Precalculus Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
The problems in this packet are designed to help you review topics from previous math
courses that are important to your success in Precalculus.
It is important that you take time during summer break to review the math concepts you learned this past school
year. In order to ensure that you are appropriately placed in, and prepared for Precalculus, you may be required
to take a course pre-assessment when you return to school next year.
It is YOUR responsibility to prepare for the course pre-assessment!
The specific math concepts that will be assessed are listed on the front page of this summer packet. To prepare
for the course pre-assessment, you are encouraged to complete this summer math packet. Please note, this
summer math packet will not be collected or graded. Instead, the course pre-assessment will be used to measure
your knowledge of the prerequisite skills.
If you have any questions, please feel free to email the resource teacher, [email protected]
Concepts To Be Assessed
on the Precalculus Course Pre-assessment.
Students should be able to:
 Simplify, add, subtract, multiply and factor polynomial expressions.
 Solve quadratic equations.
 Simplify and evaluate rational expressions and complex fractions.
 Graph and identify properties of linear, quadratic, cubic, radical and rational functions.
 Apply rules of function notation, function composition and inverse functions.
 Solve a system of linear equations in two variables.
 Add, subtract, and scalar multiply matrices.
 Use the Pythagorean Theorem and trig ratios to find missing sides or angles of a right triangle.
 Use summation notation to express and determine the value of the sum of a sequence.
Name _____________________________________
Date ___________________ Pd _______
Precalculus Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
Polynomial and operations on real numbers.
Factor Completely.
1.
t 2  4t  21
2.
x3  8
3.
27 x 6  125 y 3
4.
x3  2x 2  4x  8
Simplify the following expressions.
5. 5 x  2 x
2
8.
5
10  2 6
8  2 2
Solve each quadratic equation for x.
2
11. 2 x  32 x  0
6.
 2c 
7.
9.
t 3  t n3
10.
3 2
2
12. 2 x  4 x  3
4 hk
4 hk
3
500x 4
Precalculus Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
Graph the functions using a table of values, symmetry, rational zero theorem, or other properties of polynomials to
plot points. Verify the graph with the calculator. Describe the following characteristics of each function.
a) Domain
d) y-intercept
f) Interval(s)
g) Interval(s)
b) Range
e) end behavior
increasing
decreasing
c) zeros
13. f x   x  3x  x  1
3
14. f x   x  2 x  6
2
15. f x    x  5
2
y
y
y
x
x
a. ____________________
a. ____________________
b. ____________________
b. ____________________
c. ____________________
c. ____________________
d. ____________________
d. ____________________
e. ____________________
e. ____________________
f. ____________________
f. ____________________
g.____________________
g.____________________
x
a. ____________________
b. ____________________
c. ____________________
d. ____________________
e. ____________________
f. ____________________
g.____________________
Function Operations
If f x   x  4 and g x   2 x  4 , determine
2
16. f 3
17. f x   0 when x  ?
18. f g 4
19. f g x 
20. Domain of f g x 
21. g  f 0
Precalculus Prerequisite Packet
Updated 6/2015
22. f
1
Paint Branch High School Math Department
x 
23. Is the inverse of f a
function?
Rational Expressions and Rational Functions
Graph the following functions using a table of values. Find and Label all intercepts and asymptotes.
24. j x  
3x
2
x 1
25. k x  
y
4x2
x2  9
y
x
x
Simplify. Write your answer as a single fraction.
26.
3x 2  6 x 3
9x
27.
2x
6x 2

x  5 2 x  10
28.
2x
x

2
x3 x3
Precalculus Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
Solve each equation for y.
29. 7 y  6 x  10
30.
1
15
y  7x 
4
2
Find the solution(s) of the given systems of equations. Write answers in the form x, y 
31.
 2x  5 y  7
7 x  y  8
32.
4x  6 y  2
2x  3y  4
Use matrices to find the solution(s) of the given systems of equations. Write answers in the form x, y 
4  1  x  3
    
 3 1   y   4
33. 
34.
x  9y  9
3x  6 y  6
Precalculus Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
Pythagorean Theorem and Trigonometric Ratios
Solve for the missing side of the triangle using the Pythagorean Theorem.
35.
a  6 ft.
36.
b  17 ft.
a
b  8 ft.
c
c  19 ft.
b




Solve for x and y using a 45-45-90 triangle ratio 1 : 1 : 2 or a 30-60-90 triangle ratio 1 : 3 : 2 .
37.
38.
45°
39.
60°
x
y
x
x
4
30°
y
4 3
y
3
Given the right triangle, determine the trigonometric ratios.
B
40. sin A 
36
39
C
15
41. cos A 
42. tan A 
A
Use trig ratios to solve for x and y in each right triangle. Round answer to the nearest thousandth.
43.
x
44.
20°
x
y
12
18
y
28
Precalculus Prerequisite Packet
Updated 6/2015
Paint Branch High School Math Department
Discrete Mathematics
Expand and evaluate the following series.
5
45.
 2k
k 1
Express the following series using summation notation.
46. 4 + 8 + 12 + 16 + 20 + 24 + 28
Set Notation
Express the following sets using both interval notation and inequality notation.
47.
48.
49.
Interval: __________
Interval: __________
Interval: __________
Inequality: __________
Inequality: __________
Inequality: __________