Monmouth Regional High School
Precalculus Honors
Summer Review
This summer review consists of math problems that your teacher will expect you to
know entering next year’s Precalculus Honors class.
All work must be completed on separate sheets of paper (show all of your work),
and your answers should be recorded on the included answer sheet.
This packet will be collected at the beginning of next school year.
Precalculus Honors
Summer Exercises
These exercises represent some of the more fundamental concepts that you are
expected to know as you enter Precalculus Honors.
1.
Find the equation of the line that passes through (2, 1) and is perpendicular to
the line 2x  3y  5.
2.
Graph without a calculator:
a) y  (x  3) 2 + 2
d) y 
g) y  2sin x
e x
j) y  2x  3
b) y  (x + 1) 3
c) y  2  x
e) y  ln(x  1)
h) y  cos x
1
k) y 
x 1
f) y  3 1  x
i) y  tan x + 1
2x
.
x4
3.
Graph and label all asymptotes of y 
4.
Graph (x  2) 2 + y 2  5 and (y + 2) 2  x 2  16.
5.
Which relations are functions?
a) xy  3
e) x 2 + (y  2) 2  4
6.
b)
c) xy 2  7
y  2x
1
f)  2y  9
x
Find the domain, range, and inverse of the graph.
d) x + 3y  5
g) y 2  x 2 + 3
x
1
and g ( x ) 
, find (f  g )( x ) .
x 1
x 1
7.
If f ( x ) 
8.
Solve the following.
g) ( x  4)  5( x  4)
1
2
c) 2 ln 3x  4
b) 3 x  2  8  8
x
e) 2   5
3
a) 4t 3  12t 2 + 8t  0
x 5
d)
0
3x
6
h) 2sin 2 x  sinx + 1; 0  x  2
9.
5a  3b  9
Solve algebraically 
.
2a  4b  14
10.
 4z  13
 x

Solve using matrices  4 x  2y  z  7 .
2x  2y  7z  19

11.
Factor
12.
Simplify the following.
2
3
x
b)
1
1
x 1
a) 3x 3 + 192
5
3
1
c) 2x 4  x 4  15x 4
f) 4e 2x  5
b) 2x 3  11x 2 + 12x + 9
d) 9x 2  3x  2
a) 2 ln( x  3)  ln( x  2)  6 ln x
c) x(1  2 x )  2  (1  2 x ) 
3
1
2
13.
1 0 1
2 3 6
Suppose A  
and B  0 1 0 . Find 2A  B and 2B  A.

4  2 0
2 1 0
14.
Simplify
a) i 27
b) (7+3i)(5  i)
15.
Find the distance between
21 ,  7 and  3, 4 .

16.
17.
Find each summation.
 1
a)  3 
i 1  2 
 i
n
b)
2
 3i  2

i 1
Find the area and perimeter (or circumference) of each figure.
a)
b)
6 in
2 in
c)
7 cm
4 ft
2 in
100
8 in
18.
i 1
12 ft
Find x.
7
x
19.
13
Find the following.
a) sin
7
6
d) csc60
20.

b) cos120
c) tan
 2 
e) sec  

 3 
f) cot(135)
2
Simplify.
a) 4sin2x cos2x
d) cos 2 x  sin 2 x
b) 1  sec 2 x
1  cos 2 x
2
e) cos 2 x + sin 2 x
c)
Precalculus Honors Summer Packet Answer Sheet
Write you answers in the spaces provided.
1.
2.
a
b
c
d
e
f
g
h
i
3.
5.
j
k
4.
a _____________ b _____________ c _____________ d _____________
e _____________ f _____________
g _____________
6.
Domain __________________
Inverse
Range ___________________
7.
8.
a _____________
b _____________
c _____________
d _____________
e _____________
f _____________
g _____________
h _____________
9.
10.
11.
12.
a _____________________
b _____________________
c _____________________
d _____________________
a _____________________
b _____________________
c _____________________
13.
2A  B
2B  A.
14.
a _____________________
b _____________________
16.
a _____________________
b _____________________
17.
a _____________
b _____________
c _____________
_____________
_____________
_____________
a _____________
b _____________
c _____________
d _____________
e _____________
f _____________
a _____________
b _____________
c _____________
d _____________
e _____________
15.
18.
19.
20.