Precalculus Honors - Monroe Township School District

To: Precalculus Honors Students
Re: Summer Project 2013
Date: June 2013
Monroe Township High School
Mathematics Department
Congratulations on your acceptance into Precalculus Honors! This is quite an
accomplishment and identifies you as one of the top mathematics’ students. Keep
up the good work. You have my sincere best wishes for your continued success.
To help you begin your study of Precalculus, you will be required to complete a
review project this summer. This project consists of problems reviewing important
concepts from algebra, geometry or trigonometry. This assignment will help you
keep your skills sharp so that you will be successful next year.
Please follow these directions very carefully.
• You may use Khan Academy, Wolfram and other websites to assist you.
• Use pencil
• Work in study groups and use your text as a guide. These are the problems
that you may have forgotten how to do. Note: All students are to
document their OWN work!!
• The project is due the second time your class meets. The project, along
with an exam on the material, will be graded and carries the weight of a test.
• Please make a photocopy of the project before you hand it in. You will be
tested on this material as well.
• Show all work neatly and clearly to receive full credit!!
• Put answers on the line, if provided or circle the final answer in RED.
• All graphing questions will be assessed without a graphing calculator.
Good luck and have a happy and safe summer. I’m looking forward to seeing you in
September.

1. Match each equation with its appropriate graph. Hint: Use end-behaviors and x-intercepts.
3 4
y= 2x
− x _______ A B C D
3
y= ( x+ 2)( x−
1) _______
3 2
y=− x + 3x
________
1 3
y = x − 4x
_______
2
2. The graph of y = f( x)
is shown. Match each graph with its equation.
y = f( x)
I II III
____________________ ___________________ ___________________
A) y= f() x B) y =− f( x)
C) y = f( − x)
D) x= f( y)
E) y= f( x)
− 2 F) y= f( x+
2)
3. Sketch the graph for:
x = − 9 − y 2

4. Let f( x) =
2
x
2x
, gx ( ) = 5x+ 4,
and hx ( ) = . Find each of the following:
2
a) f( h( x )) :_________________ b) g( f( x )) :__________________
5. Identify each function as even, odd or neither.
I. II. III. IV. V.
______________ ______________ _______________ _______________ ______________
6. Let
1
3
hx ( ) = ( x+
1) .
a) Find the inverse function
−1
h ( x)
:_________________________________

) Sketch the graphs of h and
1
h − .
Hint: It is helpful to identify ordered pairs
on one curve to help sketch the second
curve.
7. Graph the specified functions. Identify at least three points that lie on the curve. Include these in
your graph.
a.. ( ) 3 x −
f x = b. gx ( ) = log 2(
x−
1)
( , ) ( , )
( , ) ( , )
( , ) ( , )

8. Express y as a function of x
ln y= 5ln(2 x)
9. One root of
________________________
3 2
Px ( ) = x + 2x−5x− 6 is x =− 1.
Use synthetic division to find the other roots.
10. Simplify: (3x − 5)(2x 2 + 4x − 6)
Factor each of the following. Be careful, there will be no partial credit.
11.
12.
________________________
________________________
2 2
a − 18ab+ 81b
_________________________
2 2
36x − 25y
_________________________

13.
3
a + 27 (Hint: Look up formula if needed.) _________________________
Simplify the expression. (leave your answer in radical form)
14.
3
1−
2
2
Solve by factoring.
15. 2x 2 − 5x − 3 = 0
Solve by using the quadratic formula or by completing the square.
16. x 2 + 6 = 10x
________________________
________________________
________________________

Solve.
17. Solve: 5a− 3 = 7
18. Solve: 8− 5+ t ≥ 6
19. Give the domain, range and zeros of each function.
a) gx ( ) = x+
2
b) gt () = 9−
t
________________________
________________________
Domain:________________ Domain:________________
Range:_________________ Range:_________________
Zeros:__________________ Zeros:__________________
20. log(x 2 −1) = 2 21. e x+2 = 12
________________________ ________________________

22.
2
3 27 9 x
= 23.
5
(8 x) 64
−
+ =
________________________ ________________________
Perform the indicated operation and simplify.
24. 5x 2
+
3x + 3 x − 7
25. 3 x
−
x +1 x −1
________________________
________________________

26.
x + 4 x + 2
÷ 2
16 − x x + 4
________________________
Simplify each of the following. All radicals must be in simplest form. There will be no partial credit.
27. 3 18+ 98
________________________
28.
29. 10
50
9
12x ________________________
________________________
30. ( 3 + 2)( 3 − 5 2)
________________________

31. Suppose that $1200 is invested at an interest rate of 3.5%. How much is the investment worth
after 18 months if interest is compounded quarterly?
________________________
32. Find the equation of the perpendicular bisector of the segment joining (2,4) and (4, −4) using
point-slope form.
________________________
33. Write in center-radius form. Give the center and radius. Hint: Use completing the square.
12x 2 + 20y 2 −12x + 40y − 37 = 0
Equation:_______________________________________
Center:_____________ Radius:_____________

34. Sketch the graphs of the given equations on a single set of axes. Then determine algebraically
where the graphs intersect.
2 2
4x + 16y = 64
2
2x− y =−4
Point(s) of intersection:_________________
35. Write the following in vertex form and sketch: x = 5 − 6y − 3y 2
Equation in vertex form _________________.
Vertex _____________________