Form 2 Math

Penerbitan Pelangi Sdn. Bhd. 80

Chapter 1 Directed Numbers

1. Find the value of each of the following.(a) 12 + (14) (25)(b) 25 (+10) + 24

2. Calculate the value of each of the following.(a) 18 (2) 6(b) 21 (7) (4)

3. Solve

(a) 57

+ 1 914 2, (b) 3

8 1 25 2.

4. Solve each of the following.(a) 0.6 + (2.7)(b) 5.3 1.9 (3.4)

5. Solve

(a) 310

56

12 14 2,(b) 13 + 4.24 3

4.

6. Find the value of each of the following and give your answer in decimal.

(a) 1 14

+ (2.6) + 10

(b) 9.6 1 35 2 8 7. Find the value of each of the following and express

your answer as a single fraction in its lowest term.

(a) 1 12

1 35 2 1.3(b) 4 11 14 2 + 12 13 2

8. Find the value of each of the following and give your answer in decimal.

(a) 5.4 25

(1.45)

(b) 9 ( 0.4) + 0.8 34

9. Evaluate 10 (5)(a) , 7 + 2 0.08 (0.2)(b) . 0.004

10. Solve(a) 12 (3) 6 + (14),(b) (25 + 11) (7).

Chapter 2 Squares, Square Roots, Cubes and Cube Roots

1. Evaluate each of the following without using a calculator.

(a) 12 12 22

(b) 13 13 22

2. List all the perfect squares between 20 and 140.

3. Evaluate

(a) AB2 ABB18 , (b) AB5 ABB20 . 4. Find the perimeter of a square of area 144 cm2.

5. Find the value of each of the following.

(a) 0.33 (b) 11 12 23

6. Find the value of

(a) 3ABBBBB 8125 , (b) 3ABBBB1 6164 . 7. Find the value of 52 3ABBBBB 8125 . 8. Solve

(a) (2)3 + AB4 , (b) 3ABBB27 32. 9. Solve

(a) ABBB144 0.32 3ABBBB0.008 , (b) 1 13 2

2

ABB49 1 12 23. 10. The total surface area of a cube is 54 cm2. Find the

volume of the cube, in cm3.

Chapter 3 Algebraic Expressions II

1. Simplify 6m 4(2 + m).

2. 5(h 3k) 5k 1 =

3. Simplify

(a) 38

a (20bc),

(b) 25

(5m 10p + 15q).

Question Bank

Penerbitan Pelangi Sdn. Bhd.81

4. If x = 3, y = 2 and z = 5, find the value of 2x + y2 3z.

5. If p = 1, q = 2 and r = 4, evaluate p2 + 2q

2pr.

6. In the algebraic term 4p2qr, state the coefficient of(a) p2, (b) pqr.

7. Simplify

(a) 23

(18a2b), (b) 3de (2ef ).

8. Simplify

(a) 10hk25k

, (b) 49pq14qr

.

9. Simplify each of the following.

(a) (4mn)(5pq)

12 (b)

(12x2y)(yz3)

4xyz

10. Simplify 2(3m 4p) 25

(10m 15p).

Chapter 4 Linear Equations

1. Given that 3x 5 = 10, find the value of x.

2. Given that 8 + m5

= 2, find the value of m.

3. Solve the equation 5k 4 = 14 4k.

4. If e 54

= 1, find the value of e.

5. If 2m3

= 1 12

, find the value of m.

6. Given that 6y 3 = 5 + 2y, find the value of y.

7. (a) Solve m2

4 = 5.

(b) If 7 n3

= 4, find the value of n.

8. Solve the following equations.

(a) m + 14

= 2

(b) n + 25

= n4

9. Solve the following equations.(a) 5 3x = 14(b) 4y + 6 = 2(y + 6)

10. (a) Solve p 5

4 =

p2

.

(b) If 53

q 1 = 9, find the value of q.

Chapter 5 Ratios, Rates and Proportions

1. Find the ratio of(a) 45 minutes to 2 hours,(b) 0.8 kg to 250 g.

2. S R

4 cm

10 cmP Q

The diagram shows a rectangle PQRS. Find the ratio of its length to its perimeter.

3. A sum of RMx is divided between Faizal and Ghafar in the ratio 3 : 8. If Faizal receives RM225, find the value of x.

4. Simplify the following ratios.(a) 5 : 25 : 10 (b) 2.4 : 4 : 1.2

5. Given that p : q : r = 1 : 5 : 3, find the ratio of(a) p + q : r, (b) p : q r.

6. Given that a : b : c = 3 : 5 : 2 and a = 15, find the value of b + c.

7. If p : q : r = 4 : 1 : 3 and p + q + r = 40, find the value of q.

8. Given that x : y = 8 : 3 and y : z = 6 : 5, find the ratio x : y : z.

9. The lengths of the sides of a triangle are in the ratio 2 : 5 : 6. If its perimeter is 78 cm, find the length of its longest side.

10. There are 58 marbles in a box. 18 of them are red, 24 of them are yellow and the rest are green. Find the ratio of the number of yellow marbles to the number of green marbles.

Chapter 6 Pythagoras Theorem

1. 1.6 cm

1.2 cmx cm

The diagram shows a right-angled triangle. Find the value of x.


2.

7 cm

10 cmx cm

The diagram shows a right-angled triangle. Find the value of x, give your answer correct to two decimal places.

3. 14 cm

12 cm

9 cm

The diagram shows a trapezium. Calculate the perimeter, in cm, of the trapezium.

4. 6 cm

10 cmP

Q R

S

T

In the diagram, PQRT is a square. Calculate the area, in cm2, of the whole figure.

5.

17 cm

6 cm

4 cm

P

Q

R S T

In the diagram, PQR and RST are straight lines. Find the length of ST.

6.

y cm

5 cm

34 cm

The diagram shows a right-angled triangle. Find the value of y.

7. J M

K L

12 cm

8 cm

The diagram shows a trapezium JKLM. Given that JL = 13 cm, find the area, in cm2, of the trapezium.

8.

Q R S

T

P

10 cm4 cm

5 cm

In the diagram, PTR and QRS are straight lines. T is the midpoint of PR. Calculate the length of QS.

Chapter 7 Geometrical Constructions

Set squares and protractors are not allowed to be used for all questions.

1. Construct a triangle PQR such that PQ = 3 cm and QR = 2 cm. Start your construction using the straight line PR given below.

P R

2. The diagram below shows a straight line KL. Construct a triangle JKL in which JKL = 45 and JLK = 60.

K L

3. The diagram below shows a straight line PQ. Construct a perpendicular bisector to line PQ.

P Q

4. The diagram below shows a straight line PR. Construct a line that passes through point Q and is perpendicular to PR.

P Q R


5. Construct PQR = 120 in the diagram below.

Q R

6. By using a pair of compasses and a ruler, construct a triangle PQR such that PQR = 30 and PR = 4 cm. Start your construction by using the line QR given below.

Q R

7. The diagram below shows a triangle PQR. Start with the triangle given, construct(a) the parallelogram PQRS,(b) QT, the bisector of PQR, where T lies on the

line PR.

Q R

P

8. Start with the straight line PQ given below, construct(a) the triangle PQR, such that PR = 3 cm and

QR = 4.5 cm,(b) the perpendicular to PQ passing through R.

P Q

Chapter 8 Coordinates

1. Calculate the distance between the points (5, 4) and (8, 4).

2. y

x

Q

P0

2

2 2 44

2

4

The diagram shows a Cartesian plane. Based on the diagram, state the coordinates of the midpoint of line PQ.

3. The diagram below shows a Cartesian plane.(a) State the coordinates of point P based on the

diagram.(b) Mark the point (4, 2) with Q on the

diagram.

y

x

P

0

2

2 2 4 6

2

4

4. Find the distance between P(5, 3) and Q(5, 9).

5. Given points R(2, 4) and S(4, 10). Find the coordinates of the midpoint of straight line RS.

6. Given points E(9, 6) and F(9, 4). Find the distance of EF.

7. y

x

RQ

P

0 2 4 6 8

2

6

4

On the Cartesian plane above, points P, Q and R are three of the vertices of the parallelogram PQRS. State the coordinates of point S.

8. Given points H(3, 6) and K(3, 10), calculate the coordinates of the midpoint of straight line HK.

9. y

x

M

G(2, 0)

H(8, 8)

0

The diagram shows a Cartesian plane. M is the midpoint of straight line GH. Find (a) the coordinates of point M,(b) the length of GH.

10. Given points P(x, 4) and Q(5, y). M(3, 1) is the midpoint of the straight line PQ. Find the values of x and y.


Chapter 9 Loci in Two Dimensions

1. Construct the locus of a moving point which is equidistant from the points E and F.

E F

2. Construct the locus of a moving point which is equidistant from the lines PQ and QR.

P

Q

R

3. In the diagram below, GH is a straight line of length 3 cm. On the same diagram,(a) construct the locus of a moving point P, such

that PG = 2 cm,(b) construct the locus of a moving point Q, such

that GQ = QH.(c) mark all the points of intersection between

the two loci with the symbol .

G H3 cm

4. In the diagram below, PQ is a straight line of length 5 cm. On the same diagram,(a) construct the locus of a moving point X,

which is 2 cm from the line PQ,(b) construct the locus of a moving point Y, such

that Y is equidistant from P and Q,(c) mark all the points of intersection between

the locus of X and the locus of Y with the symbol .

P Q5 cm

5. The given diagram shows an equilateral triangle, PQR. On the same diagram,(a) construct the locus of a moving point X, such

that XP = XR,(b) construct the locus of a moving point Y, such

that Y is equidistant from PR and PQ,(c) mark the point of intersection between the

two loci with the symbol .

P

Q

R

6. The diagram below shows a rectangle ABCD. E is the midpoint of AD. On the same diagram,(a) construct the locus of a moving point X, such

that EX = 2.5 cm,(b) construct the locus of a moving point Y, such

that AY = 3 cm,(c) mark the point of intersection between the


A DE

3 cm

5 cmB C

7. The diagram below shows a straight line PQR. Q is the midpoint of PR. On the same diagram,(a) construct the locus of a moving point X, such

that X is 2 cm from the line PQR,(b) construct the locus of a moving point Y, such

that Y is 2.5 cm from Q,(c) mark all the points of intersection between

the two loci with the symbol .

P Q R

8. The diagram below shows a triangle JKL. P and Q are points moving inside the triangle. On the same diagram,(a) construct the locus of P, such that PJ = PK,(b) construct the locus of Q, such that

JQ = 3 cm,(c) mark the point of intersection between the


J

L

K5 cm


9. A

B C

2 cm

D

EF

The diagram shows a rectangle ABDE. X is a point moving within the rectangle. Describe completely the locus of X in each of the following cases.(a) AX = XE.(b) X is equidistant from AB and BC.(c) X is 2 cm from F.

10. The diagram below shows a rectangle PQRS. X and Y are points moving inside the rectangle. On the same diagram,(a) construct the locus of X, such that X is 2 cm

from line PQ,(b) construct the locus of Y, such that Y is

equidistant from PQ and PS,(c) mark the point of intersection between the


4 cm

5 cm

P S

RQ

Chapter 10 Circles

1.

12021 cm

P

QO

The diagram shows a sector centred O. Find the

length of arc PQ. 1Use = 227 2 2.

60

A B

r cm

O

The diagram shows a sector with centre O. Given

that the length of arc AB is 3 23

cm, find the value

of r. 1Use = 227 2

3.

7 cm

P

O Qx

The diagram shows a sector with centre O. Given that the perimeter of the sector is 25 cm, find the

value of x. 1Use = 227 2 4.

15 cm

O

P

Q

R

In the diagram, OPQR is a sector with centre O. OPR is an equilateral triangle. Find the length of

arc PQR. 1Use = 227 2 5.

72 5 cm

E F

O The diagram shows a sector centred O. Calculate

the area of the sector. 1Use = 227 2 6.

120

O Q S

P

R

In the diagram, OPQ and ORS are two sectors with a common centre, O. Given that OQ = QS = 7 cm, calculate the area of the shaded region.

1Use = 227 2 7.

7 cmP O Q

The diagram shows two semicircles with diameters

PQ and OQ. Using = 227

, calculate the perimeter

of the shaded region.


8. Q R

SOP

14 cm

In the diagram, OPQR is a square and ORS is a quadrant with centre O. POS is a straight line. Calculate the area of the whole diagram.

1Use = 227 2 9. 10 cm

J

K L M

N

The diagram shows a rectangle JKMN. L is the midpoint of KM. JKL and LMN are two quadrants inside the rectangle. Calculate the perimeter of the shaded region. (Use = 3.14)

10.

Q

P

R S7 cm 12 cm

In the diagram, PQR is a quadrant centred R. QRS is a straight line. Calculate the area of the whole

diagram. 1Use = 227 2

Chapter 11 Transformations

1.

024 2

2

4

4

y

x

P

P

In the diagram, P is the image of P under a translation 1h 2k . Find the values of h and k.

2. The diagram below shows a quadrilateral drawn on a Cartesian plane. On the diagram, draw the image of the quadrilateral under a reflection in the y-axis.

024 2

2

4

4

y

x

3. The diagram below is drawn on a square grid. On the grid provided, draw the image of triangle M under a reflection in the line PQ.

P

Q

M

4. The diagram below is drawn on a square grid. On the grid provided, draw the image of triangle ABC under a clockwise rotation of 90 about point P.

P

C

BA

5.

0

2

2 4 6 8

4

6

y

x

P

R

PR

Q

Q

In the diagram, triangle PQR is the image of triangle PQR under an anticlockwise rotation of 90. State the coordinates of the centre of rotation.


6.

0

2

2 4 6

4

6

y

x

T

The diagram shows a Cartesian plane. State the coordinates of the image of point T under a

translation 1323 .

7.

0 2

2

2

2

4

4

4

4

y

x

K

The diagram above is drawn on a Cartesian plane. State the coordinates of the image of point K under a clockwise rotation of 90 about the point (0, 1).

8.

0 2

2

2

2

4

4

4

4

y

x

P

P

In the diagram above, triangle P is the image of triangle P under a certain transformation. Describe completely the transformation.

9.

0 2

2

2

2

4

4

4

4

y

x

P

The diagram shows a Cartesian plane. State the coordinates of the image of point P under (a) a reflection in the x-axis,(b) a reflection in the y-axis.

10.

0 2

2

2

2

4

4 6

4

y

x

P

P Q

The diagram above is drawn on a Cartesian plane.Given that P is the image of P under a certain reflection.(a) State the axis of reflection.(b) Find the coordinates of the image of point Q

under the same reflection.

Chapter 12 Solid Geometry II

1. The total surface area of a cube is 150 cm2. Find its volume, in cm3.

2. A cuboid is 2.4 m long, 1.5 m wide and 0.8 m high. Find its total surface area, in m2.

3. Find the surface area of a sphere with a radius of 10 cm. (Use = 3.142)

4.

PM

Q R6 cmS

V

The diagram shows a right pyramid with a square base PQRS. M is the midpoint of PQ. Given that VM = 8 cm, calculate the total surface area of the pyramid.

5. The area of the curved surface of a cone is 220 cm2. If the radius of its base is 5 cm, find the length of

its slant height. 1Use = 227 2


6.

4 cm

The diagram shows a right pyramid with a square base of sides 3 cm. Draw the net of the pyramid.

7.

15 cm

7 cm

The diagram shows a cylinder. Calculate the total

surface area of the cylinder. 1Use = 227 2 8. The surface area of a sphere is 256 cm2. Find the

radius of the sphere.

9.

8 cm

10 cm

10 cm

15 cm

4 cm

The diagram shows a right prism. Find the total surface area of the prism.

10.

14 cm

5 cm

The diagram shows a solid made of a hemisphere and a cylinder. Find the total surface area of the

solid. 1Use = 227 2

Chapter 13 Statistics

1. 32 16 25 28 25 2428 28 24 16 28 16

The data shows the temperature, in C, of twelve towns of a certain day. State the temperature with(a) the highest frequency,(b) the lowest frequency.

2. Area PArea QArea Rrepresents 25 trees

The pictogram shows the number of trees planted in three areas in a certain month. Find the total number of trees planted in these three areas.

3. JanuaryFebruary

Marchrepresents 30 calculators

The incomplete pictogram shows the number of calculators sold in a book shop in three months. If the total number of calculators sold is 390, how many symbols of must be drawn for the month of February?

4.

0 Mon. Tue. Wed.Month

Thu. Fri.

100200300

Prof

it (R

M)

400500600

The line graph shows the profit made by a cafeteria in five days. Find the difference between the highest and the lowest profit made in the five days.

5.

0 Jan. Feb. Mar.Month

Apr. May

100200300

Expe

nditu

re (R

M)

400500600

The line graph shows the monthly expenditure of Daisy. Based on the line graph, calculate the mean monthly expenditure, in RM.


6.

02468

1012141618

Jan. Feb. Mar.

Month

Apr. May June

Num

ber o

f stu

dent

s

The bar chart shows the number of students in a class who scored grade A in six Mathematics monthly tests. Find the greatest increase between two consecutive months.

7.

0Jan. Feb. Mar.

MonthApr.

100200300

Num

ber o

f car

s

400500600

The bar chart shows the monthly production of cars in a factory for the first four months of a year.Find the ratio of the number of cars produced in January to the total number of cars produced in the four months.

8. Factory AFactory BFactory C

represents 40 malesrepresents 40 females

The pictogram shows the number of male and female workers in three factories. Find the total number of female workers in the three factories.

9.

0

we

ek

1

we

ek

2

we

ek

3

we

ek

4

1020304050607080

Num

ber o

f boo

ks re

ad

The line graph shows the number of books read by a group of students in four weeks. Find the percentage increase of number of books read in Week 4 as compared to the number of books read in Week 1.

10. The incomplete bar chart below shows the daily saving of Joey in five days. If the total saving in the five days is RM24, complete the bar chart below for Thursday.

0123456

Savin

g (R

M)

Mon. Tue. Wed.Day

Thu. Fri.

Form 2 Math

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