Try our Free Online Math Solver!

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
Factoring
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 4142, 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:
Prev  Next 