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MATH 20 SAMPLE QUESTIONS

The following questions are a small sample of the material covered in Math 20. You will find the answers at the bottom of the page. If you wish to print this sheet, click on the pdf icon to view a printable version.

For a sample of Math 15 questions click here or for Math 40 click here.



1. Simplify the expression: \( (2x^{4} - 3x^{2} + 4) + (-5x^{4} + 7x^{2} + 3) \)

A. \( -3x^{8} + 4x^{4} + 7 \) B. \( -3x^{4} + 4x^{2} + 7 \) C. \( -3x^{4} + 4x^{2} + 4 \) D. \( -x^{4} + 10x^{2} + 7 \)



2. Simplify the expresssion: \( (8y^{3} - 11y + 7) - (-5y^{3} + 4y - 6) \)

A. \( 3y^{3} - 7y + 1 \) B. \( 13y^{3} - 7y + 1 \) C. \( 3y^{3} - 15y + 1 \) D. \( 13y^{3} - 15y + 13 \)



3. Solve the equation: \( 4x + 9 = 3-(x - 2) \)

A. \( \dfrac{4}{3} \) B. \( -\dfrac{8}{5} \) C. \( -\dfrac{4}{5} \) D. \( 2 \)



4. Solve the equation: \( 3(x + 5) - 1 + 2x = 2 - (3 - 2x) \)

A. \( -5 \) B. \( -2 \) C. \( \emptyset \) D. \( -\dfrac{15}{7} \)



5. Solve the equation: \( \dfrac{x}{4} - 4 = \dfrac{3x}{2} + \dfrac{3x}{4} \)

A. \( -\dfrac{1}{2} \) B. \( 2 \) C. \( 0 \) D. \( -2 \)



6. Solve the equation: \( \dfrac{1}{2}(4x + 3) - 1 = 2x - 3 \)

A. \( 0 \) B. \( -6 \) C. \( \emptyset \) D. \( -3 \)



7. Determine the greatest common factor: \( 60x^{8} + 72x^{5} + 36x^{4} \)

A. \( 4x^{4} \) B. \( 6x^{8} \) C. \( 3x \) D. \( 12x^{4} \)



8. Factor out the greatest common factor: \( 8x^{3}y^{2} + 24xy^{3} \)

A. \( 4xy^{2}(2x^{2} + 6y) \) B. \( 8xy^{2}(x^{2} + 3y) \) C. \( 8xy(x^{2}y + 3y^{2}) \) D. \( 4xy(2x^{2}y + 6y^{2}) \)



9. The complete factored form of \( 5a^{2} + 15ab - 2ac - 6bc \), is:

A. \( (5a - 2c)(a + 3b) \) B. \( (5a + 2c)(a + 3b) \) C. \( (5a + 2c)(a - 3b) \) D. \( (5a - 2c)(a - 3b) \)



10. One factor of \( x^{2} - 13x - 30 \), is:

A. \(x - 6 \) B. \(x - 3 \) C. \(x + 10 \) D. \(x + 2 \)



11. One factor of \( 6x^{2} + 11x - 10 \), is:

A. \(3x - 2 \) B. \(6x + 5 \) C. \(3x + 2 \) D. \(2x - 5 \)



12. One factor of \( 2x^{2} - 5xy - 3y^{2} \), is:

A. \(x + 3y \) B. \(2x - y \) C. \(x - 3y \) D. \(2x - 3y \)



13. One factor of \( 16x^{2} - 81 \), is:

A. \( 4x - 9 \) B. \( 2x - 3 \) C. \( 4x + 3 \) D. \( 8x + 9 \)



14. One factor of \( 25x^{2} - 9y^2 \), is:

A. \( 5x + 9y \) B. \( 5x - 3y \) C. \( 5x - 9y \) D. \( 5x + 3 \)



15. Choose the answer below that best describes the type of equation: \( 9x^{2} + 12x = -4 \)

A. Linear B. Rational C. Quadtratic D. Radical



16. Choose the answer below that best describes the type of equation: \( \dfrac{1}{x + 4} + \dfrac{x}{x - 4} = \dfrac{-8}{x^{2} - 16} \)

A. Linear B. Rational C. Quadtratic D. Radical



17. Solve the equation: \( 9x^{2} + 12x = -4 \)

A. \( \dfrac{2}{3} \) B. \( \dfrac{3}{2} \) C. \(-1\), \( \dfrac{4}{9} \) D. \( -\dfrac{2}{3} \)



18. Solve the equation: \( \dfrac{1}{x + 4} + \dfrac{x}{x - 4} = \dfrac{-8}{x^{2} - 16} \)

A. \( -4 \) B. \( -1 \) C. \( 2 \) D. \( 1 \)



19. Graph the line \( 5x + 2y = -10 \) and identify the slope of the line

A. \( m = 5/2 \) B. \( m = -5/2 \) C. \( m = -2/5 \) D. \( m = -5/2 \)
linear graph 1 linear graph 2 linear graph 3 linear graph 4



20. Graph the line \( 4x - 3y = 12 \) and identify the slope of the line

A. \( m = 3/4 \) B. \( m = 4/3 \) C. \( m = -4/3 \) D. \( m = 4/3 \)
linear graph 7 linear graph 5 linear graph 6 linear graph 8



21. Graph the line \( y = -\frac{4}{5}x + 3 \) and identify the slope.

A. \( m = -4/5 \) B. \( m = 4/5 \) C. \( m = -4/5 \) D. \( m = -5/4 \)
linear graph 10 linear graph 11 linear graph 12 linear graph 13



22. Graph the line \( y = 2 \) and identify the slope.

A. \( m = 0 \) B. \( m = -2 \) C. slope is undefined D. \( m = 2 \)
linear graph 14 linear graph 15 linear graph 16 linear graph 17




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1. B   2. D   3. C   4. A   5. D   6. C   7. D   8. B   9. A   10. D   11. A   12. C   13. A   14. B   15. C   16. B   17. D   18. B   19. D   20. B   21. C   22. A  

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