Algebra Placement Test Practice

The following multiple choice algebra questions guide you in assessing your skills and abilities in the following topics: substituting values into algebraic expressions, setting up equations for given situations, basic operations such as multiplication and division of polynomials, factoring polynomials, solving linear equations in one variable, exponents and radicals, rational expressions and linear equations in two variables are presented along with their answers and detailed solutions.

1. If a = -2 and b = -2, what is the value of (a³ - 1) / (b - 1)
   A) 3
   B) -9
   C) -3
   D) 9
   E) 6
   Detailed Solution.
   
   
   

2. If -2(x + 9) = 20, then - 4x =
   A) -76
   B) -19
   C) 0
   D) 76
   E) 90
   Detailed Solution.
   
   
   

3. x is a variable such that if 20% of it is added to its fifth the result is equal to 12 subtracted from seven tenths of x. Find x.
   A) 0.2
   B) 1/5
   C) 7/10
   D) 20
   E) 40
   Detailed Solution.
   
   
   

4. The area A of a trapezoid is given by the formula A = 0.5(b + B)h, where b and B are the sizes of the bases and h the size of the height of the trapezoid. Express B in terms of A, b and h.
   A) 0.5Ah - b
   B) 2A/h - b
   C) (2A - b)/h
   D) 2A/h + b
   E) (2A + b)/h
   Detailed Solution.
   
   
   

5. Tom, Linda and Alex have $120 dollars. Alex has the third of what Tom has and Linda has twice as much as Alex. How much money, in dollars, does Linda have?
   A) 10
   B) 20
   C) 40
   D) 60
   E) 80
   Detailed Solution.
   
   
   

6. Which of the following is equivalen to 6x² - 11x - 2?
   A) (6x - 1)(x + 2)
   B) (3x - 1)(2x + 2)
   C) (3x + 1)(2x - 2)
   D) (6x + 1)(x - 2)
   E) (x + 1)(6x - 2)
   Detailed Solution.
   
   
   

7. Which of the following is a factor of x² - 7x - 8?
   A) x + 1
   B) x + 8
   C) x + 7
   D) x - 1
   E) x - 7
   Detailed Solution.
   
   
   

8. (2xy² - 3x²y) - (2x²y² - 4x²y) =
   A) 2x²y²
   B) -2x²y² -7x²y - 2x²y²
   C) -2x²y² + x²y - 2x²y²
   D) 2x²y² + x²y - 2x²y²
   E) -2x²y² + x²y + 2xy²
   Detailed Solution.
   
   
   

9. During the same journey, Stuart drove x miles for 2 hours, and 200 miles for 3 hours. Find x if the average speed for the entire journey is 70 miles per hour.
   A) 166
   B) 167
   C) 150
   D) 140
   E) 120
   Detailed Solution.
   
   
   

10. Given the equations of the lines
    (I) 2y + 3x = 3
    (II) -3y - 2x = 5
    (III) -6y + 4x = 9,
    (IV) 2y + 6x = 9
    which two lines are perpendicular?
    
    A) (I) and (II)
    B) (II) and (III)
    C) (III) and (IV)
    D) (I) and (III)
    E) (IV) and (II)
    Detailed Solution.
    
    
    

11. If f(x) = (x + 1)², then f(t + 2) =
    A) t² + 2t + 4
    B) t² + 4
    C) t² + 6t + 9
    D) t² + 9
    E) t² + 2t + 1
    Detailed Solution.
    
    
    

12. For x > 0 and y > 0,
    (√x + √y) (√x - √y) - (√x - √y)² =
    A) -2√x√y - 2y
    B) x - y
    C) 0
    D) -2√x√y + 2y
    E) 2√x√y - 2y
    Detailed Solution.
    
    
    

13. What is the slope of the line whose equation is given by
    x/2 - y/4 = 7
    A) 2
    B) 1/2
    C) -1/4
    D) -1/2
    E) -2
    Detailed Solution.
    
    
    

14. For x > 3,
    (x / (x - 3) + 1 / 2)(2/(x - 1)) =
    A) (x + 1) / ((x - 3)(x - 1))
    B) 3 / (x - 3)
    C) (x + 3) / (2(x - 1))
    D) 2x / ((x - 3)(x - 1))
    E) 1 / (x - 3)
    Detailed Solution.
    
    
    

15. In a standard rectangular system of axes, point A has the coordinates (2 , 1). What must be the coordinates of point B if M(3 , 2) is the midpoint of the segment AB?
    
    A) (1 , 1)
    B) (4 , 3)
    C) (3 , 4)
    D) (3 , 2)
    E) (2 , 3)
    Detailed Solution.

1. A
2. D
3. E
4. B
5. C
   
6. D
7. A
8. E
9. C
10. D
11. C
12. E
13. A
14. B
15. B

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