Accountants

1. Haramaya University
College of Natural and Computational Sciences
Department of Mathematics
Mathematics for Social Science Assignment
1. Solve the inequality 2x2
− 5x − 12 ≥ 0.
2. If the roots of q(x) are r1 and r2 with r1 + r2 = −10 and r1r2 = 21. Find the quotient and
remainder such that the polynomial P(x) = x4
+ 5x3
− 10x + 20 divided by q(x).
3. Let f(x) = x−2
x2−5x+6
. Then find their domain, intercepts, asymptotes and sketch the graph
of f(x).
4. Solve each of the following equations.
(a) 24y+1
− 8y
= 0.
(b) 2 log
√
x
9 − log6x−1
9 = 0
(c) 2e2x
− 7ex
= 15
5. Find the minor, cofactor, adjoint and inverse of the given matrix.
2 1 −3
1 −1 0
−2 1 4
!
6. Let f(x) = 2x+1
x−1
. Then show that f is one to one and find its inverse.
7. Let f(x) = x−5
x+1
and g(x) = x+2
x−3
. Then find
(a) (fog)(x) and its domain
(b) (gof)(x) and its domain
8. Suppose A, B and C are square matrices with AB = 3C where C is a 3 × 3 scalar matrix
whose trace is 6. If det(B) = 4, find det[3A−1
B2t
C].
9. If A has m rows and m + 5 columns and B has n rows and 11 − n columns, find m and n
so that both products AB and BA exist.
10. Let A =
x 0 0
9 −5 y
z −4 8
!
Find the values of x, y and z when matrix A is
(a) Symmetric
(b) Skew-Symmetric
11. Find c such that the matrix A − cI2 is not invertible where A =
4 6
−1 −3
1