Homework
Properties of Circles
1. The diagram shows a circle with centre O. TB is a tangent to the circle at B, OB intersects
AC at D, BC / TO and BTO 32 o . Find
(a) OAC , and
(b) BDC .
2. In the diagram, UT is the tangent to the circle, centre O, at T.
Practice
Properties of Circles
1. In the figure, O is the centre of the circle. A, B, C and D lie on the circumference of the
circle. Given that the line BC is parallel to the line AD, BAC 30 o and OCD 46 o ,
calculate
(a) ABC , and
(b) ADC .
2. In the fi
Homework
Linear Inequalities
1. A wallet contains 10-cent and 50-cent coins. If it contains 25 coins altogether, find the
greatest number of 10-cent coins such that the total value of the coins exceeds $5.
2. (a) State the largest prime number k such that
Practice
Linear Inequalities
1. If x is an integer, solve the inequality 8 < 2x 3 13.
2. (a) If x is an integer and 2x 1 < 10 < 5x + 3, find all the values of x.
(b) If x is not an integer, represent the solution set on a number line.
3. Solve the inequal
Indices
1. (i) Evaluate m + n if 3m = n3 = 27.
(ii) Evaluate n if xn xn = 1/x.
2. Express each of the following as a power of 25.
(i)
(iv)
(vii)
625
3125
1/5
(ii)
(v)
(viii)
5
1/25
5
(iii)
(vi)
(ix)
125
1/625
50 250
3. Write the value of 0.06250.75, witho
Homework
Functions and Graphs
1. Express each of the following equations in the form a(x + b)2 + c. Hence, sketch each of
the following graphs, stating clearly the coordinates of the points of the x-intercept and yintercept (if any) and the coordinates of
Practice
Functions and Graphs
1. Express each of the following equations in the form a(x + b)2 + c. Hence, sketch each of
the following graphs, stating clearly the coordinates of the points of the x-intercept and yintercept (if any) and the coordinates of
Homework
Fractional Equations and Problem Sums involving Quadratic Equations
x3 4x 7
x 1 , giving your answers correct to 4 significant
x2 7x 5
figures where necessary.
1. Solve the equation
2. Two positive numbers differ by 4 and the reciprocals of thei
Practice
Fractional Equations and Problem Sums involving Quadratic Equations
1. Solve the following equations.
(a)
1
1
5
a 10 25 a 42
(b)
3x 1 2 x 1
1
x 1
x 1
(c)
4
5
6
c 3 c 4 c 7
(d)
10 1
3 0
x2 x
2. The sides of a right-angled triangle are (x 3) cm, (
Homework
Cumulative Frequency Distribution
1. A test is given to two classes, A and B. The test scores for the two classes are shown in the
following box-and-whisker plots.
Which class achieves the better results and which class has more variability? Givi
Practice
Cumulative Frequency Distribution
1. Answer the whole of this question on a sheet of graph paper.
The table below shows the frequency distribution of the weekly pocket money (x) of 60
boys in a village.
x ($)
Frequency
5 < x 10
7
10 < x 15
5
15 <
Homework
Coordinate Geometry
1. Find the equation of the line passing through the point (2, 5) with gradient 2. Hence, find
the coordinates of the point where this line cuts the y-axis.
2. The line 3y = kx + 9 passes through a point A on the y-axis, where
Practice
Coordinate Geometry
1. (a) Find the equation of a line, l, which makes an intercept of 3a on the x-axis and 5a on
the y-axis.
(b) The line, l, passes through the point (a2, 1). Find the numerical values of a.
2. Given that P(0.8, 2) and Q(1.5, 5)
Homework
Congruent and Similar Triangles, Area and Volume of Similar Figures
1. In the diagram, AC = BD, AD = BC and BDA 34 o .
(a) Show that triangles ABC and BAD are congruent and find ACB .
(b) Name another pair of congruent triangles.
2. In the diagra
Practice
Congruent and Similar Triangles, Area and Volume of Similar Figures
1. (a) Find a pair of similar triangles from the figure and prove that they are similar.
(b) Calculate the length of CD.
2. The ratio of the volumes of two cubes is 5 : 4. If the
Sec 2N(A) Mathematics
End-of-Year Examination Paper 2
1. Simplify
(a)
15b 2
4a 3 b
8a
45ab 5
[2]
4
p 21
(b) p 3 p 2 9
2. (a) If
[3]
3a 5b 2
7a
, find the value of
.
4a b
5
b
(b) Simplify
3 xy 15 y x 2 5 x
.
2 x 2 11x 5
[3]
[3]
3. During the annual primar
Sec 2 N(A) Mathematics
End-of-Year Examination Paper 1
1. Expand and simplify each of the following.
(a) (a + 2b + c)(a 2b c)
[2]
(b) (5k 2)(2k + 3) 2(5k 3)(k + 1)
[2]
2. Factorise the following completely.
9pq2 3r + 27rq2 p
[2]
3. Without the use of a ca
Sample Mid-year Examination Paper 2
1. Simplify
/50
3m 2 4 11m
.
8 6m 2 26m
[4]
2. Expand the following.
(a) (7x 3)2
[2]
(b) (ab + 8)2
[2]
3. Simplify the following.
(a)
5
2
x 3 x
[2]
3
(b) 2 y 2 y 1
[2]
4. In the following table, F is inversely proportio
Homework
Arc Length and Sector Area
1. (a) Convert 120o to radians
(i)
in terms of , and
(ii)
correct to 3 significant figures.
(b) Convert 79o to radians
(i)
in terms of , and
(ii)
correct to 3 significant figures.
(c) Express 13.75 radians in terms of .
Practice
Arc Length and Sector Area
1. (a) Covert 50o to radians
(i)
in terms of , and
(ii)
correct to 3 significant figures.
(b) Convert 1.6 radians to degrees, correct to 1 decimal place.
(c) Convert 2.2 radians to degrees, minutes and seconds. Give you
Homework
Applications of Trigonometry
1. The figure shows a building TF, where F is the foot of the building. Given that the angle
of elevation of the top of the tower, T, from B, is 50o, TAF = 40o and BF = 45 m,
calculate the
(a) height of the tower, and
Practice
Applications of Trigonometry
1. The shadow of a pole when the angle of elevation of the sun is 32o is 5 m longer than the
shadow of the pole when the angle of elevation of the sun is 48o. What is the length of the
longer shadow of the pole?
D
32o
Homework
Cartesian Coordinates and Graphs of Linear Equations
1. (a) State the coordinates of the points marked on the Cartesian plane below.
(b) On the same Cartesian plane, plot the following points.
(i)
F(0, 2)
(ii)
G(6, 5)
(iii) H(5, 0)
(iv)
I(4, 1)
(
Homework
Polygons and Geometrical Constructions
1. Find the value of the unknown in each of the following figures.
2. Find the value of the unknown in each of the following figures.
Page 1 of 4
3. Find the value of the unknown angles x and y in each of th
Practice
Cartesian Coordinates and Graphs of Linear Equations
1. (a) State the coordinates of the points marked on the Cartesian plane below.
(b) On the same Cartesian plane, plot the following points.
(i)
A(0, 3)
(ii)
B(5, 0)
(iii) C(4, 2)
(iv)
D(3, 3)
(
Homework
Probability
1. There are 12 oranges, 14 apples and 16 pears. A fruit is picked at random from the basket.
Find the probability that the fruit picked is
(a) an orange,
(b) an apple,
(c) not a pear.
2. Mr Chua has 8 red ties, 10 blue ties and 22 gr
Practice
Probability
1. A box contains 2 red balls and 3 green balls. A ball is chosen at random from the box.
(a) Given that A is the event that a green ball is chosen, state the number of favourable
outcomes of A.
(b) Find the probability that a green b
Homework
Algebraic Fractions, Equations and Inequalities
1. Simplify the following.
64 y
(a) 16 xy
m
(b)
3m 3
50ab
(c)
35a 2 b
81a 2 b 3 c
(d)
27 ab 2 c 3
(e)
6 x y
26 x y
(f)
18a b 4 b 4
2
8a 2 b 4
3
2. Simplify the following.
pq
2r
(a) 16 p
(b)
9
3k