Download ACCELERATED MATH 1-2-3

ACCELERATED MATH 1-2-3
ALGEBRA I REVIEW
PACKET
NAME:
DUE DATE:
This packet contains review problems for all of the algebra topics taught in the
Accelerated Math course during the freshman year. Please spend some time each
week over break working these problems. About a week after school starts in July,
there will be a test over the problems in this packet.

The point of doing these problems is to solidify the concepts in your flipchart
into your brain!

For any applicable problem, you MUST SHOW WORK in order to receive credit!
CLASSIFYING NUMBERS
List all of the groups each number belongs to…
1. –4
2. 0
3. 
6. –2.487
7. –2.487…
8. –5
4. 4. 5
5.
9.
5
8
56
10. 4
Classify what number set each order of operation problem starts and ends in...
Expression
Begin
End
11.
83 9
12.
0  20  15
13.
52  12
14.
15.
1
 5  0.04
5
10  6  12  ( 12)
DISTANCE
Find the length of the line segment with the given endpoints…
1. (4, 5) and (-2, -7)
4. (-2, 1) and (3, -4)
2. (0, -2) and (5, 1)
5. (6, -1) and (5, 2)
3. (-1, -1) and (4, -4)
6. (6, 5) and (3, -4)
EXPONENT RULES
Simplify each expression…
1. 3x 2  4 y 2  (2x )2
2. (3x 2 )(4 y 2 )(2x )2
4. (2x 4 y 3 )2 (3x 3 y ) 3
5. 2x (3x 2  4 y 2 )
7. (2x y ) (4x )
10. (2x )(3x )2 (4 y )2
11. (8 y 3 )( 9y 2 )
13. (x 5 y 8 ) 3
14.
16.
2
3 2
(2x )(5x 2 ) 2
4x 3
(12x 3 )2
19.
(2x 4 )2
  
20. 2 x 5 x
2
2
12. 2x 3 ( 3x 2  2x  5)
15. 4x 3 (3x 2 ) 3
(3x )2 (x 5 y 8 )2
3 2
2
2
)
6. 5b 5  6b 7
17. (3a 4 )2 (2a 4 )3
5
3x 2 y (2 x
 2x3 y 

9. 
3 
 6 xy 
12x 3 y 5
8.
4x 2 y
2
3.
18. 5x (3xy )
 a 10 y 5 
21.  3 8 
a y 
2
FUNCTIONS
Tell whether each relationship is a function.
If it’s NOT, tell why not. If is it IS, give the domain and range.
1.
2.
3.
For each relation, write F if it’s a function, and NF if it’s not a function.
4. {(1, 2), (2, 2), (3, 2)} 5. {(-1, 0), (0, 1), (1, 2), (2, 3)}
7. {(1, 7), (2, 5), (3, 6), (2, 4)}
6. {(2, 1), (2, 2), (2, 3)}
8. {(0, 1), (-1, -2), (-2, -3), (-3, -4)}
Fill in the blank to…
a.
make the set a function
b.
make the set NOT a function
9. {(3, -3), (-10, 4), (6, 0), (
a. (
,
)
b. (
,
)}
,
10. {(0, 7), (7, 0), (-9, -7), (
)
a. (
,
)
b. (
,
,
Find the value of each…
11. If f (x )  x 2  5x  10
12. If g (x ) 
h(x )  3  5x 2
find f(-4)
find f(0)
find g(-4)
find g(0)
x 2  2
x 4
13. If
find h(-4)
find h(0)
)}
)
LINES-GRAPHING
Answer the questions…
1.
How would the graph of y  2x  1 change if the constant term was changed
to 5?
2.
How would the graph of y  2x  1 change if the coefficient term was
changed to 5?
3.
What would need to change in the equation y  
would rise as it goes from left to right?
4.
3
x  4 so that the line
4
How would the graph of y  4x  3 change if the coefficient of x was changed
to become –3?
Find the x- and y-intercepts for the graph of each function.
5. 3x  4 y  24
6. y  2x  4
7. y  4
8.
y  4 x 2  16
What is the equation of a line with…
9. an undefined slope through (5, -4)
10. with slope = 0 through (5, -4)
11. a slope of ½ and through (5, -4)
12. with slope = 0 through (4, -1)
Graph the line…
13. 3x+3y=15
14. 2x  3y  12
15. 4x  6y
16. x  3
13. x  3y  21
14. 4 y  8x  12
LINES-GRAPHING (cont.)
Write the equation of each line…
L3=
L7=
L5=
L2=
l1=
L8=
LINES-SLOPE
Find the slope for each situation below…
1.
between the points (-4, 5) and (5, 10)
3. slope of the line 4x  9  2y
2. slope of the line y=4
4. slope of the line containing the points
(-2, 5) and (-2, 6).
5. of this line:
6.
X
Y
-1
5
-1
10
-1
11
7. The line containing the points (-4, 3) and (6, 5)
8. 3x  5y  21
9. The line containing the points (5, -8) and (6, 12)
10. x  5y  20  x
Find the slope and the y-intercept of the graph of each equation…
11. y  2x  3
12.
y  x 4
13. x  y  1
14.
15. 3x  4 y  12
16. 3x  6y  18
2x  2y  5
LINES-SLOPE (cont.)
Find the slope between each pair of points.
1.
(-5, 1) and (-8, 13)
2. (-5,- 2) and (4, 0)
3. (11, 3) and (22, -4)
4. (2, 1) and (12, 5)
5. (3, -6) and (3, 10)
6. (4, 14) and (4, -4)
LINES-WRITING AN EQUATION FROM A TABLE
Write an equation for each table.
x
0
1
2
3
7.
Y
12
15
18
21
10.
8.
x
-5
0
2
4
Y
16
1
-5
-11
11.
2
4
6
8
8
10
12
14
13.
14.
3
5
7
9
8
10
12
14
9.
x
1
-2
3
6
12.
x
-3
1
Y
8
-4
5
3
-16
-10
x
1
-2
3
6
Y
5
-10
15
30
Y
2
-10
10
22
x
1
-2
3
6
Y
5
-10
15
30
15.
x
-5
0
2
4
Y
½
3
4
5
LINES-WRITING AN EQUATION FROM A TABLE (continued)
Follow the instructions:
STORY: In a race, Charlie has a 12 m headstart, but unfortunately, he gets confused
and runs the wrong way at 4 meters per second.
RECURSIVE ROUTINE:
EQUATION:
TABLE:
0
5
10
15
GRAPH:
USE THE EQUATION TO FIND:
*Where is he after 12 seconds ?
Find the x- and y-intercept for each equation.
1. 5x-3y=30
2.
2x+y=9
3. y=x
4.
y=2x+3
LINES-WRITING AN EQUATION FROM SLOPE + ONE POINT
Find the equation of the line through the given point with the given slope.
1. m = 
4
; through (-1, 5)
3
3. m = 0; through
2. m = 5; through
16
,9
3
3
,0
2
4. m = undefined; through (4, -3)
LINES-WRITING AN EQUATION FROM TWO POINTS
Write the equation of the line passing through each given pair of points.
5. (-2, 10) and (3, -5)
(3, 7)
8. (-12, 1) and (-12, 4)
6. (-4, -3) and (6, 2)
9. (5, 2) and (-5, -2)
11. the y-intercept is 5 and the x-intercept is 2.
7. (-4, 7) and
10. (-1, 5) and (2, -1)
12.
3
1
,0 and
,4
2
2
LINES-WRITING AN EQUATION FROM TWO POINTS (cont.)
Write the equation of the line passing through each given pair of points.
2. (4, 5) and 4, -12)
1. (-23, 1) and (5, 1)
(9, 5)
4. (-1, 4) and (-4, -5)
5.
3. (3, 1) and
1
3
,2 and
,4
2
2
6. (-3, 4) and (-5, 8)
X- AND Y-INTERCEPTS OF LINES
Give the x-intercept and the y-intercept of the graph of each equation below.
1.
2 x  5 y  20
2.
4 x  6 y  24
3. 9 y  3 x  45
4.
y  3 x  8
MIDPOINT
Find the midpoint between each set of points.
7. (-4, 2) and (0, 8)
(-3, ½)
8. (4, 3) and (-2, -1)
9. (5, 1) and
Segment AB has midpoint M. Find point B if point A has the given coordinates.
10. A=(-2, 3) and M=(5, 6)
and M=(2, 6)
11. A=(-1, -1) and M=(10, 12)
12. A=(5, -3)
MULTIPLYING BINOMIALS
Write each equation in standard form…
1. y  (x  4)(x  5)
2. y  (2x  6)(x  3)
3. y  (2x  6)(x  3)
1
4. y   (x  4)2  9
2
5. y  4  7x  2x 2
6. y  2(x  4)2  3
7. y  (x  4)(x  5)
8. y  (x  4)(x  5)
9. y  (x  3)(x  3)
1
10. y   (x  6)2  3
3
11. y  (2x  1)(x  4)
12. y  (2x  1)2
PARALLEL LINES
Find the equation of a line that’s PARALLEL to the given line and goes through the
given point.
13. Parallel to 6x + y = 4 through (-2,3)
15. Parallel to 4x + 2y = 8 through (1,3)
14. Parallel to y 
1
x  7 through (2, -5)
3
16. Are these lines parallel, perpendicular,
coinciding, or none of these?
2x  y  5
8x  4 y  20
PARALLEL LINES (continued)
Study the graph shown and answer the following questions…
1.
Write the equation of a line that is parallel to this line but
goes through (0, 2).
2.
Write the equation of a line that is perpendicular to this line
but goes through (0, -4).
PERPENDICULAR LINES
Find the equation of a line has the given information.
3. perpendicular to y =
3
x – 6 through (3, 4).
4
4. Perpendicular to
3x+8y=4; through (0,4)
5. Perpendicular to y=3x-2; through (6,-1)
through (8,-2)
6. Perpendicular to 5x-3y=7;
PROPERTIES OF REAL NUMBERS
Rewrite each expression to demonstrate the property asked for...
1. 2a  (5  6a )  _____________ Associative Property of Addition
2. 4  (2  8)  ________________Commutative Property of Addition
3. (10)(4)  (10)(7)  ________________Distributive Property of Multiplication over
addition
4. 4 (5  8)  _______________Associative Property of Multiplication
5. 4 (5  8)  _______________Commutative Property of Multiplication
Tell which property is being demonstrated for each statement below…
6. 5  0  0
7. 5  0  5
8. 5  1  5
1
9. 5   1
5
QUADRATIC EQUATIONS-GRAPHING
Tell whether each parabola will open UP OR DOWN and HOW IT WILL BE
TRANSFORMED from the graph of y  x 2 .Make a rough sketch for each equation.
Include the vertex, line of symmetry, and two other points using the stretch factor.
1. y  2x 2  3
3. y  2(x  3)2  4
2. y  (x  4 )2  2
4. y  (x  4 )2
Graph these equations and tell the x-intercepts, y-intercept, LOS, vertex, and include
5 points.
5. y  (x  4)(x  5)
6. y  x 2  2x  8
QUADRATIC EQUATIONS-GRAPHING (continued)
Graph these equations and tell the x-intercepts, y-intercept, LOS, vertex, and include
5 points.
1. y  x 2  3x  10
2. y  x 2  10x  21
Find the x-intercepts of the graph of each equation shown below.
3. y  (x  4)(2x  5)
4. y  x 2  10x  24
5. y  x 2  5x
QUADRATIC EQUATIONS-SOLVING
Solve for x in each equation below…
6. 3x 2  75
7. (x  5)2  12  156
8. 2x 2  5  7
9. x 2  x  20  0
10. x 2  3x  10
11. 2x 2  3x  4
QUADRATIC EXPRESSIONS-FACTORING
Factor each expression…
1. x 2  49
5. 2p 2  2p  4
2. x 2  2x  35
6. 3x 2  2x  5
3. 5x 2  20x  20
7. 4x 2  17x  4
4. 4 x 2  12x  9
8. 15x 2  27x  6
RADICAL EXPRESSIONS-SIMPLIFYING
Simplify the following expressions (“take out the twins or triplets!”)
9.
3
81p 4 r 6z 3
10.
(144 x 10 y 16 )
11.
12.
484
125a 30b 3
13. (3 2x 2 )3
14. 3 200n 6
15.
3
1000x 6 y 9
16. 4 44x 6 y 5
SEQUENCE NOTATION
1. What are the next three terms in the following arithmetic sequence?
1, 5, 9, 13…..
2. Using the sequences 1, 5, 9, 13…., find the 10th, 20th and 25th term in the arithmetic sequences.
3. Which equation represents the rule when finding the nth term of the sequence below?
2, 8, 18, 32…..
a)
an =n+1
b)
an =n2+1
c)
an =2n2
d)
an =2n+1
4. Using the formula and sequence from question 3, find the 10th term in the sequence listed above.
5. Using the geometric sequence formula, what are the next three terms in the sequence below?
4, 20, 100, 500…..
6.
Sequence application: A Hamilton High intern was offered a starting salary of $10,000, with an
annual raise of $500. What will her salary be after 10 years?
For questions #7 & 8, find the first 4 terms of the sequence.
7. A1=7
For n> 1, An= A(n-1) -5
8. A1=-12
For n> 1, An= A(n-1) +5
9. Find the 3rd & 4th term of this sequence. A1=-2 For n> 1, An= 2A(n-1) +5
SIMPLIFYING EXPRESSIONS
Simplify each expression…
17. 3x2 + 3y – (5 – 5x2)
18. cd + 5cd
19. 4 (2x  3)
20. 3x (3  4)  2(2x  1)
4x  (x  2)  2(3x  1)
22. 5x  x
21.
SOLVING EQUATIONS-ABSOLUTE VALUE
Solve each absolute value equation… (how many answers should you get for each?)
1. 2 x  1 = 15
4. m - 4 = 3
2. 2x  4  8  20
5. 3a  5  20
3. 2 x  4  4  6
6. 2 + 5x  2
+ 5 = 16
SOLVING EQUATIONS-CONTAINING SQUARE ROOTS
Solve each equation below…
7. 2 2x  1  5  19
8. 2 5  4 x
9. 2 x  1  3  13
SOLVING EQUATIONS- INCLUDING THOSE WITH
FRACTIONS
Solve each equation below.
10.
x x
 5
3 2
14. 5x  7  3x
11. x 
15.
x 7

2 8
3  (x  5)
2
2
12.
x 3 1
 
8 4 8
16. 5(x  3)  (x  2)  5(x  1)  1
SOLVING EQUATIONS- INCLUDING THOSE WITH
FRACTIONS (cont.)
Solve each equation below.
1.
2
1
x  10  x
3
4
4.
x  1 2x  2

5
3
7. 5x  7  3x
3.
x  4 2x

5
3
5.
8.
2x
4 2
5
3  (x  5)
2
2
2. 14  3(5x  12)  1  (20x  1)
6. 3(4x  12)  (2x  3)  4x  1
9.
1
k=8
4
SOLVING A FORMULA FOR A SPECIFIC VARIABLE
Solve each formula for the indicated variable.
1.
S  DT
3.
5.
2.
I  PRT , for T
y  mx  B , for y
4.
y  mx  B , for x
Ax  B  C , for B
6.
y
, for D
mx  b
, for b
A
SOLVING INEQUALITIES
Solve and graph each inequality…
10. y  2x  3
11. x  y  3
12. 3x  y  6
13.  x  3  4
1
2
SOLVING INEQUALITIES (continued)
Solve and graph each inequality…
3x
 6
4
1. 4  2(3  2y )  6y  20
2. 
3. 12x  8y  16
4. 4x  3y  6
SYSTEMS OF EQUATIONS ALGEBRAICALLY
Solve each system of equations. Remember to give your answer as an ordered pair…
5.
8.
y  x3
2x  5 y  7
6x  3y  2
4 x  2 y  8
6.
3x  y  5
3x  y  7
9.
7.
x y 6
2x  y  12
10  5 x  9
12  2 x  3 y
10.
3( x  y )  15
2x  y  7
SYSTEMS OF EQUATIONS ALGEBRAICALLY
Solve each system of equations. Remember to give your answer as an ordered pair…
1.
y  2x  1
3 x  2 y  16
2.
y  3 x  19
3.
y  x 1
5(2 x  y )  x  20
3x  8  4 x  2 y
SYSTEMS OF EQUATIONS BY GRAPHING
Graph the system and state the solution.
4.
2x  y  7
 3x  2 y  0
x  y  2
6. 
4x  2y  4
5.
x y 5
 2 x  y  4
6x  9y  27
8x  12y  36
7. 