Trig Pre Calculus Honors

Welcome to Pre-Calculus Honors!!
Attached is a packet containing items we feel are necessary for you to have mastered without
the use of a calculator to do well in Pre-Calculus Honors.
So, when you have a rainy day or are just sitting around on the beach, try solving these
problems and give your mind some “mathercise” so that you are at your best come the first day
of school!
This packet must be completed by the second day you are in math class and it will be
graded. We will go over all items in the packet for the first two or three days and then you will
be tested on this material.
Enjoy your summer and we look forward to meeting you in September!
Sincerely,
BHS Math Teachers
PS: A good website to check out if you need some help would be www.purplemath.com.
P.S.S.: You should be familiar with the graphs of y = x, y = x 2 , y = x 3 , y = x , y= e x , y = ln x.
There will be a quiz on day 2 of class.
Pre-Calculus Honors Summer Math 1

1. Real Numbers
Pre-Calculus
Summer Assignment
All Work MUST be shown on answer sheet!!
Find the decimal form for the rational number. State whether it repeats or terminates.
37
a.
8
13
b.
6
Use an inequality to describe the interval of real numbers.
c.
d.
2. Simplify
a) 100
b) 4 6
3 3 2 3 4
c) 2x
4x
2 y y
3. Factor completely
a)
2
6x
7x
5
b)
4x
16x
5 3
c) x
3 8
d)
3 2
x x x
2 4 8
e) x
3 2x
2 4x
8
Pre-Calculus Honors Summer Math 2

4. Simplify each expression (write with no negative exponents):
a)
2 5
5x 2x
2 2 2
b) 3
4xyz
3x y z
m n n
c) n m
x
x
d)
e)
f)
2 3
6xy
2 xy
1 0 1
2x2 x1
5x
2 x
3 2
4a b 3b
2 3 2 4
a b 2a b
5. Linear Functions
a) Write the equation of the line through the points (-1, 16) and (4, 2)
b) Write the equation of the line through (1, 3) and parallel to 2x3y 5
c) Write the equation of the line through the point (3, 2) with slope
d) Write the equation of the line through (2, 4) with m 0
e) The table below represents a linear function. Fill in the missing values.
4
m
5
6. Given f ( x)
x 2 4 and g ( x)
2x
4
Find
a) f(3)
b) f(g(x))
c) Domain of f(g(x))
d) g(f(x))
e) g(f(0))
f) the inverse of f(x)
Pre-Calculus Honors Summer Math 3

7. Solve
a) 7z – (2 + z) = 3(3z – 1)
b) 5(c + 3) + 4 < c – 1
c) |y + 2| = 5
d) 2 4 - 3x 7
e)
2
2
2x
32x
16x
y 2 y 1
f) 1
3 6
g)
3 2
6 34 20
x x x
8. Word Problems
a) Tickets to a concert are $5 for balcony seats and $10 for orchestra seats. If attendance was 600 and total
receipts were $4750, how many people bought orchestra seats
b) A commercial jet airplane climbs at takeoff with slope m=4/9. How far in the horizontal direction will
the airplane fly to reach an altitude of 20,000 ft above the takeoff point
c) Last week a theater purchased an air conditioner for $24000. The air conditioner’s value will depreciate
$4000 a year for each of the next 6 years. The equation y 24000 4000x,
0 x 6 models the air
conditioner’s value, where y is the value of the air conditioner and x is the number of years after the
purchase. In how many years will the value of the air conditioner be $8000
d) In a college meal plan you pay a membership fee; then all your meals are a fixed price per meal. If 30
meals costs $152.50 and 60 meals cost $250, find the membership price and the cost per meal.
o Write an equation for the cost of a meal plan, C, in terms of the number of meals, n.
o Find n in terms of C.
o Determine the maximum number of meals you can buy on a budget of $300. (algebraically)
e) An open box is formed by cutting squares from the corners of a regular piece of cardboard (15in. by
18in) and folding up the flaps.
o What size corner squares should be cut to yield a box with a volume of 225 in. 3
o What size corner squares should be cut to yield a box with a volume more than 225 in. 3
o What size corner squares should be cut to yield a box with a volume of at most 225 in. 3
Pre-Calculus Honors Summer Math 4

f) The former Republic Of Yugoslavia exported cars called Yugos to the United States between 1985 and
1989. The car is now a collector’s item. The table below gives the quantity of Yugos sold and the price
from 1985 to 1989.
Year Price in $ Number Sold
1985 3990 49000
1986 4110 43000
1987 4200 38500
1988 4330 32000
o Using the table, explain why Q could be a function of p.
o What does the rate of change of this function tell you about Yugos
g) Sammy sells pretzels for $2.25 each on a street corner in Boston. His average weekly costs for vendor
permit, pretzels, propane gas to heat them, and paper products is $315.00.
o Write an equation modeling Sammy’s weekly profit (P) as a linear function of the number (n) of
pretzels he sells each week.
o Use your equation to evaluate Sammy’s weekly profit when he sells 140 pretzels
o What is his weekly profit when he sells 450 pretzels
o Graph this situation, properly labeling the axes with the variables P and n. Include the points you
found in above on your graph.
Pre-Calculus Honors Summer Math 5

Pre-calculus Answer Sheet
1. Real Numbers
a. b.
c. d.
2. Simplify
a. b.
c.
3. Factor Completely
a. b.
c. d.
e.
Pre-Calculus Honors Summer Math 6

4. Simplify the Expression
a. b.
c. d.
e. f.
5. Linear Functions
a. b.
c. d.
e. f.
Pre-Calculus Honors Summer Math 7

6. Functions
a. b.
c. d.
e. f.
7. Solve
a. b.
c. d.
e. f.
g.
Pre-Calculus Honors Summer Math 8

8. Word Problems
a. b.
c. d.
e. f.
g.
Pre-Calculus Honors Summer Math 9