Download Resources for students entering Algebra II w/ Trigonometry

NAME: _____________________________
ALGEBRA II W/ TRIGONOMETRY
OPTIONAL SUMMER WORK
I. Evaluating Algebraic Expressions & Functions
To evaluate an algebraic expression:
 Substitute the given value(s) of the variable(s).
 Use order of operations to find the value of the resulting numerical expression.
Evaluate.
1)
b  b 2  4ac
if a  1, b  4, c  21
2a


2) A  P  1 
nt
r

n
if P = 650, r = 6%, n = 2, t = 15
Evaluate the following functions given:
x
f(x) = 4x – 12x + 7x
2
3) f(–3)
3
4)
æ1ö
g(x ) = 2 çç ÷÷
è 3ø
h(x ) =
g(2)
5)
4-x
-x 2
h(f(1))
II. Simplifying Radicals
An expression under a radical sign is in simplest radical form when:
1) there is no integer under the radical sign with a perfect square factor,
2) there are no fractions under the radical sign,
3) there are no radicals in the denominator
Express the following in simplest radical form.
1)
æ
è
öæ
øè
ö
ø
2) ç3 + 2 3 ÷ ç2 - 5 3 ÷
50
3) 3 2 + 4 8 - 5 50
4)
6
27
III. Properties of Exponents
PROPERTY
Product of Powers
a  a =a
x  x =x
Power of a Power
(am)n = am  n
(x4)2 = x8
Power of a Product
(ab)m = ambm
(2x)3 = 8x3
Negative Power
EXAMPLE
m
n
m+n
1
an
a-n =
Zero Power
a0 = 1
Quotient of Powers
am
= am – n
n
a
Power of Quotient
am
a
=
 
bm
b
4
2
1
x3
(a  0)
x-3 =
(a  0)
40 = 1
(a  0)
x8
 x6
2
x
3
m
(b  0)
x
x3

 
y3
 y
6
Simplify each expression using the exponent rules. Answers should be written using positive
exponents.
1)
g5 · g11
__________
2)
(b6)3
__________
3)
w-7
__________
4)
y 12
y8
__________
5)
(3x7)(-5x3)
__________
6)
(-4a5b0c)2
7)
- 15x 7
25x 9
__________
8)
æ 4x 9
çç
4
è 12x
9)
(
28m 3n -2
-2
4m -11n 4
)
__________
10)
ö
÷÷
ø
__________
3
__________
(3d m ) (2d m)
(4d m )
4
2
2
-2
-7
__________
7
IV. Solving Equations
Solve for the indicated variable. Express all answers as fractions in lowest terms. Circle your
answers.
1) 2[x + 3(x – 1)] = 18
3)
2x2 = 50
2) 6 + 2x(x – 3) = 2x2
4)
x + 4 + 8 = 2x + 4
5)
2
3
x - 18 =
x
6)
6
x -2
3
=
2x + 1
4
V. Operations With Polynomials
Perform the indicated operations and simplify (meaning collect similar terms).
1) (5x2 - 4) – 2(3x2 + 8x + 4)
2)
3) (5x – 6)2
(7x - 3)(3x + 7)
VI. Inequalities
Solve and graph the following inequalities on a number line. Write your final answer in interval
notation.
1) 4(x + 5) > 2x - 8
2) 2x - 3 > 9 or 3x £ 12
3) -3 £ 2x - 11 < 7
VII. Factoring Polynomials
Factor the following completely.
1)
16y2 + 8y
2)
x2 + 11x + 24
3)
3m2 - 3m + 10mn – 10n
4)
x2 - 2x – 63
5)
6y2 - 13y – 5
6)
4x2 - 121
VIII. Linear Equations in Two Variables
1) Write an equation, in slope-intercept form using the given information.
a. (5, 4) m = -
2
3
b. (-2, 4)
m = -3
c. (-6, -3) (-2, -5)
2) In 1998, Margo had $429 in her bank account. By 2010, she had $2540. Find the rate of change
for her bank account.
3) Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per
month and charge $40 per hour per student.
a) Write a linear equation to represent this situation.
b) If they have 15 students each for one hour per week how much income do they make together
in a month? (assume 4 weeks per month)
c) If they earn a total of $3760 in February, how many tutoring sessions did they provide that
month?
IX. Graphing Linear Equations
Graph each of the following linear equations.
y=
1)
2
3
x -4
2)
x + 3y = 6
3)
y+2=7
X. Solving Systems of Equations
Solve each system of equations algebraically.
1)
y = 2x + 4
-3x + y = - 9
2) 2x + 3y = 6
-3x + 2y = 17
XI – Right Triangles
Find the missing side length(s):
Pythagorean Theorem:
1)
2)
41
3 5
3 2
9
Special Right Triangles (30-60-90)
Special Right Triangles (45-45-90)
Trigonometry (SOHCAHTOA)
XII. – Scatter Plots
Below is a chart showing number of calories in food served at Wendy’s as well as the calories of
fat in the specific food. Draw a scatter plot (use an appropriate scale!!) for the information
and then answer the questions below. (3 pts)
# calories (x-axis)
# g of fat (y-axis)
530
28
500
24
180
12
450
30
580
31
670
32
500
33
310
16
1090 290
66
13
1. What type of correlation is there on the scatter plot you drew below?
2. Draw a line of best of fit for the graph and find the equation for the line of best fit.
Round all numbers to the nearest thousandth
3. How many calories would you expect something to have if it had 44 g of fat?
4. How many grams of fat would you expect something with 800 calories to have?