity p partly varies as the square of x and partly varies as x. When x=3, p=48 and when x=5,p=110.Determine a).the equation that connects p and x b).the value of p when x =6
20.
Under a transformation whose matrix is
(
k
-
1
2
-
k
k
)
A figure whose area is
4.5
c
m
2
is mapped on a figure whose area is
54
c
m
2
.Find two possible values of k.
21.
a) Given the matrix A=
(
3
1
2
4
)
,Find
A
2
b) Find matrix B such that
A
2
=
B
–
2
A
.
22.
A bus travelled from Nairobi to Mombasa a distance of 500km and back. The average speed for outward journey was 75km/h and the average speed on the return journey was 50km/h. Calculate the average speed for the round trip.
23.
The velocity v metres per second of an projectile after a time t seconds is given by the equation
v
=
3
t
2
–
4
t
+
9
Determine a).the acceleration when t = 1.5 seconds. b).the total distance moved by the projectile between time t =1 and t =4 seconds.
24.
Make r the subject of the formula.
s
=
√
r
2
+
t
r
t
25.
Two quantities X and Y are such that X partly varies as the square of Y and partly varies as inversely as the Y. When Y =2, X = 68 and when Y = 3,X = 58. a).Write down an equation that relates X and Y. b).Find the value of X when Y = 4.
26.
Solve the equation
2
(
x
+
1
)
5
-
5
-
2
x
6
=
3
x
-
2
4
27.
Solve the following inequalities and represent the solution on a single number line
x
-
3
≤
3
x
+
1
.
12
x
-
x
>
2
x
+
3
28.
The sum of the first n terms of the series 5+15+25+35….is 845.Find the value of n
29.
Given that a = 5i +4j, b=3i -2j and c = 7i +10j.Find the parameters
λ
and µ such that µa +
λ
b = c
30.
Find the value of
log
5
89.54
31.
Given that
a
2
=
b
5
=
c
6
,find the value of
2
a
+
3
b
-
c
3
a
-
b
+
2
c
32.
Olando drove from his home to a town 120 km away at the legal speed limit. If he had travelled 30km/h faster he would have reached there 40 minutes earlier. Determine the legal speed limit.
33.
In a certain town the African population exceeds the Asian population by 50%.The Asian population on the other hand exceeds the European population by 20%.By what percentage does the African population exceed the European population?
34.
A quantity Q is partly constant and partly varies as the square of e. When e =2, Q =560 and when e = 3,Q = 510.Find a).an equation which connects Q and e. b).the value of Q when e = 5.
35.
It would Kamau working alone 30 days,Wanyonyi 40 days and Matano 60 days to complete digging a shamba.All the three start working together but after five days Kamau falls sick and cannot continue to. Determine how many more days it will take wanyonyi and matano to complete the job.
36.
The area of triangle ABC is
14.5
c
m
2
.This triangle is mapped onto a triangle A’B’C’ by a transformation given by the matrix
M
=
(
(
3
,
-
3
)
,
(
5
-
4
)
)
Find the determinant of the M and hence calculate the area of the triangle A’B’C’
37.
The high quality Kencoffee is a mixture of clean Arabica coffee and clean robusta coffee in the ratio 1:3 by mass. Clean Arabica coffee costs sh 180 per kg while the clean robusta coffee costs sh 120 per kg.Calculate the percentage profit made when Ken-coffee is sold at sh 162 per kg.
38.
Anita deposited sh 50000 in a bank that paid compound interest at the rate of 15% per annum. At the end of the third year she withdrew all her money and bought three shares from a land buying society at sh 24500 each. Determine how much money she was left with.
39.
The cost of one magazine is sh m and the cost of one newspaper is sh n .Alice spent sh 395 to buy 3 magazines and 7 newspapers while Joyce spent sh 275 to buy 2 magazines and 5 newspapers. a).Form two simultaneous equations to represent this information. b).Use the matrix method to solve the above simultaneous equations.
40.
Solve for x in the equation
log
10
(
3
x
+
4
)
-
log
10
(
3
-
x
)
=
1
41.
A minor arc of a circle subtends an angle of
70
0
at the centre of the circle. If the length of the arc is 22cm, calculate the radius of the circle
(
t
a
k
e
π
=
22
7
)
42.
A curve passes through the point (0,9) and its gradient function is given by
d
y
d
x
=
4
x
+
8
Determine a).the equation of the curve b).the coordinates of the turning points of the curve.
43.
For the last three years the value of a car has been depreciating at a uniform rate of 10 percent per annum. If the present value of the car is sh 328050, calculate the initial value of the car at the beginning of the 3 year period.
44.
The radius of a sphere is increased by 10%.Find the percentage increase in the volume of the sphere.
45.
The number of buffaloes in a game reserve was originally 1.5 million. This number doubled after every 5 years. What was the number of buffaloes in the game reserve at the end of
10
t
h
year.
46.
Make d the subject of the formula
S
=
n
2
(
2
a
+
(
n
-
1
)
d
)
47.
A quantity F varies as E and partly varies as the square of E.When E = 2,F = 36 and when E = 3,F= 69.Find a).an equation connecting F and E. b).the value of F when E= 4.
48.
Find the value of
log
2
73.45
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