Page 1

STANDARD FORM 1

Round off 0.08305 correct to three significant figures. A 0.083

2

Express 0.00000007620 in standard form.

C 0.0830 A

B 0.084

D 0.0831 B

3

A B

5

4

0.08 = 500000 1.6 × 10 3 1.6 × 10 4

C D

A 0.019

C 0.020

1.6 × 10 −8

B 0.02

D 0.0200

6

3 × 10 −8 − 4 × 10 −10

C 0.0000243 D 0.00000243 B

7 Express

9.57 × 10 −3

A 0·000957

D

7.62 × 10 8

Round off 0.01998 correct to two significant figures.

A B 0.000243

7.62 ×10 6

C

7.62 × 10 −8

1.6 × 10 −7

2.43 × 10 −3 A 0.00243

7.62 × 10 −6

8 as a single number

2.96 × 10 −5 2.96 × 10 −6

Express

C 0·0957 A

0.00000392

3.92 × 10 −6

C D

2.96 × 10 −7 2.96 × 10 −8

as a single number C

392 × 10 −8


B 0·00957

D 0·957 B

9

(9.24 ×10 )

−3 2

6 × 10 − 2

A

B

10

=

1.54 × 10 −4

1.54 × 10 −1

C

D

1.42 × 10 −3

392 × 10 8

D

5.32 × 10 −7 − 3.7 × 10 −8

A

1.42 × 10 −4

3.92 × 10 6

B

4.95 × 10 −8

C

4.95 × 10 −7

1.67 × 10 −7

D

1.62 × 10 −8

NUMBER BASES 1

Convert 2178 as a number in base 2

2

Given that 26 + 20 + 111102 = N Value of N in base two , is

3

A 100011112

C 111001102

A 1011111

C 1000111

B 100111102

D 110101112

B 1001111

D 1000011

1100012 - 10112

4 Express

( )

2 5 3 + 3( 5) + 4

as a number in base five

A 100102

C 1110012

A 2345

C 23045

B 110112

D 1001102

B 20345

D 30345


5

( )

6

2 53 + 4 Express

110012 + 10112 =

as a number in base five

A 245

C 20045

A 1001002

C 11001002

B 2045

D 30045

B 110112

D 1001102

POLYGON 1

In DIAGRAM 1 , KLMP and MNOP are two rhombus. KPN is a straight line. The value of x is

2

Diagram 2 shows a pentagon ABCEF ABF is an isosceles triangle and DEF is a straight line. The value of x + y =


DIAGRAM 2

3

A 130

C 150

A .750

C .1250

B 140

D 160

B .1150

D .1350

In Diagram 3, GHJKLM is a regular hexagon. HJN and MKN are straight lines. The value of x =

4

Diagram 4 shows a rhombus PQRS. Find the value of z

DIAGRAM 3 DIAGRAM 4 A .300

C .900

A .800

C .1000

B .600

D .1200

B .900

D .1200


CIRCLES 1

In Diagram 2, LJK is a tangent to the circle JNM at J and KMN is a straight line.

2

Arc MN = Arc MJ. The value of x is

3

In Diagram 3, DCE is a tangent to the circle ABC at C. O is the centre of the circle. The arc AB is of the same length as the arc BC. The value of x is

A 150

C 350

A .250

C .650

B 250

D 650

B .400

D .1300

In diagram below, GHIj is a quadrilateral and JKL is an isosceles triangle. Find the value of x

4

Diagram below shows a hexagon PQRSTU. Find the value of x + y


A 950

C 1100

A 1320

C 3340

B 1050

D 1950

B 2570

D 5140

VARIATIONS 1

p ∝ q2 If and p = 64 is

q=3

q = 3 when

p = 36

2 , the value of q when

S If R varies directly as

and R = 10 when

S = 25, find the value of R when S = 9.

A ½

C 4

A 2

C 5

B 3

D 6

B 3

D 6


3

M∝ Given that

P T2

4

E∝

1

F G Given that and E = of G when E = 4 and

. and M = 4 when

P = 6 and T = 3, express M in terms of P and T.

1 3

when F = 12 and G = 16, find the value

F = 8.

M= A B

6P T2

M= C

M = 3PT 2

M=

D

5

3P T2 PT 2 4

It is given that y varies directly as the square root of x and y = 6 when x = 9. Calculate the value of x when y = 10. A 5

A

B

6

1 4

C 2

1 2

D 4

P varies directly as the cube of q and inversely as r. The relationship between P, q and r is

B 10

P∝

q3 r

A C 15

D 25 P∝ B

q

P∝

C

1 3 1

r2

D

q3 r

q3 P∝ 2 r


7

Table 1 shows some values of variables m, n and h such that m varies directly as the square root of n and inversely as h.

8

Table shows the relationship between three variables w, t and h.

Table 1

w=

m

3

3

n

36

81

h

10

15

Given that

t h

w

t

h

2

2

4

4

m

9

calculate the value of m.

Find the relationship between m, n and h. m=

A m= B

9

5 n h

n h

m=

3 n h

A 3

C 12

m=

3n 2 h

B 6

D 18

C

D

It is given that y varies directly as xm and y = 8 when x =1. Calculate the value of m when y = 72 and x = 3. A 1

10

Based on the table below, if q varies inversely as the square of p. Find the reaction between q and p

B 2

q = 12 p 2

q=

A C

12 p2


C 3

D 4

q= B

MATRICES

1. – + = ..85..34. 21..86

A. ..154

B. ..912

C. ..513

D. ..1315

2. Given that = ( 18 ), find the value of x. ..x3..

3 2 p 4

q= D

3 4 p2


. . .. . . .1x

A. 9

B. 4

C. -3

D. -6

3. = .. . . ..


. . 4315 .. . . .. . .. 42

A. .. . . .. . .. 106

B. .. .


. .. . .. 2812

C. .. . . .. . . . . 166410

D. .. . . .. .


... 1612210

4. Given the matrix equation 2 + k = , find the value of h+ k ..h4..21..813

A. 4

B. 8

C. 10

D. 11


5. 2 - = .. . . .. . . 6413 .. . . .. . . .4101

A. .. . . ..


. . 41024

B. .. . . .. . . 4734

C. .. . . .. . . 2525

D. ..


. . .. . . 8925

6. Given = , calculate the value of k ..5k.. . . .. . . .103k ..524

A. 8

B. 3


C. -1

D. -12

7. Given the matrix equation 3 - k = , ..h2..34..1526.

find the value of h – k

A. 5

B. 9

C. 25

D. 45


8. = .. . . .. . . .2041 .. . . .. . . .35

A. .. . . .. . ..


6567

B. ... . .. . .. 60125

C. ..65

D. .. . . .. . .. 67


9. Given that 2 + = , calculate the value of k. .. . . .. . . k3 .. . . .. . . .24 .. . . .. . . k310


A. -2

B. -1

C. 1

D. 2

10. Given = , calculate the value of x and y. .. . . .. . .. x4 ..5y..


. . .. . . . . 112020

A. x = -, y = -5 51

B. x = , y = -5 51

C. x = 5, y = -

D. x = 5, y =


ANSWER MATRICES

1. C

2. A

3. C

4. A

5. C

6. D


7. A

8. D

9. A

10. A


TOPICS:BEARING

1 North

B

580

A DIAGRAM 1


In Diagram 1, point A and point B are two points on a horizontal ground. The bearing of point B from point A is

A 032ยบ

B 058 ยบ

C 232 ยบ

D 302 ยบ


2 North

V

620


W DIAGRAM 2

In Diagram 2, point V and point W are two points on a horizontal ground. The bearing

of point V from point W is

A 0620

B 1520

C 2320

D 2980


3 North

L

DIAGRAM 3

530

K

In Diagram 3 , point K and point L are two points on horizontal ground. What


is the bearing of point L from point K

A 0370

B 0530

C 3070

D 3530

4 Diagram 4 shows the position of point P and Q.


North

North

1450

P DIAGRAM 4


Q

Find the bearing of point P from point Q

A 0350

B 0550

C 1250

D 2150


5. Point E , F and G lie on a horizontal ground. Point F is due north of point G.

The bearing of point F from point E is 0750 and the bearing of point E from

point G is 3050. Which of the following diagrams shows the location of point

E, F and G ?

A North B North

F

F

E


G

EG

C North D North

G

F


E

F

E

G

6. In Diagram 5, points M, P, Q and R are on a horizontal plane.

DIAGRAM 5

M is due south of R. Given that MP = MQ and the bearing of P from M is


2500. Find the bearing of Q from M.

A 3300

B 3000

C 2500

D 1500


7

Q DIAGRAM 6

720

1250

P

R


Diagram 6 shows three point, P,Q and R, on a horizontal ground. The bearing

of point R from point Q is

A 0720

B 1080

C 1270

D 2350


8 In Diagram 7, P, Q and R are points on a horizontal plane with PQ = PR.

P is due north of Q and the bearing of R from P is 126째 .


DIAGRAM 7

The bearing of Q from R is

A 063째


B 243째

C 270째

D 306째


9. P

250 North

Q DIAGRAM 8

M


Diagram 8 shows three points, M, P and Q, on a horizontal ground. If the bearing of point M from point P is 1280, find the bearing of point P from point Q

A 025째

B 155째

C 283째

D 355째


10

North

p

DIAGRAM 9

R


Q

Diagram 9 shows point P, Q and R which lie on a level ground. If the bearing of point Q from point P is 1050 and PQ = QR, then the bearing of point R from point Q is

A 075째

B 105째

C 255째

D 305째


ANSWER BEARING

1

B


2

A

3

C

4

A

5


B

6

A

7

C

8

B


9

C

10

C


TOPICS: PROBABILITY

1.A factory employs 45 workers. Eighteen of them are men. A worker is picked at

random from the factory. What is the probability of picking a man?

A 92

B 154

C 52


D 53

1. Set M = {8, 12, 23, 39, 42, 51, 61, 73, 88}. An element is chosen at random from set M. What is the probability of choosing a prime number?

A 91

B 103


C 31

D 73

2. A box contains 30 coloured marbles. 12 of them are green marbles. A marble is picked at random from the box. What is the probability that it is not a green marble?

A 85


B 83

C 53


D 41

3. P is the event of rolling a dice . Which of the following represents the possible

outcomes of the event of obtaining a prime number or a number that is greater

than 2?

A { 3, 5}

B { 2, 3, 5}


C { 3, 4, 5, 6}

D {2, 3, 4, 5, 6}

4. Given that box A contains 6 cards numbered from 2 to 7 and box B contains 2

white cards and 4 black cards. What is the probability of obtaining an even

number and a white card?

A 61


B 51

C 31

D 21

5. There are eight boys in a group of students. If a student is picked at random

From the group, the probability of picking a boy is 1/5. It is given that the


Number of girls who wear glasses in the group is 4. If a student is picked at random from the group, what is the probability of picking a girl who does not wear glasses?

A 101

B 32


C 107

D 109

6. A box contains 25 blue balls and several yellow balls. If a ball is drawn at random

From the box, the probability of drawing a blue ball is 5/8. If x black balls are

Added and a ball is drawn, then the probability of drawing a black ball is 1/6.

The value of x is


A5

B8

C 15

D 20


7. Wan has 75 bags of graded eggs. 30 bags are grade P eggs and the rest are

grade B And grade C eggs. If a bag is picked at random, the probability of picking a bag of Grade B eggs is 1/3. Calculate the probability of picking a bag of grade C eggs.

A 154

B


3516

C 43

D 52

8. A jar contains 1 yellow, 1 red and 2 blue marbles. 2 marbles are chosen at

random From the jar one after another with replacement. Find the probability that the first marble chosen is red and the second one is blue.


A B C D 10. The table shows the probabilities of the customers choosing brands X, Y and Z. 91 81 61 41

Brand

X

Y

Z

Probability


11/24

3/8

1/6

If a survey is carried out on 1200 customers, find the number of customers who

Choose brand Y or Z.


A 550

B 650

C 680

D 700


ANSWER PROBABILITY

1. C 2C 3C 4D 5A 6C 7B 8A 9B 10 B


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