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Form 3 Mathematics Revision Questions and Answers Set 3
Simplify the following without using table or a calculator:
log
27
–
log
9
log
3
(1m 32s)
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1.
In what ratio should grade P of tea costing sh.450 per kg be mixed with grade Q of tea costing sh.350 per kg so that a profit of 10% is made by selling the mixture at sh. 451 per kg?
2.
In the figure below, line CD = 4cm, line DT=8cm and BT = 6cm. At and CT are straight lines meeting at point T. Find the value of y
3.
Find the value of X in the equation
log
3
x
–
4
log
x
3
=
-
3
4.
Quantity Q partly varies as quantity R and partly varies inversely as the square of R. Given that Q=3 when R=1 and Q=5 when
R
=
1
2
i).Find the equation connecting Q and R ii) Find the value of Q when
R
=
3
2
5.
Find the radius and centre of the circle whose equation is
3
x
2
+
3
y
2
–
12
x
+
18
y
–
9
=
0
6.
a).Find the inverse of the matrix
(
4
3
3
5
)
b). Hence solve the simultaneous equations using matrix method 4x + 3y = 6 5y + 3x – 5 = 0
7.
a) Expand
(
1
-
2
x
)
6
in ascending powers of x up to
x
3
b) Hence evaluate
(
1.02
)
6
to 4 d.p
8.
The measurements of the radius and height of a cylinder are given as 8cm and 9.5cm respectively. Calculate the percentage error in the volume of the cylinder.
9.
Simplify and rationalize the denominator giving your answer in the form a + b v ?? where a,b and c are constants
11
7
-
√
3
-
5
7
+
√
3
10.
Make t the subject of the formula
x
=
3
√
h
(
t
-
h
)
t
11.
The third and fifth terms of an arithmetic progression are 7 and -7 respectively i).Determine the first and the common difference ii) The sum of the first 14 terms
12.
The mass of a solid sphere of radius 0.14m is 7.89kg, find its density in g/
c
m
3
Take
π
=
22
7
13.
A basketball team play 10 matches in a tournament. The following are scores in each match. 9, 15, 17, 16, 7, 20, 21, 15, 10, 12. Determine: (a) The mode. (b) The median.
14.
Given x = 13.4cm and y=4.3cm. Calculate the percentage error in
x
y
correct to 4 decimal points
15.
Evaluate without using Mathematical tables or a calculator.
2
log
5
-
1
2
log
16
+
2
log
40
16.
Solve for x given that the following is a singular matrix
(
1
2
x
x
-
3
)
17.
Without using mathematical tables or calculators express in surd form and simplify
1
+
cos
30
1
-
sin
60
18.
Peter operates a printing firm and the cost of printing a book is partly constant and partly varies as the number as pages. If a book has 200 pages, the cost in sh 400 and if it has 100 pages, the cost is sh 240. Find the cost of printing a book with 400 pages.
19.
The figure below is a velocity – time graph for a car. (Not drawn to scale). a) Find the total distance traveled by the car (b) Calculate the deceleration of the car.
20.
Evaluate the value of x in
81
x
+
1
+
3
4
x
=
246
21.
A straight line passes through A (-2,1) and B(2,-K). This line is perpendicular to the line 3y+2x=5. Determine the value of k.
22.
Two dogs which are regarded to be similar have length of their tails in the ratio 4:3. If the bigger dog has a tail 64cm long; find the length of the tail of the smaller dog.
23.
Simplify the expression
4
y
2
-
x
2
2
x
2
-
x
y
-
6
y
2
24.
The position vectors of points P and Q are P=2i + 3j – k and Q=3i – 2j +2k respectively. Find magnitude of PQ correct to 4 significant figures
25.
Find the minimum possible perimeter of a regular hexagon whose side measures 12.6cm to one decimal place.
26.
Find y if
log
2
y
–
2
=
log
2
92
27.
Solve the following equation using completing the square method:
x
2
-
8
x
–
30
=
0
28.
Simplify the following without using table or a calculator:
log
27
–
log
9
log
3
29.
A positive two-digit number is such that the product of its digits is 24. When the digits are reversed, the number formed is greater than the original number by 18. Find the number.
30.
Round off 395.184 to four significant figures.
31.
Truncate to three decimal place: 17.3489
32.
The average lap time for 3 athletes in a long distance race is 36 seconds, 40 seconds and 48 seconds respectively. If they all start the race at the same time, find the number of times the slowest runner will have been overlapped by the fastest at the time they all cross the starting point together again.
33.
The mean of five numbers is 20. The mean of the first three numbers is 16. The fifth number is greater than the fourth by 8. Find the fifth number.
34.
Show that the points P(3, 4), Q(4, 3) and R(1, 6) are collinear.
35.
A solid metal cylinder with radius 7cm and height 5cm is melted down and recast into a spherical ball. Calculate to 1 decimal place the surface area of this ball.
36.
In a class there are thrice as many boys as girls
1
3
of the boys are from poor families while
1
5
of the girls are from rich families. Find the percentage number of pupils from rich families in the class.
37.
Paul bought a refrigerator on hire purchase by paying monthly instalments of Ksh. 2000 per month for 40 months and a deposit of Ksh. 12,000. If this amounted to an increase of 25% of the original cost of the refrigerator, what was the cash price of the refrigerator?
38.
Find all the integral values of x which satisfy the inequality
3
(
1
+
x
)
<
5
x
–
11
<
x
+
45
39.
A school decided to make a beautiful picnic site to be used by students and teachers as a resting point. The site was designed to be triangular in shape measuring 40 metres, 60 metres and 80 metres. Calculate the area of the picnic site. (Answer correct to 1 d.p)
40.
A regular n-sided polygon has its interior angle equal to 4 times its exterior. Find n.
41.
Solve for x given that
5
2
x
+
2
–
20
×
5
2
x
=
625
42.
A straight line through the point A(2,1) and B(4,m) is perpendicular to the line whose equation is 3y=5–2x, Determine the value of m.
43.
Okoth deposited some money at 10% compound interest compounded annually. How long will it take to double the amount to the nearest year?
44.
Chebet has 5 brown chicken and 3 black ones.She picks two of them for slaughter at random, one after the other.What is the probability that the two are of different colors.
45.
Solve the equation
x
+
1
2
-
x
-
3
3
=
4
46.
Find the equation of a line which passes through (-1,-4) and is perpendicular to the line y+2x-4=0
47.
Simplify
12
x
2
-
16
x
20
-
11
x
-
3
x
2
48.
A lorry travelling at an average speed of 64km/hr left station at 7:05 am. A car left the same station at 8:50 am and caught up with the lorry at 10:20am.Find the average speed of the car.
49.
Given that Z =
a
2
-
x
2
a
w
-
x
w
express x in terms of a,z and w.
50.
Find the distance between the centre O of a circle whose equation is
2
x
2
+
2
y
2
+
6
x
+
10
y
+
7
=
0
, and a point B(-4,1)
51.
Without using tables or calculators, evaluate
log
27
1
2
+
log
8
1
2
-
log
125
1
2
log
6
-
log
5
52.
Find the acute angle x in the following equation.
2
sin
(
2
x
-
30
)
=
√
3
53.
Determine the value x for which the matrix below is singular.
(
2
x
12
6
x
)
54.
Use binomial expansion to expand and simplify
(
x
-
2
y
)
5
up to the third term. Hence use the expansion to evaluate
(
2.02
)
5
.
55.
The length and the width of a rectangular paper were measured as 18cm and 12 cm to the nearest 1mm, find the percentage error in the area of the paper, correct to 2 significant figures.
56.
Without using a mathematical table or a calculator, evaluate
3
√
675
×
135
√
81
×
25
57.
The image of point A(1, 2) after a translation is AI (-1, 2), what are the coordinates of a point P whose image PI is (-3, -3)after this translation.
58.
There are two bags A and B.Bag A has 4 white balls and 6 red balls. Bag B has 2 white balls and 3 red balls. Each bag has an equal chance of being picked.If a bag is selected randomly and 2 balls picked with replacement in bag A and without replacement in bag B. Find the probability that: a).They are both white. b).They are of different colors. c).At least one ball is red. d).None of the balls is
59.
Find the values of a, b and c. Given that
3
2
-
√
18
+
5
2
+
√
18
=
a
+
b
√
c
60.
Make A the subject of the formulae
log
10
(
A
–
B
)
–
log
10
(
4
+
K
)
÷
log
b
b
2
=
1
.
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