Download Given the sets below answer the following questions.

SUMMER REVIEW
ACCELERATED ALGEBRA II
DIRECTIONS : COMPLETE ALL EXERCISES. SHOW ALL STEPS
NECESSARY TO COMPLETE EACH PROBLEM. IF ADDITIONAL
SPACE IS NEEDED, COMPLETE WORK ON LOOSE LEAF PAPER,
AND ATTACH THIS TO THE PACKET WHEN IT IS RETURNED.
1
SUMMER REVIEW FOR ACCELERATED ALGEBRA II
SETS OF NUMBERS ( GO TO SETS ON THE MATH PACKET HELP PAGE)
State which of the following are infinite and which are finite.
1. {residents of North America}
Ans. ____________________
2. {the fractions between 0 and 1}
Ans. ____________________
3. {words in your dictionary}
Ans. ____________________
4. {the odd integers greater than 5}
Ans. ____________________
In column II find a set equal to each set in Column I
Column I
Column II
5.
{0, 1, 4, 9, 16, …}
a.
{1}
6.
{0, 1}
b.

7.
{integral multiples of 4 }
c.
{squares of the integers}
8.
{the integer equal to its double }
d.
{nonnegative even integers less than 3 }
9.
{integers between 1/2 and 3/4 }
e.
{ integers which equal their squares}
f.
{ …, 12, 8, 4, 0, 4, 8, 12, …}
10. {the number whose sum with 5 is 5}
11. {negative integers between 1
3
g.
{0 }
and 4}
4
12. { 0, 2 }
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2
Replace each
with one of the symbols
There may be more than one correct answer.
, , , , ,  to make a true statement.
1. heart ______ { the organs in the human body }
Ans. _____
2. { March } ______ { the months of the year }
Ans. _____
3.
9  6 ______  3  4  
4. {5, 4, 3 } ______
Ans. _____

Ans. _____
5. { the letters in the word “net” } ______ { the letters in the word “entry”}
1 
9  5

 ______  21  
3
 2 

Ans. _____
4,5, 6 _____ 6,
Ans. _____
6. 
7.

1
2
8.  ,
9.
10.
10
1

, 2  2
2

3
1 
, 1 ,  ______ 0, 0.75, 1.25, 0.5
4
4 
4  3 ______ 8,10,12
 4  3 
______ 8, 10, 12
Ans. _____
Ans. _____
Ans. _____
Ans. _____
Let K = {7, 27, 14 }. List all the subsets of K that:
11. Have exactly one element
12. Have exactly two elements
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13. Have three elements
14.
Have {7, 7+7 } as a subset
15.
Have no elements
16.
Are subsets of {multiples of 7}
Given the sets below answer the following questions.
1. P = {3, 5, 7} and Q = {7, 9, 11}. Give P  Q and P  Q
Ans. P  Q = {
PQ={
};
}
2. C = {4, 2, } and D = {2, 4, 6}. Give C  D and C  D.
Ans. C  D = {
};
CD={
}
3. Give the intersection of the set of negative integers greater than 6 and the set of
integers between 4 and 4.
Ans.  = {
}
4. Give the union of the set of whole numbers less than 5 and the set of positive integers between 1/3 and 4/5
Ans.  = {
}
5. Give the intersection of the set of natural numbers less than 5 and the set of whole numbers less than 5.
Ans.  = {
}
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SIMPLIFYING NUMERICAL EXPRESSIONS (GO TO SIMPLIFYING NUMERICAL EXPRESSIONS
ON THE MATH PACKET HELP PAGE)
Simplify each expression
4
1.
(18)(5)
 
6.
2 43  3 4 2  5 4  7
7.
 2  7  2   32  3
8.
5 23  1 2 2  9 2  1
1

10
2.
27

2
(18)(0)
3
3.
4.
5.
144
   

1
1
1
6
2
3
32 6  3
9.
1
18     5  9
2
2 1   3  1
2
10.
8 2  2  3   32  1
11.
5 2 5 2
5 5
22  1
1
59   8  7  1  5
2
SIMPLIFYING POLYNOMIAL EXPRESSIONS ( GO TO SIMPLIFYING POLYNOMIAL
EXPRESSIONS ON THE MATH PACKET HELP PAGE)
Add the polynomials
1)
2z3 - 3z2 + 2z + 5
z3 + z2 - 2z + 3
2)
t4 - 3t3 + 2t2
- 4
2t3 + 3t2 + 2t + 1
4)
4p2q - 3pq2 + 4pq - 5
p2q - pq2 - pq + 5
Subtract the lower polynomial from the one above.
3)
5n5 - 3n3
+ 2n - 1
2n5 + n3 - 3n2
+ 2
Give the sum when the second polynomial is added to the first.
5)
12x3 - 5x2 - 3x + 15
,
 19x3 + 4x2 - 10
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Give the difference when the second polynomial is subtracted from the first.
6)
5n2 - 3n + 2
,
2n2 + 4n - 3
5
Simplify each expression.
7)
3t2 + 4t - t2 - 4t Ans. _____________
9)
3y + 2(y + 1)
11)
(z2 - 3z + 5) - (2z2 - 3z + 2)
Ans ___________
8)
10)
4x2 - (4x2 - 3x + 2) Ans. _______________
12)
(4r3 - 3r + 7) + (2r2 - 2r + 1)
11. Ans. ____________________
13)
4x + 7x2 - 2x - 6x2 Ans. ___________
12. Ans. ___________________
(5x2 - 3x + 2) - (3x2 + 5x - 1) + (2x2 - 3)
13. ____________________________
14)
3(4y2 - 7y +4) - 4( -2y2 + 5y + 3)
14. ___________________________
15) (3 - 4a - 2a2) - (3a + 2a2) - (4 - 4a2)
15. ___________________________
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SOLVING LINEAR EQUATIONS (GO TO SOLVING LINEAR EQUATIONS ON THE MATH
PACKET HELP PAGE)
6
Solve each equation over 
1.
6n  2  2n  5  6 5  n 
2.
3 7  2 x   30  7  x  1
3.
3 t   2t  3  2t    9
4.
2  z   z  1    3  z  1
5.
8
 11  7
r
6.
7
16
 1
k
Compiled by Hatboro-Horsham Mathematics Dept. Not to be duplicated
There are a number of ways to solve the following equations which contain fractions. One suggestion is
to first multiply both sides of the equation by the least common denominator (LCD) to remove the
fractions. Then continue as usual.
7
7.
y 3y

 2
5
5
8.
1
2
 n  5    4  2n    6
3
3
9.
1
7
 a  a   21
4
4
10.
3
5
 2b  5   3b  9    6
4
4
12.
3
6
x  13

 2
x
x 1
x x
11.
y 5
3 y

 1
12
8
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PROBLEMS INVOLVING FUNCTIONS (GO TO FUNCTIONS ON THE MATH PACKET
HELP PAGE)
8




Evaluate each function for the given values of x.
1. f(x) = 20x – 4 for x = -2 and x = 8
2. f(x) = 3x – x2 for x = -1 and x = ½
Find (f+g)(x) and (f-g)(x) for each of the following.
3. f(x) = 7x2 + 5x, g(x) = x2 – 13
4. f(x) = -9x2 + 6, g(x) = 12x2
f
Find  f  g x  and   (x) for each of the following. State any domain restrictions.
g
2
5. f(x) = 2x + 4, g(x) = x2 – 4
6. f(x) = 3x + 6, g(x) = 9x
Let f(x)  2x2, g(x)  x  5, and h(x)  x  1 . Evaluate the following.
7. f(g(-1))
8. f(f(2))
9. h(g(-10))
10. g(f(–3))
GRAPHING LINEAR EQUATIONS ( GO TO GRAPHING LINEAR EQUATIONS ON THE MATH
PACKET HELP PAGE)

Find the slope of the line containing the following pairs of points
1. (2., 5) and (-4, -8)

2. (-1, -6) and (4, -10)
3. (0, 8) and (-5, -7)
Write an equation in standard form for the line with the following properties.
1. Passes through (2, 10) and (3, 35)
2. Passes through (-3, 0) and (2, 2)
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3. m = -24, passing through (-8, 6)
4. m = 4, passing through (0.8, 10)
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5. x-intercept of 5, y-intercept of 3

6. Passing through (3, 5) and (3, -8)
Write an equation in slope-intercept form for the line with the following properties.
7. Passing through (-1, -4) and (3, 5)
1 3
8. Passing through (3,1) and ( , )
2 2
DETERMINING THE EQUATION OF A LINE (GO TO DETERMINING THE EQUATION OF A
LINE ON THE MATH PACKET HELP PAGE )
 Write an equation in standard form for the line with the following properties.
1. Parallel to y = 3x – 2, passing through (6, -4)
2. Parallel to x + 2y = -6, passing through (2, -2)
3. Perpendicular to y = 5x, passing through (10, 2)
4. Perpendicular to 2x–3y = 7, passing through (1, –1)
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SOLVING TWO EQUATIONS IN TWO VARIABLES (GO TO SOLVING TWO EQUATIONS IN
TWO VARIABLES ON THE MATH PACKET HELP PAGE )
10
Choose the most appropriate method for finding the solutions to the following systems. Then solve.
1.
5 x  9 y  7
2 x  3 y  1
2
1
x  3y 
3. 3
5
2x  9 y  4
5.
y  5x  2
y  2x 1
2.
2x  3y  7
6 x  9 y  10
1
3
x  y  10
4. 2
4
2x  y  8
6.
3x  4 y  11
2x  4 y  8
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CRAMER’S RULE (GO TO CRAMER'S RULE ON THE MATH PACKET HELP PAGE)

Use Cramer’s Rule to find the solutions to the following systems.
11
8x  7y  5
1. 
 4x  9y  65
7x  5y  14
2. 
 4x  3y  9
3x  7y  25
3. 
5x  8y  27
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SOLVE THE FOLLOWING WORD PROBLEMS INVOLVING SYSTEMS OF EQUATIONS .
(GO TO SOLVING TWO EQUATIONS IN TWO VARIABLES ON THE MATH PACKET HELP
PAGE)
1. Tickets to a class play were 25 cents for students and 50 cents for adults. In all, 275 tickets were sold, and
the total receipts were $118.75. Find the number of tickets sold at each price.
2. Mary weighs 3 pounds more than Jane, and together they weigh 16 pounds less than the center of the
football team, who weighs 213 pounds. How much does each girl weigh?
3.
In a two-digit number, the tens digit is 5 more than the units digit. If the digits are interchanged and the
number represented by the resulting numeral is added to the original number, the sum is 143. Find the
original two digit number.
4.
A boat can travel 6 miles downstream in 40 minutes. The return trip requires an hour. Find the rate of
the boat in still water and the rate of the current.
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INEQUALITIES ( GO TO SOLVING TWO EQUATIONS IN TWO VARIABLES ON THE MATH
PACKET HELP PAGE )

Solve and graph the following compound inequalities.
1. 2x  3  5 and 3x  7  8
4. 5x  1  19 and10  x  4
2. 8x  7  13 or 6x  5  16
5. 2x  6  10 or  3x  5  20
3. 3(x  2)  9 and
2
x 5  7
3
ABSOLUTE VALUE INEQUALITIES (GO TO SOLVING ABSOLUTE VALUE INEQUALITIES ON
THE MATH PACKET HELP PAGE )
Solve and graph the following absolute value inequalities.
1.
5x  2  7
2.
6x  4  3
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Compiled by Hatboro-Horsham Mathematics Dept. Not to be duplicated
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