Basic Algebra Practice Test Questions

Basic Algebra questions are common on most College Entrance exams, High School exams, Nursing Entrance Exams and High School Equivalence exams.

Algebra Practice Test Questions


1. It is known that x2+4x=5. Then x can be

  1. 0
  2. -5
  3. 1
  4. Either (b) or (c)


2. (a+b)2 = 4ab . What is necessarily correct?

  1. a>b
  2. a<b
  3. a=b
  4. None of the Above


3. Sum of the digits of a 2-digit number is 12. If we switch the digits, the number we get will be greater than the initial one by 36. Find the initial number

  1. 39
  2. 48
  3. 57
  4. 75

4. Two friends traveled to a nearby city. In the second day they travelled 75 miles more than the first day, and in the third day, they travelled a third of the distance covered in the second day. How many miles did they cover in the first day, if the total travelled was 170 miles?

  1. 30 miles
  2. 35 miles
  3. 105 miles
  4. 135 miles

5. Kate’s father is 32 years older than Kate. In 5 years he will be five times older than his daughter. How old is Kate?

  1. 2
  2. 3
  3. 5
  4. 6

6. If Lynn can type a page in p minutes, what portion of the page can she do in 5 minutes?

  1. 5/p
  2. p – 5
  3. p + 5
  4. p/5

7. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both of them to paint the house together?

  1. 2 hours and 24 minutes
  2. 3 hours and 12 minutes
  3. 3 hours and 44 minutes
  4. 4 hours and 10 minutes

8. Employees of a discount appliance store receive an additional 20% off of the lowest price on any item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?

  1. $280.90
  2. $287
  3. $292.50
  4. $306


Answer Key

1. D
x2 +4x=5, x2+4x-5=0, x2+5x-x-5=0, factorize x(x+5)-1(x+5)=o, (x+5)(x-1)=0.  x+5=0 or x-1=0, x=0-5 or x=0+1,  x= -5 or x=1, either b or c

2. C
Open parenthesis: 2a + 2b = 4ab, divide both sides by 2 = a+b=2ab or a+b=ab + ab, therefore a=ab and b=ab, therefore a=b

3. B
Let the XY represent the initial number, X + Y = 12, YX=XY+ 36, Only b=48 satisfies both equations above from the given options

4. A

5. B

Let the father’s age=Y, and Kate’s age=X, therefore Y=32+X, in 5yrs y=5x,substituting for Y will be 5x = 32+X, 5x – x = 32, 4X=32,X= 32/8, x = 8, Kate will be 8 in 5 yrs time, so Kate’s present age = 8-5=3

6. D

7. A

Let X represent the house, Sally paints X in 4hrs or ¼ X per 1hr or 60 minutes, John paints X in 6 hours or at 1/6X per 1hr or 60mins. Working together, they will paint 1/4x + 1/6x in 1hr or 60minutes = 10/24x = 5/12x every 60 minutes, to paint x = 60 minutes x 12/5 = 144 minutes or 2 hrs and 24 minutes

8. D

Cost of dishwasher = $450, 15% discount = 15/100 x 450 = $67.5, new price = 450 – 67.5 = $382.5, 20% discount on lowest price = 20/100 x 382.5 = $76.5, final price = $306
Algebra tutorial at Wikipedia

Comments (1)

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  1. Ann McCallum says:

    Good morning,
    With Pi Day just around the corner, I can’t help it; food and math are on my brain. In fact, I would love to share a recipe with you called Variable Pizza Pi. Though the name kind of speaks for itself, the recipe involves constants, variables, and of course Pi. It’s just one of many mathe-licious recipes to get kids to love math. What better way to engage young learners than through their stomachs?
    I am writing to see if you would be interested in sharing this recipe (and possibly others) with your readers? I am a teacher and the author of the “Eat Your Homework” series and am serious about getting children engaged in math and science. Please let me know how I can work with you toward this mission. For example, I would be honored to share this or other recipes and/or provide you with a review copy of my books, illustrated by the amazing Leeza Hernandez. In this series so far are “Eat Your Math Homework” and “Eat Your Science Homework” (Charlesbridge Publishing). I would also be happy to send a press release specifically for Pi Day.
    I hope you are as hungry for more math and science as I am! I look forward to hearing from you soon.
    Best Wishes,

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