# 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

passes through (-2,-3). Write your answer in slopeintercept

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 .

** Quadratic Equations
**Rewrite the following equations in general quadratic

form:

Complete the square for the following functions:

10. 2x^{2} − 8x + 5

11. − x^{2} − 4x − 7

12. 2x^{2} − 4x

Factor:

13. 4x^{3} y −16x^{2} y − 28y

14. x^{3} + 2x^{2} − 7x −14

15. 5xy^{2} + 5y^{2} + 3ax + 3a (Group in pairs)

16. (x + 3)^{3} −1

17. a^{3} − 64

18. 9y^{2} − 64

**Finding Zeros/Roots**

19. Use Descarte’s Rule of Signs to determine the

possible number of positive and negative zeros :

f (x) = x^{3} +1

20. Given f (x) = x^{4} − 3x^{3} + x^{2} − 6x − 5 ,

determine the possible number of negative zeros.

21. List the possible rational zeros of the function :

f (x) = 3x^{5} + 2x^{2} − 3x + 2

22. List the possible rational zeros of the function:

f (x) = 4x^{3} + 3x^{2} − 5x + 6

23. Use the fact that i is a zero of f to find the

remaining zeros:

f (x) = x^{4} − 5x^{3} + 7x^{2} − 5x + 6

24. Find all of the zeros of the

function: f (x) = x^{4} + 25x^{2} +144

25. Find all the real zeros of the polynomial function:

g(t) = t^{3} + 3t^{2} −16t − 48

26. Use the Intermediate Value Theorem to estimate

the real zero in the interval [1, 2]:

− 3x^{4} + 2x^{3} − x^{2} + x + 2

27. Use the Intermediate Value Theorem to estimate

the real zero in the interval [3, 4]:

2x^{3} − 5x^{2} − 7x +11

28. Use the Intermediate Value Theorem to estimate

the real zero in the interval [0, 1]:

3x^{3} + 7x − 9

**Long and Synthetic Division **

29. Find all of the real roots:

2x^{3} + 5x^{2} − x − 6 = 0

30. Find all of the real zeros of the function:

f (x) = 2x^{3} − 7x^{2} + 7x − 2

31. Write as a product of linear factors:

f (x) = x^{4} − 6x^{3} − 4x^{2} + 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**

67. x > 3x − 2

68. 3x < 4x +1

69. x −1 ≤ 3x + 2

73. x^{2} +1 > x + 3

74. x^{3} − 2x^{2} + 6x + 3 ≤ x^{2} +10x + 3

75. x^{2} − 4x + 4 < x^{3} − 6x^{2} +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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