Algebra Sample Problems With Solutions

MATHEMATICS ALGEBRA REVIEWER
(Practice problems with solutions)




- Greatest common factor
- Least common denominator
- Algebraic expressions
- Arithmetic progression
- Geometric progression
- Age problems

, Greatest common factor
1. Determine the greatest common factor of the expression:
−48𝑎3 𝑏 4 + 36𝑎2 𝑏 + 84𝑎2 𝑏 2
Solution:
Each number can be divided by 12:
−48 36 84
= −4, 12 = 3, 12 = 7
12

Determine the lowest power of each variables: 𝑎2 𝑏
Answer:
GCF = 12𝑎2 𝑏


Least common denominator
1. Find the least common denominator of:
𝑥 2 − 6𝑥 + 9 and 𝑥 2 + 4𝑥 − 21

Solution:

Factor each expression:
(𝑥 − 3)(𝑥 − 3) and (𝑥 − 3)(𝑥 + 7)
The LCD is the set of all unique factors with the highest exponent
Answer:
LCD = (𝑥 − 3)2 (𝑥 + 7)


Algebraic expressions
1. During the storm, it is recorded that the rain fell at a rate of x cm per
minute. How many hours would it take y cm to fall?


Solution:
𝑑𝑒𝑝𝑡ℎ 𝑜𝑓 𝑟𝑎𝑖𝑛 𝑓𝑎𝑙𝑙
Rate of rain fall = 𝑡𝑖𝑚𝑒
𝑦
𝑥= 𝑡𝑖𝑚𝑒

𝑦 𝑐𝑚 𝑦 1 ℎ𝑟
𝑡𝑖𝑚𝑒 = = min ( )
𝑥 𝑐𝑚/𝑚𝑖𝑛 𝑥 60𝑚𝑖𝑛