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Garnet Valley High School
Practice Set of Required Math Skills for
Algebra III
Students should practice each of the following skills to prepare for your next math
class. The math packet will be collected on the first day of class. A graded
assessment about these skills will be given and will count as your first math
grade for the school year. For extra practice on each topic, go to the following
websites:
http://www.khanacademy.org/math/algebra2
http://www.kutasoftware.com/freeia2.html
Part A: Simplify Algebraic Expressions:
Simplify the following.
2
1. 8 3
4.
2.
x
1
8.
1
x 1
12
3.
5. 45x7 y 4 z  9 x 2 y8 z 4
16 x2  3x3
7.
81x5
3x
6.
1
3

x x 1
9. (2 + i)2
6 x  18
x2  9

x2  4 x2  5x  6
Part B: Factor Polynomials
Factor each expression completely.
1. 3 x 2  5 x  2
2. 4 x 2  8 x  4
3. b 2  11b  26
4. 3x3  9 x 2  7 x  21
5. 5 x 2  7 x  6
6. 6 x  24 y
Part C: Solve the equations with logarithms
7) log3 x  2
8)
log2 16  x
9)
log x  log 4 x  2
Part D: Solve linear equations, inequalities, linear systems, quadratic, absolute
value and polynomial equations.
1. 3 y  9  6  6 y
3x  3 y  18
2. 3 y  20  y  6  3 y  6
2x  3y  8
3. 3x  15
1
1
1
 x  2    x  3 
4
5
2
5x  2 y  1
6.
x w
 , for z.
y z
9. C  2 r , for r.
10. 2 x 2  7 x  15
11. x3  x 2  x  1  0
12. x 2  4 x  6  0
13. 2 x  4 3
14. 2 x3  10 x  0
15. x 2  144  0
17. x 2  14 x  45  0
18. 2 x 4  32
20. 3x  1  3
21. 2 x  3  1
4.
7.
16.
4x  y  5
2 x
5
5
5x  4  12
19. 3  2x 1  4
5.
8.
Part E: Evaluate functions , write equations for functions, and graph functions.
Given
1) f(-2)
f  x   3x  2, g  x   2x2 , and h  x   2 x. Answer the following 4 questions:
2) f(g(-3))
3) f(g(x))
4) h(f(0))
5) Write the equation in standard form of the line through the two points:
(1, -3) and (4, -2)
6) Find an equation in slope-intercept form of the line containing (2, -5) and parallel to
the line 4x + 5y = 8
7) Find all x-intercepts and y-intercepts for the equation f(x) = 2x2 – 16
8) A cubic polynomial has at most how many x-intercepts?
9) Write the function g(x) if the parent function f(x) = x2 is vertically stretched by a
factor of 3, reflected across the x-axis, translated 2 units to the right and 5 units up.
Graph the linear systems to determine the solution:
10)
y = -3x + 4
11)
x<5, y≥0
3x – 2y = 12
5y < 3x– 1
Graph the following quadratic functions and answer the questions that follow:
16) a) Graph y = x2 – 4x + 2
17) a) Graph y = -2(x – 1)2 + 3
b) Find the vertex
b) Find the vertex
c) Find the y-intercept
c) Find the y-intercept
d) Find the x-intercept(s)
d) Find the x-intercept(s)
e) Find the domain and range:
e) Find the domain and range:
Part F: Solve word problems
1) Niko’s pool table is 1 foot longer than twice the width. The area of the pool table is
15 ft2. Find the dimensions of the pool table. Find the perimeter of the pool table.
2) If a mixture of a 6% acid solution with an 11% acid solution is to be made, how much
of each solution is needed to make 10 liters of an 8% acid solution?
3) The sum of twice a number and -6 is nine more than the opposite of the number.
Find the number.
4) A car uses 15 gallons of gas to go 330 miles. How much will the car need to go 450
miles?
5) Wayne buys a motorcycle for $8000. Each year, the motorcycle loses 20% of its
resale value from the previous year. How much is the motorcycle worth after 3 years?
Part G: Geometry/Trigonometry
1) Solve the right triangle (find all the missing parts) if the right angle is angle C, angle
A is 25˚ and side b is 8 inches.
Special Right Triangles: Leave answers as simplified radicals.
Find the missing sides.
2.
3.
4.
60
t
10
7
r
x
3
y
v
s
5. Use a calculator to solve the following. For letter b – solve for Y given 0˚≤Y≤360˚.
8
m
a. sin 47 = X
b. tan Y  3.223
c. cos 41 
d. sin 83 
z
45
Use the diagram below to answer
each of the questions to the right.
12
6. Give sin B to 4 decimal places. ____________
7. Give cos B to 4 decimal places. ____________
A
8. Give tan A to 4 decimal places. ___________
5
13
B
9. Find  A. ___________
Find x and/or y in each of the following:
2
10.
y  80
3
100  2x
11.
11x 110
4x  5
130
2( y  3)
12.
4 x
2
x 16
3
13.
4
x
5
122
y 2 15
Selected Answers:
4x 1
x( x  1)
9) 3  4i
Part A:
4) 4 x 2 3x
6)
Part B:
1) (3x + 1)(x – 2)
4) (x – 3)(3x2 – 7)
Part C:
8) x = 4
9) x = 5
Part D:
5) (1, -2)
12) 2  i 2
Part E:
3) 6x2 – 2
7) x-int: ( 2 2 , 0) y – int: (0, -16)
Part F:
2) 6 liters of the 6% solution, 4 liters of the 4% solution
Part G:
B  65, c  8.827, a  3.730
18) x  2, 2i
5b) Y = 72.76˚ or 252.76˚