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Algebraic Expressions and Geometry Practice Test

Practice algebraic expressions and geometry problems with this test. Solve equations, factor expressions, and calculate geometric figures.

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Algebraic Expressions and Geometry Practice Test

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  1. COMPASSPractice Test 12

  2. ¡ A. 36 ¡ B. 20 ¡ C. -20 ¡ D. -36 ¡ E. -44 4x3 - 2xy 4(-2)3 – 2(-2)(-3) = 4(-8) – 2(-2)(-3) = -32 – 12 = -44 Answer E 1. If x = -2 and y = -3, what is the value of the expression 4x3 - 2xy ?

  3. ¡ A. x2 – 4x – 12 ¡ B. 2(x2 – 4x – 12) ¡ C. 8x2 – 48x ¡ D. 2x2 +16x + 24 ¡ E. 2x2 – 16x – 24 Answer B (2x + 4)(x – 6) 2x2 – 12x + 4x – 24 2x2 – 8x – 24 Factor the common 2 2(x2 – 4x – 12) 2. Which of the following expressions represents the product of four more than twice x and six less than x?

  4. 3. A student earned scores of 85, 76, and 78 on three of four tests. What must the student score on the fourth test to have an average (arithmetic mean) of exactly 80? ¡ A. 79 ¡ B. 80 ¡ C. 81 ¡ D. 82 ¡ E. 83

  5. ¡ D. ¡ E. ¡ A. ¡ B. ¡ C. 4. Which of the following is an equation of the line that contains the points (2, 3) and (4 , 6)?

  6. 4. Which of the following is an equation of the line that contains the points (2, 3) and (4 , 6)? Find slope Now find b Answer B

  7. 5. For all x ¹ ±6, ¡ A. ¡ B. ¡ C. ¡ D. ¡ E.

  8. 5. For all x ¹ ±6, • Pay close attention to the signs. Every possibility is covered in the distracters. Answer D

  9. 6. Each circle has a diameter of 6. What is the location of point B the center of the bottom circle.? ¡ A. (6, -15) ¡ B. (6, -18) ¡ C. (3, -15) ¡ D. (3, -18) ¡ E. (1, -3) 6 -15 6 3 (3, -15) 3 B

  10. 7. For all x, (x2 + 3x + 9)(x - 3) is ¡ A. x3 + 3x2 - x - 3 ¡ B. x2 + 2x - 3 ¡ C. 3x - 3 ¡ D. x3 - 27 ¡ E. x3 - x2 + 3x - 3

  11. 7. For all x, (x2 + 3x + 9)(x - 3) is (x2 + 3x + 9)(x - 3) = x3 + 3x2 + 9x -3x2 - 9x - 27 Answer D x3 - 27

  12. ¡ A. 20 ¡ B. 23 ¡ C. 17 ¡ D. 9 ¡ E. 5 Substitute 2A + 3B = 2(4) + 3(5) = 8 + 15 = 23 Answer B 8. If A ° B = 2A + 3B, find 4 ° 5

  13. 9. What is the perimeter of ABC? B C ¡ A. 8 ¡ B. 10 ¡ C. 14 ¡ D. 24 ¡ E. 28 A

  14. 9. What is the perimeter of ABC? Count the blocks to find the lengths of the legs. BC = 8 AC = 6 B 8 C Now use the Pythagorean Theorem to find the length of the hypotenuse. 6 10 A Add the three sides to find the perimeter. 8 + 6 + 10 = 24 Answer D

  15. 10. What is the value of 642/3? ¡ A. 4 ¡ B. 16 ¡ C. 21.3 ¡ D. 96 ¡ E. Note that the denominator becomes the index of the radical

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