Class X
Mathematics
Instruction:





Shaba Middle Secondary School
Paro
Midterm Examination – 2014
Writing Time: 3 hours
Maximum Marks: 100
Do not write for the first 15 minutes. This time is to be spent on reading the questions,
you will be given Three Hours to answer all the questions.
In this paper there are three sections: Section A, Section B and Section C. You are
expected to answer All the questions in Section A and Section B. Under section c, there
are 8 questions (question numbers 14 – 21 ). Each question has two parts A and B.
Attempt either A or B from each question. The intended marks for each question or its
parts are stated in the brackets.
Remember to write quickly but neatly.
Do not leave the examination hall before you have made sure that you have answered
all the required number of questions.
The use of calculator (fx-82/fx-100) is allowed without memory.
Section A
Answer all the questions
Question 1
[2 X 10 = 20]
Choose the most appropriate answer from each question and write it in the
answer sheet provided.
a) Suppose you were to multiply a 4 X 3 matrix by a 3 X 3 matrix, the
dimension of the resulting matrix will be
 4X3
 8X6
 3X4
 3X3
b) How many two stop over trips are there from B to C?
A
B
C
D
1
3
2
4
c) You invest Nu.35000 in a bank saving account that earns 6% p. a.
compounded annually. Determine the value of the investment after one
year.
 Nu. 32900
 Nu.2100
 Nu. 37100
 Nu.210000
Page 1 of 8
d) Horgola buys stock at a discount of 15%. Each share has a face value of
Nu.100. How many shares can she buy with Nu.59, 500?
 595
 892
 396
 700
e) Identify the correct inequality for the graph given below
 y> x–2
 Y˂ x–2
 y≤ x–2
 y≥ x–2
f) Determine the point of intersection of the pair of lines
y  2 x  7 and
y  5x  4
 ( –9, – 1)
 (–1, – 9)
 (1,– 9)
 ( – 1 ,9)
g) Determine the number of significant figures in the number 0.03400
3
5
4
6
h) If you have a cup with a dimension as given in the diagram, the capacity of
the cup in liters is
 4.848L
21 cm
 4.448L
 4.884L
14 cm
 4.484L
i) A salesperson has a total sale of Nu.120 000. If he is awarded a commission
amount of Nu.6000, determine the rate of commission?
 15%
 5%
 20%
 10%
Page 2 of 8
j) Which of the following matrices can be multiplied?
1
1
A= 
0

1
0 0 0
1 0 0
0 0 1

0 0 2
2
4
B= 
1

2
1 0 0 2 
C = 2 1 1 0
1 0 0 0 
3
5
0

5
1 5 5
D = 0 0 1
1 1 0
 AXD
 BXD
 AXC
 AXB
Section B (32 Marks)
Answer all questions
Question 2
Given matrices A and B, calculate each
a) 2A – 3B
b) A – 2B
 4 0  5
A = 3 2 3  B =
0 2 4 
[3 marks]
2 0 1 
1  6 4 


0 4 4
Question 3
[3 marks]
Deki bought 300 shares that had a face value of NU.100 for Nu.85 each. She sold the
shares for Nu.340 each. What was her percent profit?
Question 4
[2 marks]
Simplify
45X 8
40
Question 5
[3 marks]
Suppose you made a table of values. The inputs are the name of the students in your
class and the outputs are their marks in mathematics. Would the table represent a
function? Justify your decision.
Page 3 of 8
Question 6
Write down the inequality for the graph given below
[3 marks]
Question 7
[3 marks]
Determine the values of x and y in the diagram given below. Show your work.
Y0
(2y+40)0
x0
90 0
Question 8
[2 marks]
Round off each numbers as indicated
a) 7.938 to 2 significant figures
b) 0.0675 to 1 significant figure
c) 6924 to 2 significant figures
d) 5.390 X 104 to 5 significant figures
Question 9
[2 marks]
Without measuring, predict which of these shapes with the same perimeter would have
the greatest area. Explain.
A
B
D
C
Page 4 of 8
Question 10
[3 marks]
Determine the total surface area of the cylinder with a diameter of 36 cm and a height
of 36 cm?
Question 11
a) Create an adjacency matrix for this digraph
[1 Mark]
A
B
C
b) Use the matrix to find out the number of one stop over trips between each pair of
vertices.
[2 marks]
Question 12
An amount of Nu.12000 is invested in a saving account earning 5% interest p. a
compounded semi annually. How much money will be in the account at the end of the
first year?
[3 marks]
Question 13
[2 marks]
Simplify
96  k  2 6
Section C [48 Marks]
Under this section, there are 8 questions (question number 14 – 21). Each question has two parts A
and B. Attempt either A or B from each question
Question 14 (A)
(Use graph paper for this question)
[6 marks]
The coordinates of the three vertices of a triangle are listed in this matrix.
0 10
i)
ii)
iii)
iv)
6
T= 

 4 8  2
Plot the points on a grid.
Multiply the matrix by 1.5?
Plot the new coordinates?
What happened to the shape?
OR
Question 14(B)
i)
Create an adjacency matrix for the digraph given below.
A
B
C
D
Page 5 of 8
[2 marks]
ii)
iii)
Use the matrix to find the number of one stop trips between each pair of
vertices?
[2 marks]
Use the matrix to find the number of two stop trips between each pair of
vertices?
[2 Marks]
Question 15(A)
Tashi borrowed Nu.50, 000 at 15% p.a compounded annually. He agreed to the
following payment plan.
 Nu.15,000 at the end of the first year
 Nu.25,000 at end of the second year
 A final payment of the remaining amount at the end of the third year
i)
Determine the amount of the final payment?
[4 Marks]
ii)
Find the amount of interest Tashi paid altogether?
[2 Marks]
OR
Question 15(B)
i)
Kumar earned a dividend amount of Nu.990 from 50 shares of a stock with a
face value of Nu.100. What was the dividend rate?
[3 Marks]
ii)
Find the value of x ( x  22 )( x  22 )  22
[3 Marks]
Question 16(A)
You withdraw Nu.11200 in NU.100 and Nu.1000 notes from the bank.
i)
Write an equation to model this situation?
[2 Marks]
ii)
Write a function that tells the number of Nu.100 notes, if you know the
number of Nu.1000 notes?
[2 Marks]
iii) Find the number of Nu.1000 notes, if there are 12 Nu.100 notes?[2 Marks]
OR
Question 16(B)
Sketch the graph of
10 x  3 y  60
[6 marks]
Question 17(A)
i)
Determine the volume of a cylinder with a diameter of 22cm and a height of
22cm?
[3 Marks]
ii)
Determine the total surface area of a sphere with the same volume as that of
the cylinder in part (i)?
[3 Marks]
OR
Question 17(B)
i)
A square-based prism has a total surface area of 120cm2. Calculate the height
of a prism with the square base 3cm X 3cm?
[3 Marks]
Page 6 of 8
ii)
How many significant figures are there in each number?
a) 7.9 X 103
b) 0.00400
c) 3.00200
Question 18(A)
i)
Find the value of x, y and z in the matrices below?
 y 3


1 0  1 2   2 1  2 z 
0 x 1  1 X  1 0 = 3 1






 0 1
ii)
Create adjacency matrix for each digraph
A
a)
b)
A
B
B
C
[3 Marks]
[3 Marks]
[3 Marks]
C
D
OR
Question 18(B)
i)
Multiply these two matrices two ways A X B and B X A?
3 0 


A = 1 2
0 3
[5 Marks]
1  1 0
B= 

3 0 2
ii)
What do you notice about the dimensions of the product matrices?
[1 Mark]
Question 19(A)
Which is the best option to pay off a loan of Nu.80, 000? Show your work
[6 Marks]
Option 1: Pay Nu.92, 000 at the end of one year
Option 2: Pay off the loan at the end of one year at an interest rate of 16.6% p.a.
compounded semi-annually.
Option 3: Pay off the loan at the end of one year at an interest rate of 16% p.a.
compounded monthly.
OR
Page 7 of 8
Question 19(B)
Tshering has Nu. 10,00,00 to invest in a stock of shares each with a face value of Nu.100
selling at a premium of 25%
i)
How many shares can he purchase?
[2 Marks]
ii)
Calculate the dividend amount if the company issuing the shares declares a
25% dividend rate?
[2 Marks]
iii)
Calculate the yield percent for the stock?
[2 Marks]
Question 20(A)
i) The sum of two numbers is 61 and the difference is 11. What are the two
numbers?
[3 Marks]
ii) Sanju wrote a 30-item multiple choice exams and answered every question. He
got 8 points for each correct item and lost 2 points for each incorrect item. His total
score was 150 points. How many item did he answer correctly?[3 Marks]
OR
Question 20(B)
i)
Rewrite 10x – 3y = 30 to describe x as a function of y? [2 Marks]
ii)
Sketch the graph of this function?
[4 Marks]
Question 21(A)
These two triangles have the same area but different perimeters.
1.8cm
Triangle 1
3.4cm
Triangle 2
0.9cm
6.8cm
i) Which triangle has a shorter perimeter? Explain your prediction?[2 Marks]
ii) Check your prediction by calculating the perimeter?
[4 Marks]
OR
Question 21(B)
a) Determine the area of an equilateral triangle with perimeter 24 cm[3 Marks]
b) Determine the area of a square with perimeter of 24 cm? [3 Marks]
ALL THE BEST
Page 8 of 8