# DRUKGYEL HIGHER SECONDARY SCHOOL

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```					                 DRUKGYEL HIGHER SECONDARY SCHOOL
MID TERM EXAMINATIONS 2011
MATHEMATICS
(The first 15 minutes of the examination are for reading the paper only..
Candidates must NOT start writing during this time).

Class: X                                                              Total marks :100
Time : 3¼ Hrs
--------------------------------------------------------------------------------------------
           Section A composed of 10 multiple choice questions, and will
Carry a total of 20 marks.
           Section B composed of 12 questions requiring short answers,and
Will carry a total of 32 marks.
       Section C composed of 8 pairs of questions. Candidates are required to
attempt only one question from each of the pairs provided.
And will carry a total of 48 marks.
           The intended marks for questions or parts of questions are given in
bracket ( )
           The use of calculator (Fx-82) (Fx-100) is allowed.

SECTION --- A
(10x2 =20)
Direction: Read the following questions carefully. For each question there are four
alternatives A, B, C and D. Choose the correct alternative and write it in your

i)     One dimension of the product matrix of two matrices is 5 × 2. What are the
dimensions of the two matrices?

a) 5×2, 4×2       b) 5×4, 4×3     c) 2×5, 5×2         d)    5×2, 2×2

ii)        The number of one stopover trips from A to C in the given digraph

a)    3    b) 2      c)      1     d)    4

1
iii) Identify the element in the 3rd row 2nd column in the matrix

A    E G L 
           
F    B K O 
H    P C J 
           
M    N I D
a) B     b) N        c) P          d) E
iv) Choden buys stock at a discount of 18%. Each share has a face value of Nu.100.
How many shares can she buy with Nu.20000.
a) 244 b) 200 c) 169 d) 224
v) The value of P in the equation 5  p  75
a)    15     b) 15       c) 375        d)    375
vi) Write ‘w’ as the function of ‘x’ in the expansion 3w + 8x = 7 is

7  8x                           7  3w
a)    f x                  b)       f w 
3                                8
8x  7                             3w  7
c ) f x                    d)       f w 
3                                  8
vii)  A computer is sold for Nu.4500. Find the percent markup if the shop
owner paid a cost price of Nu. 15000.
a) 200%        b) 300%         c) 50%       d) 400%
viii) The value of ‘m’ in the radical 5  3  4  3  32  60  m 2
a) 6      b) 3       c) 4       d) 1
ix) Which of the following graphs represent functions?

A                                                     B

6                                                6

4                                                4

2                                                2
0    2       4   6                               0   2         4        6

C                                             D
6
4
4

2                                                          2
-4       -2    2    4       6
0    2       4   6
-2
-2                                                             -4
2
x) The slope and y intercept form of the given inequality, 10x > -3y + 5 is

10x 5                     10 x 5                   10x 5              10 x 5
a) y                 b)    y                  c)    y           d) y          
3   3                     3     3                   3   3              3     3

1. Create an adjacency matrix for the digraph below

[1 1 2 ]
2. Create a digraph for the adjacency matrix given below
0 1 1 
1 1 0                                                               [1 1 2 ]
      
0 2 1 
      

3)    Transform the linear equation 3x – 4y = 12 to slope and y-intercept
form.                                                               [3]

2    3               4 2               1 0
4)    If A =                   B=              C=      , then find
0 1                 0 0             0 1 

i) 2A + 3B       ii) A(B+C)                                          [3]
5)    Which of the following option is better for a buyer
Option I : 20% markup on an item with a cost price of Nu. 480.
Option II : 15% discount on the same item that has a marked price of
Nu. 700.                                                [3]

6)    Solve the system of linear equation given below
Y = 4x – 3 and 2y + 5x = 72                                                              [3]

32       50  8  72
7) Simplify                                                                                     [3]
2

8) Pema invested Nu.25000 in RICBL shares with a face value of Nu.100 and
sold at par.
a) How many shares can he buy?
b) If a dividend of 15% is paid, find the annual dividend earned by him?
c) What will be the yield percentage on his investment?                  [4]

3
9) Manju wrote a 30 – item multiple choice exam and answered every question
She got 8 points for each correct item and lost 2 points for each incorrect item.
Her total score was 150 points . How many item did she answer correctly? [3]

10) Zangmo invested some money in a bank account earning 4.2% interest.
The bank then improved its rates , so she invested in an account earning 4.5%
interest.
a) Write an equation to describe the total interest.
b) Write a function that will calculate the amount invested at 4.5% if you
know the amount at 4.2%.                                                 [3]

SECTION - C (8x6 = 48 marks)
(Answer ‘A’ or ‘B’ from each question)
Question1 A
a) what numbers are missing in the matrices below

?        3
2        1
1 0  1 2               2    ?
0 ? 1  1   1      0   3    1
(3)
                                 
          
0        1
b) The coordinates of the three vertices of a triangle are listed in the matrix
given below.
4   8    1
M =
0       3     2

i.     Plot the points on the grid.
ii.    Multiply the matrix by 1.5.
iii. Plot the new coordinates on the same grid.                                    [3]
OR
Question 1 B
a)   Use a matrix to show the numbers of times the prime factors 2,3,5 and 7
appear in each of the multiples of 4 from 4 to 40.                   [3]

b)
B
A             E

D             C

i) Create an adjacency matrix for this digraph.
ii) What does the number in the position ( 4, 2 ) in the matrix tell you?
iii) How many two-stopover paths are there from B to E ?                   (3)
4
Question 2 A
a) The number of students who signed up for football in four different schools
in one year are listed below,
42   65 21 38 

Suppose the number grew by 10% the following year.What would the new
Matrix look like?                                                  [3]

b) Nima withdrew the following notes from a bank:
Types of Notes                     No. of Notes
Nu. 10                                100
Nu. 50                                 20
Nu. 100                                10
Calculate the total value of the notes by multiplying two matrices. [3]
OR
Question 2 B
a) Create two 2 x 2 matrices A and B . Find AB and BA.
Is AB equal to BA?                                                       [3]
b) Use a digraph to describe an ecosystem. Draw a digraph to represent this
information.
Predator             Food
Insects
Caterpillars        Plants
Songbirds
Songbirds
Songbirds            Caterpillars
Songbirds          Insects
Insects

Question 3 A
a) Pema is a car salesperson. He is paid Nu.1000 each week plus an additional
3% commission on sales.
i.     Determine Pema’s total income for a week in which sales were Nu.70,000.
ii Pema’s goal is to earn Nu.5000 each week. What is the minimum amount
of weekly sales required to earn this level of income?               [4]
b) Simplify     68    17    8    98                                       [2]
OR
Question 3 B
a) Yuden invested Nu. 2500 in an account. After four years, the amount of money
had grown to Nu. 2903.91. What was the annual interest rate compounded
monthly?                                                                 [4]
5
 30 p      p
b) Find the missing value                             54                          [2]
5
Question 4 A
a) A loan for Nu.13000 is to be repaid in monthly payments of Nu.350.what
is the balance on the loan after each period of time, if the interest rate is 13%
Compounded monthly?
i) one month ii) two month                                                      [4]
b) Simplify 3 5  11  4  2 11                                                 [2]

OR
Question 4 B
a) Sonam earned a dividend amount of Nu. 990 from 50 shares of stock with
a face value of Nu. 100.
i.     What was the dividend rate?
ii.   How much more would he have earned if the rate had been 5% higher?
iii. If he sells his shares at a premium of 10%, how much money will he

b) Simplify            27 x 6       4x          12 x 2    x5                   [2]

Question 5 A
a) Sketch the graph of      3x + 4y ≥ 24                                            [3]
b) A rectangle has these vertices. A(2,2), B(2,6), C(4,6) and D(4,2)

B     C

A     D

Determine the equation of the diagonal, AC.                                        [3]

OR
Question 5 B
a) Write an inequality for the graph.

[3]

6
b) A team bought 20 basketballs for a total of Nu. 8800. Practice balls cost
Nu. 400 and official balls cost Nu. 600. Use a system of equations to determine
How many of each type of ball they bought.                                  [3]

Question 6 A
a) Determine the unknown values in the digram

[3]
b) Determine the solution of this system of linear equation
1    2
x y 2
2    3
[3]
3    1
x  y 11
4    3

OR
Question 6 B
a) You withdraw Nu. 2000 in Nu.20 and Nu.50 notes from the bank.
i. Write an equation to model this situation.
ii. Write a function that tells the number of Nu.20 notes, if you know the
number of Nu. 50 notes.                                                [3]

b) Without graphing, describes how the graphs of each pair of inequalities
Are alike and different.
2y ≤ x – 5      and    2y < x – 5                                  [3]

Question 7 A
a) A shopkeeper offers a 25% discount on an item marked at Nu. 300. An
identical item at another shop is marked at Nu. 280 but is on sale at a discount
of 15% . Which item can be purchased for less money?                        [3]
b   Simplify
5x 3      9x 6                      5 27  3 12
i)                         ii) solve for x,                    3         [3]
80 x                                  x

OR
Question 7 B
a) Chandra invested a total of Nu. 2500 in two investments. One investment
earned 4% interest and the other earned 5% interest. The total interest earned
was Nu. 115.
7
i.      Write an equation to model the total amount invested and the total interest
earned.
ii.     Solve the system of equations to determine the amount invested at each
interest rate.                                                              [4]

b)Raju kept a record of his archery scores in his last five matches.
125   134   122   117   109 
What are the dimensions of this row matrix, and how could a matrix with
different dimensions show the same information?                                     [2]

Question 8 A
a) How does this diagram show that                   18  3 2

[4]

b)      Solve the system of linear equations.
3X – 4Y = -15 and 2X + 3Y = 7                                              [2]

OR

Question 8 B         .
a) The perimeter of one rectangle is 120cm.Another rectangle with twice the length
and one third the width has a perimeter of 170cm. What are the dimensions of the
two rectangles                                                                 [4]
b) Create a table of values for f(x) = 10 - 3x, how do you know it is a function.
[2]

*********************

TASHI DELEK

8

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