Mathematics Department
Dr. Hassan Ibrahim
Math101 - Quiz 1
Student Name: . . . . . . . . . . . . . . . . . .
ID: . . .
Tutorial Number: . . .
Duration: 35 min
Note: show all details of your answers.
1. Simplify as much as possible each of the following expressions.
(3 points)
a. 4−1/2 43/2
b. (2a2 )(5a7 )
!
1 2
(y 0 x 2 ) 3
c.
y
x6 y −3
p
27 3 y 5
!− 13
1
2. Find the value of the integer n if:
x 2 x3
= xn
(x4 )4
(1 points)
3. Solve the following inequalities and express their solution sets as intervals or unions of
interval. Show each solution set on the real line.
(3 points)
(a) 2x + 3 ≤ 3x + 5
(b)
3
−2 ≤1
2x
(c) |x2 − 1| > 1
2
3
4. Find the real solutions of each of the following equations. Give your answers accurate to
2 decimal places.
(2 points)
4
x
r 8
a. 3x = −11 +
b. 3 = 2 1 +
3
4
.
5. Complete the square in the expression P = x2 + 5x then deduce that P ≥ − 25
4
(1 point)
5
Draft
6