Download PreCalculus

NAME:______________________
For: Students entering PreCalculus
Summer Review Packet
The problems in this packet are designed to help you review
topics that are important to your success in your next level of
math. Show all your work for each problem. You may want
to work with one or more people on this, but each student
must submit his/her own packet. All work should be
completed and ready to turn in on the first day of school.
You will be held accountable for this material.
HAVE FUN!
1. Simplify: a. 3 63
b.
10 ( 2 + 2)
2. The lengths of the legs of a right triangle are 3 cm and 6 cm. Find the length of the hypotenuse.
3. Multiply: a. (2x – 5)2
b. ( 3 + 2) ( 3 – 2)
b. x2 - 25
c. 5x3 – 20x
6. Solve for x: a. (x – 2)2 = 9
b. 4 + 3(x – 1) = 511
c. x(5 + 3x) = 175
2
7. Simplify: a. x3  x2 (4x3)2
b. (3x)3y4
(6xy2)2
c. 2x -2
6y -3
4. Factor:
a. x2 – 5x + 6
5. Complete the square: x2 – 4x = 8
8. Solve the system of equations:
2x + 5y = -11
3x – 7y = 27
9. Triangle ABC has vertices A(0, 0), B(4, 8) and C(10, 0).
a. Find the coordinates of the midpoint, M of line segment AB.
b. Find the slope of BC.
c. Find the equation of the line that contains M and is parallel to BC.
10. Simplify the complex numbers:
a. (1 – 3i) + (1 + 3i)
b. (1 – 3i)(1 + 3i)
c.
2
1 – 2i
11. Sketch each function and identify the domain and range.
a. y = x2
b. y = x3
c. y = x
Domain____________
Range _____________
Domain____________
Range _____________
Domain____________
Range _____________
Sketch:
Sketch:
Sketch:
Use the definition of the three trigonometric ratios to complete each statement.
Simplify answers.
13. sin <R = _____
cos <R = _____
14. cos <B = ______
tan <B = ______
15. sin<C = ________
tan<C = ________
T
Y
r
sS
S
s
R
30
R
O
t
B
C
A
3 2
34
Set calculator to degree mode. Use a 4 place decimal.
16. sin 57° = __________
17. cos 9° = ___________
Give answer to the nearest degree.
18. sin <A = 0.5447
<A = ___________
19.
cos<B = .0696
<B = ____________
Write a trigonometric equation and solve. Find the answer to the nearest whole number.
20.
21.
68°
42°
x
12
28
22°
48°
Equation: _______________________
x
Equation: _________________________
x = ______________
x = _____________
22.
23.
15
14
x°
25
x°
30
Equation: _______________________
Equation: _________________________
x = _____________
x = _____________
Draw a figure and show your work.
24. The angle of elevation from a ship to the top of a 40 meter lighthouse on the shore is 18 degrees.
How far is the ship from the shore to the nearest meter?
25. Jim is flying a kite with 300 meters of kite string out. His kite string makes an angle of 64 degrees
with the level ground. To the nearest meter, how high is his kite?
26. Juliet on her balcony 15 feet off the ground spots Romeo approaching on the ground level. She
uses her angle measuring device and finds his position to be 3 degrees from the horizontal ( angle of
depression is 3 degrees) How far away is Romeo from the base of her balcony?