# Math 119 Pretest Review Questions

Linear Equations
Find the slope of the line passing through the given
points:

1. (2, -5); (0, 2)

2. (3, -4); (3, 0)

3. (-1, -2); (1, 4)

4. Find the equation of the line with slope 2 that
form.

5. Find the general form of the equation of the line
that passes through (-1,6) and is parallel to the graph
of 2x + 3y − 4 = 0 .

6. Find the general form of the equation of the line
that passes through (4,-2) and is parallel to the graph
of x − y − 3 = 0 .

Rewrite the following equations in general quadratic
form:

Complete the square for the following functions:

10. 2x2 − 8x + 5

11. − x2 − 4x − 7

12. 2x2 − 4x

Factoring

Factor:

13. 4x3 y −16x2 y − 28y

14. x3 + 2x2 − 7x −14

15. 5xy2 + 5y2 + 3ax + 3a (Group in pairs)

16. (x + 3)3 −1

17. a3 − 64

18. 9y2 − 64

Finding Zeros/Roots

19. Use Descarte’s Rule of Signs to determine the
possible number of positive and negative zeros :
f (x) = x3 +1

20. Given f (x) = x4 − 3x3 + x2 − 6x − 5 ,
determine the possible number of negative zeros.

21. List the possible rational zeros of the function :
f (x) = 3x5 + 2x2 − 3x + 2

22. List the possible rational zeros of the function:
f (x) = 4x3 + 3x2 − 5x + 6

23. Use the fact that i is a zero of f to find the
remaining zeros:
f (x) = x4 − 5x3 + 7x2 − 5x + 6

24. Find all of the zeros of the
function: f (x) = x4 + 25x2 +144

25. Find all the real zeros of the polynomial function:
g(t) = t3 + 3t2 −16t − 48

26. Use the Intermediate Value Theorem to estimate
the real zero in the interval [1, 2]:
− 3x4 + 2x3 − x2 + x + 2

27. Use the Intermediate Value Theorem to estimate
the real zero in the interval [3, 4]:
2x3 − 5x2 − 7x +11

28. Use the Intermediate Value Theorem to estimate
the real zero in the interval [0, 1]:
3x3 + 7x − 9

Long and Synthetic Division

29. Find all of the real roots:
2x3 + 5x2 − x − 6 = 0

30. Find all of the real zeros of the function:
f (x) = 2x3 − 7x2 + 7x − 2

31. Write as a product of linear factors:
f (x) = x4 − 6x3 − 4x2 + 40x + 32

32. Simplify the rational expression:

33. Simplify the rational function:

34. Simplify:

Absolute Value

Solve the following equations for x:

35. |x − 3| = 2

36. |x| = 5

37. |x + 5| = −1

Simplify the following expressions involving
absolute values:

Pythagorean Theorem

For questions 41-42, consider a right triangle with
sides of length a, b, and c:

41. If the lengths of sides a and b are six and eight
inches respectively, how long is side c?

42. What is the length of side b in terms of the sides a
and c?

Distance Formula
Find the distance between the given points:

43. (2, 5); (-1,9)

44. (-1, 3); (5,1)

45. (10, -3); (3, 0)

Simplifying Expressions

Simplify:

46. (Assume all variables represent positive
real numbers)

Rationalize the denominator and simplify:

Solving Equations

Solve for x or y:

Inequalities

Solve each inequality :

67. x > 3x − 2

68. 3x < 4x +1

69. x −1 ≤ 3x + 2

73. x2 +1 > x + 3

74. x3 − 2x2 + 6x + 3 ≤ x2 +10x + 3

75. x2 − 4x + 4 < x3 − 6x2 +11x − 5

Solve each absolute value inequality:

76. |x − 3| < 2

77. |x + 5| ≤ 0

78. |x + 2| ≥ 3

Logarithmic, Exponential and Logistic Functions

79. Write as the logarithm of a single quantity:

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