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) Nam
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.
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
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 compl
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 signi
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) Conver
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 an
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. Wha
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 numer
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
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
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 dia
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 OC
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 exceed
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
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)
1
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-i
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-i
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 p
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
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 be
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
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. Fin
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
Homework
Data Analysis
1. Samuel threw a fair die a few times and recorded the number shown on the die after each
throw. He recorded the results using a dot diagram as shown below.
(a) How many times
Practice
Probability
1. What is the probability of throwing a 6 with two dice?
2. What is the probability of throwing a 12 with three dice?
3. Three dice are thrown. What is the probability that not a