Pre-Calculus Midterm Review Packet
1. Describe each graph by stating if it is a relation or function.
2. State the domain of each function: f (x) =
2x +1
x - 3x + 2
2
3. Find (g f )(x) if f (x) = x 2 -1, and g(x) = 3x - 5
4. Find the x- and y-intercept for x – 2y + 5 = 0
5. Find the zero of the function f(x) = -5x + 10
6. Sam is opening his own business. He determined that he will need $3,200 to but supplies to start. He
expects expenses for each following month to be $500. Write an equation that models the total
expense y after x months.
7. Determine whether the graphs of the pair of equations x + y = 6 and 2x + 3y = 12 are parallel,
coinciding, or neither.
8. Write an equation of the line that passes through the points (-1,4) and (5,-2)
9. Write an equation of a line that has no slope and passes through the point (3,-10)
10. How can you tell if two lines are perpendicular?
æfö
11. Given f(x) = x2 - x + 3 and g(x) = 2x + 1, find ç ÷(x)
è gø
2x + y - z = 3
12. Solve the system of equations by elimination.
x+y+z =5
x - 2y + z = 2
é
ù
é
ù
13. If A = ê 0 1 ú and B = ê 2 -1 5 ú , find the product of A and B.
ë -1 3 û
ë -1 0 3 û
14. Find the value of
3 -1 0
1 5 1
4 0 -1 .
15. Find the f(3a3) for f(x) = 2x2 – 5x
16. Find the zero of the function f(x) = -2x – 3,
then graph the function.
17. Find the values of x and y for which the matrix equation is true. éë 2x
é
ù
18. Given B = ê 0 1 2 ú , C =
ë -1 -1 0 û
é2 1 3ù
ê
ú
ê-4 0 -2 ú Find 2B – C
êë 5 2 1 úû
y ùû = éë y -1 x + 5 ùû
é
ù
19. Find the inverse of ê 1 2 ú .
ë -5 3 û
20. Graph the inequality 4x + y - 3 > 0?
21. Determine the intervals on which the function f(x) = x3 - x2 + 2x is increasing and the intervals on
which the function is decreasing.
(x -1)2 (y + 3)2
22. For which line(s) is the graph of
+
=1 is symmetric?
4
1
23. Which is the graph of f(x) = x2 - 3 and its inverse?
24. Determine whether the given critical point of x = -5 is the location of a relative maximum, relative
1
minimum, or a point of inflection for the function f (x) = x 2 + 5x +1
2
25. Approximate the real zero(s) of f (x) = x 3 - 2x 2 + 5x - 5 to the nearest tenth.
26. Solve the system of inequalities by graphing.
x-y ≤2
3x - y < 1
y ≥0
27. Sean has $10,000 to deposit in two different savings accounts. He wants at least $4,000 in the account
with 5% interest. He wants no less than $6,000 in the account with 4% interest. For the equation
l(x,y) = 30x + 70y find the maximum interest if the vertices are (3,5), (3,7), and (5,5).
28. Determine the equation of the vertical asymptote for the function f (x) =
29. Graph the function f (x) =
x-2
3(x -1)
x 2 -1
x -1
30. Find the roots of x 3 + 3x - 4 = 0
31. In a polynomial equation, if there are two changes in sign of the coefficients of the terms, _______.
32. In
if A = 53°, B = 72°, and b = 15, find a to the nearest tenth.
ì x 2 + 3 x >1
f (x) = í
î2x x £1
B. point discontinuity
D. infinite discontinuity
33. Determine the type of discontinuity this function exhibits.
A. jump discontinuity
C. none of these
34. Find the maximum value of f(x, y) = 2x + y - 4 for the system of inequalities:
y ≤ ⅓x + 1
y ≤ 2x - 1
x≥0
y≥0
A. Unbounded
C. 1
35. Solve
B. alternate Optimal solutions
D. Infeasible
x
> 0.
x -4
2
36. If sin q =
3
find csc θ
5
37. Evaluate tan
7p
3
38. Which is an odd function?
A. y = x
B. x 2 + y 2 =1
C. y = x 3
39. List the possible rational roots of 5x 3 + 5x 2 - 2x + 2 = 0
P
40. Find cos P.
8 cm
2 cm
D. y = x 2
41. Use the unit circle to find sec (-270°) .
5
42. State the amplitude for the function y = - cosq
3
æq p ö
43. Find the period of the function y = sec ç - ÷
è2 4 ø
44. Use the parent graph f(x) =
1
1
to graph the function g(x) =
+ 4.
x
x-3