1. This document provides a practice work assignment for a senior secondary course in mathematics. It contains 14 multiple part questions testing a variety of algebra skills. 2. Students are instructed to show their work on separate paper, including their identifying information, and have their teacher check their work for feedback before submitting. 3. The questions cover topics like solving systems of equations, roots of polynomials, mathematical induction, and maximizing profit in an industrial problem.

1. Practice Work
SENIOR SECONDARY COURSE
MATHEMATICS
Practice Work - Algebra
1
Maximum Marks : 50 Time : 1 Hours
2
Instructions
1. Answer all questions on a separate sheet of paper.
2. Give the following information on your answer sheet:
• Name
• Enrolment Number
• Subject
• Assignment Number
• Address
3. Get your assignment checked by the subject teacher at your study centre so that you get positive
feedback about your performance.
Do not send your assignment to the National Institute of Open Schooling
1. Find the values of x and y if
( x − iy ) + 7 − 2i = 9 − i (2)
2. Prove that the quadratic equation x 2 + py − 4 = 0 has real and distinct roots for all real values
of p (2)
1 2   0 −2 
If A =  −  and B = 
0 1 
3. ,
0 0 
find AB and BA. Is AB = BA? Is it true in general? (2)
4. If 18C r = 18C r+2 find the value of rC 5 (2)
1 2   0 −2 
A=  −  B= 
0 0  0 1  
a −b−c 2a 2a
b −c −a = (a + b + c )
3
2b 2b
5. Show that (3)
2c 2c c −a −b
MATHEMATICS 305

2. Practice Work
6. Using the principle of mathematical induction prove that
3 n ≥ 2n + 1
for any natural number n. (3)
7. If  ,  are the roots of the equation 2 x 2 − 6 x + 5 = 0, find the equation whose roots are
1 1
+ and  + (3)
 
8. Assuming that the expansions are possible, determine the coefficient of y 3 in
1
(1 − 4 y )
2
(1 − 2 y 2 ) 2 . (3)
9. Using Cramer's rule, solve the following system of equations:
x − 2y = 3+ z
2x + z = y (4)
3 − x = 2z − 3y
10. Solve:
1 5 1
+ = (4)
3 − 2x 5 + 2x 2
11. 4 boys and 3 girls are to be seated in 7 chairs such that no two boys are together. In how
many ways can they be seated? (4)
2 −1 1
3 0 −1
12. Find the inverse of   and verity that A A−1 = I3 . (6)
2
 6 0

13. In a small scale industry, a menufacture produces two types of book cases. The first type of
book case requires 3 hours or machine A and 2 hours on machine B for completion, where as
the second type of book case requires 3 hours on machine A and 3 hours on machine B. The
machine A can run at the most for 18 hours while the machine B for at the most 14 hours per
day. He earns a profit of Rs 30 on each book case of first type and Rs 40 on each book case of the
second type.
How many book cases of each type shoul he make each day so as to maximise profit? What is
the maximum profit? (6)
14. Assuming y to be so small that y2 and higher powers of y can be neglected, find the value of the
following:
1
(1 − 4 y )
−3
(1 − 2 y )
2 2
3 (6)
(4 − y )2
306 MATHEMATICS