Worksheet on Algebra

Solved Questions on Algebra

1. If m = 12, evaluate the algebraic equation

a) 51
b) 61
c) 71
d) 91

Answer: b) 61

Explanation: If m = 12, the value of the algebraic expression is:

2. What is the value of the algebraic expression if a = 7 and b = −2?

a) −21
b) −14
c) −7
d) 2

Answer: b) −14

Explanation: If a = 7 and b = 2, the value of the algebraic expression is:

3. The salary $S of Dmitri Mendeleev earning $p per hour for t hours is given by the formula S = pt − 3. What is his salary for working 20 hours at a rate of $47.95 per hour?

a) $953
b) $956
c) $959
d) $1059

Answer: b) $956

Explanation: t = 20 hours
p = $47.95
S = pt − 3
   = (p × t) − 3  
   = ($47.95 × 20) − 3
   = $959 − 3
   = $956

4. The number of shops on the ground floor of a building is 5 less than twice the number of shops on the first floor. The ground floor has x shops and the first floor has y shops. How many shops does the ground floor have if the first floor has 14 shops?

a) x = 21
b) x = 23
c) y = 21
d) y = 23

Answer: b) x = 23

Explanation: Number of shops on the ground floor = x

Number of shops on the first floor = y

The number of shops on the ground floor of a building is 5 less than twice the number of shops on the first floor.

Number of shops on the ground floor = (2 × Number of shops on the first floor) − 5
⇒ x = (2 × y) − 5
⇒  x = (2  × 14)  − 5
⇒ x = 28  − 5
⇒ x = 23

5. At a marriage party, the chairs are arranged in r2 rows and each row contains 3ar chairs. What is the total number of chairs in the party?

a) 3r3
b) r3/3
c) 3ar3
d) ar3/3

Answer: c) 3ar3

Explanation: Number of rows = r2

Number of chairs in each row = 3ar

Total number of chairs in the party = Number of rows × Number of chairs in each row
                                                    =   r2 × 3ar
                                                     =   3ar3