Form 2 Revision Exercise

Form 2 Revision Exercises

Form 2 Mathematics Revision Exercises 1

Section A

1 Find cosθ if cos3θ = 0.9.

2 If a : b = 2 :3 and a : c = 1 :5, find a : b :c.

3 Factorize x2 + 3ay - xy - 3ax.

4 Evaluate 0.217 × 0.252 to 3 significant figure.

5 Find the value of x in the following figure.

x

70°

60°60°

80°

6 s = ut +21

at2 . Find a when s = 100, u= 5 and t = 10.

7 Find the quotient and remainder of (x+ x2 - 9) ÷ (x - 3).

8 Simplify (x - 3)(x2 + 1) - (x3 + 2).

9 A(1 , 3), B( 2 ,4) and C(a , 0) are the vertices of triangle such that ∠ABC = 90°. Find the value of a.

10 The figure shows a circular sector of radius 10cm. Find the perimeter of the sector to 4 significant figures.

60°

10cm

11 If a = 1.3, find a3a2 + .

12 The figure shows two gears. Gear A has 16 teeth and gear B has 24 teeth. If gear A makes 24 revolutions, then how many revolutions will gear B make?

13 Make k the subject of the formula C =31

(h - 3k).

A B


Section B

14 A square ABCD of side 4cm is inscribed in a circle of centre O.

4 cm

B C

DA

O

(a) Find the radius of the circle.

(b) Find the area of the shaded part.

15 Simplify the expression 2

141 1−

+− +x

xx x( )( )

16 ABC is a triangle with AB = 8cm. D is a point on AC such that DB = 7cm and DC = 4 c m . I f A D = x cm and BC = y cm, find the values of x and y.

A

8 cm

4 cm 7 cm

D

C B

x cm

y cm

17 (a) Factorise abc - b - 1 + ac.

(b) If each interior angle of a regular n-sided polygon is 140° , find the value of n.

18 The figure shown is formed by three semi-circular arcs. If the diameters of the two smaller semi-circular arcs are 4 cm and 2 cm respectively, find

2cm4cm

(a) the perimeter of the figure;

(b) the shaded area.


19 (a) Given that abx c

xd+

−= . Find x.

(b) Make B the subject of the formula EB K

DS=

−+

2 42

.

Section C

20. A(1,6), B(3,3) and C(6,5) are the vertices of a triangle.

x

y

O

A(1,6)

B(3,3)

C(6,5)

(a) Find the lengths of AB, BC and CA.

(Give your answers in surd form i.e. in form.)

(b) Hence, or otherwise, show that AB⊥BC.

(c) Find the area of ∆ABC.

(d) Find ∠ACB.


Form 2 Mathematics Revision Exercises 2 Section A

1. How many sides has a polygon so that the sum of its interior angles is 2700° ?

2. Find x in the proportion $x : $2.2 = 2 kg : 160g .

3. Round off the number 349.49701 to 5 significant figures. 4. Find the lower limit of 2000 m which is correct to 2 significant figures. 5. Referring to Fig. A5, find the unkown k. 6. Referring to Fig. A6, the length of the minute-hand of a clock is 12 cm.

Find the area swept by the minute-hand in 16 minutes.

7. Factorize )()( xybyxa −+− .

8. Simplify mm

m125

854

2 −+

− .

9. Find the value of u from the formula uaua

x−+

=2

, when x = 5 and a = 9.

10. A car travels 35 km in 43

hour. How far will it travel in 27 min?

11. Change the suject of the formula 2=−dx

cx

to x.

12. Calculate the distance between A(3, -5) and B(6, -2).

Fig. A5

Fig. A6


13. Find the slope of the straight line joining P(-2, 3) and Q(3, -2).

14. Refferring to the Fig. A14, find b. Section B

15. The measure of an interior angle (?) of an n-sided regular

polygon is given by the formula n

)2n(180 −°=ϑ

(a) Express n in terms of ?.

(b) The Fig. B1 shows a portion of an n-sided regular polygon. Find n.

16. 4 men have enough food for 20 weeks. How long would the food last for 10 men?

17. In the Fig. B3, ABCDE is a pentagon (5-sided). Find x.

18. In the Fig. B4, Show that ∠B is a right angle.

19. Referring to Fig. B5, find the unknown k.

Fig. B5 Fig. B4

Fig. B1

Fig. A14

Fig. B3


20. Referring to Fig. B6, find the shaded area.

Section C

21. The Fig. C2 shows a retangular pentagon ABCDE and the length of each side is 21 cm. Within the pentagon, there are five arcs PQ, QR, RS, ST and TP. The centers of the arcs PQ, QR, RS, ST and TP are A, B, C, D and E respectively.

(a) Find the sum of the interior angles of the pentagon.

(b) Find the sum of the arc lengths.

(c) Find the total area of the 5 sectors (the shade region).

Fig. C2

Fig. B6


Form 2 Mathematics Revision Exercises 3 Simultaneous linear equations in two unknows and inequalities

1. Solve

(a) 2 3 4

5 6( )a b

a b+ =

− =

(b) 2 2 3 3 3 2

1 2 5 32 2

( ) ( )

( ) ( ) ( )

a b a b

a a a b

− − − =

+ − − − + =

(c) 3 2 103 5 16x yy x− = −− =

(d)

32

210

54

32

132

x y

x y

− = −

− =−

2. Sally is 4 years older than her sister Sandy. Their ages add up to 20. How old is

each of them ? [12, 8]

3. A bag contains five-dollar coins and two-dollar coins amounting to $110. If the number of two-dollar coins exceeds the number of five-dollar coins by 6, find (a) the number of each kind of coins in the bag;

(b) the ratio of the number of five-dollar coins to the number of two-dollar coins.

[14, 20, 7 : 10 ]

4. (a) Copy and complete the following tables: y = 2x + 1 2x + y + 4 = 0 x -2 0 2 x -4 -2 0 y y

(b) Draw the lines representing the given equations in the same coordinate plane.

(c) Write down the coordinates of the point of intersection of the two lines.

(d) Hence solve the simultaneous equations:

=+++=

04yx21x2y

[-3, 1, 5, 4, 0, -4] [(-1.25, -1.5)]


5. The length of a rectangle is 5 cm longer than the breadth. The perimeter is 42 cm. What are the length and the breadth of the rectangle ?

[13, 8] 6. Solve and represent the solution graphically.

(a) 6 – 3(x + 1) > 18 (b) (x + 1)2 – (x + 2)2 ≥ x

7. If the sum of two consecutive even numbers is not greater than 28, find the

greatest value of the smaller number. [14]


Answers :

Revision Ex. 1

Section A

1. 0.989 2. 2:3:10 3. (x − 3a)(x − y) 4. 0.0547

5. 90o 6. 1 7. x + 4 … 3 8. −3x2 + x − 5

9. 6 10. 30.47 cm 11. 291 12. 16

13.3

C3h −

Section B

14.(a) 22 cm (b) 8π − 16 cm2 or 9.13 cm2

15.1x

2+

16. x = 1.57, y = 5.74

17. (a) (b + 1)(ac − 1) (b) 9

18. (a) 6π cm or 18.8 cm (b) 6π cm2 or 18.8 cm2

19. (a) x = dba

c−+

(b) K4)SE(D4B 22 +−=

Section C

20. (a) 26,13,13 (c) 6.5 (d) 45o

Revision Ex. 2

Section A

1. 17 2. 27.5 3. 349.50 4. 1950 m

5. k = 2 6. 90.48 cm2 7. (a − b)(x − y) 8. 2m24

15m2 −

9. u = 4.5 10. 21 km 11. cd

cd2−

12. 4.243

13. −1 14. 15.97


Section B

15. (a) n = θ−o

o

180

360 (b) n = 12

16. 8

17. 52o

19. 3

16

20. 235.6 cm

Section C

21. (a) 540o (b) 98.96 cm (c) 519.5 cm2

Form 2 Revision Exercise

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