# ECAT – Mathematics (Algebra)

The following questions are from essentials of Algebra at middle level. The topics that are included are Exponents and Radicals, Polynomials, Systems of Equations and Inequalities.

## Mathematics-Algebra Sample Questions

1. 42 + |4| + |−4| − 42 = ?
(A) −4
(B) 0
(C) 4
(D) 8

2. $\frac{3^5}{3^3}=?$
(A) 1
(B) 3
(C) 9
(D) 27

3. $3^2\times3^3\times\frac{1}{3^4}=?$
(A) 1
(B) 3
(C) 9
(D) 27

4. $\sqrt[3]{\sqrt{64}}=?$
(A) $\sqrt{2}$
(B) 2
(C) 4
(D) 8

5. What is the value of x in the equation

(A) 12
(B) 14
(C) 16
(D) 18

1. D
2. C
3. B
4. B
5. A

6. What is the solution interval of the inequality $6x-2\geq3x+10$
(A) (∞,4)
(B) (−∞,4]
(C) (−4,∞)
(D) [4,∞)

7. What is the value of x in the equation

(A) 0
(B) 2
(C) 4
(D) 6

8. The price (in cents) of one orange is 5c. What is the price (in dollars) of one dozen of oranges?
(A) 30c
(B) 60c
(C) $\frac{3c}{5}$
(D) $\frac{5c}{12}$

9. At present, the age of Alice is x–10 years. What will be her age after 12 years?
(A) x+2
(B) x–2
(C) x+12
(D) x–12

10. Mr. A can do a particular work in 6 hours, and Mr. B can do the same work in 14 hours. How much time it will take if they do the work together?
(A) 4 hours and 6 minutes
(B) 4 hours and 12 minutes
(C) 4 hours and 18 minutes
(D) 4 hours and 24 minutes