Download summer review packet for students entering algebra 2

SUMMER REVIEW PACKET
FOR STUDENTS ENTERING
ALGEBRA 2
Freeport Junior High School
Mrs. Fello
Note: All problems should be completed WITHOUT a calculator with work shown for
each problem.
Concept 1: Solve Linear Equations and Systems of Equations
Solve each equation for x. Show all work.
1.
7x – 10 = -4
2.
4.
8x + 14 – 25 = 17 – 10x + 18x
5.
7.
15x + 18 – 24 = -4( 80 – 4x )
8.
6( 4x – 7 ) = -246
3.
3x – 2 ( x + 1 ) = -10
6.
-125 = -7( 2x – 4 ) + 8x
14 – ( 3 – 2x ) = 3x – x + 11
9.
5x + 4y = 2
3.
Solve each system of equations. Show all work.
1.
-2x + y = 8
2.
y = -3x – 2
4.
x = 4+y
4x + 2y = -2
5.
Y = -20 – x
5 =
2x – 7y = -14
y =
6.
3x = 20 – 4y
7x + y = 5x + 4
2x + y = 6
Solve each literal equation for the specified variable.
1.
2x – 3y = -24 for y
2.
A =
for h
3.
X = (2y – 18 )5 – 3y for y
Concept 2: Solve Quadratic Equations by factoring
Solve each quadratic equation by factoring.
1.
X2 – 196 = 0
2.
X2 = 8
3.
4x2 + 12x = 0
4.
x2 – 9x -22 = 0
5.
X2 = -7 – 8x
6.
-60 = -x2 – 4x
7.
x2 -12x + 32 = 0
8.
5x2 – 3x = -7x + 2x2 + 32
9.
4x2+ 10x – 6 = 0
11.
-66 = x2- 17x
12.
2x = -1 – x 2
10. 44x2 = 99
Concept 3: Solve linear inequalities and graph the solution.
Solve each inequality. Then graph the solution on a number line.
1. 2x – 3 > 11
2.
-8 ≤ 2x – 12 < 10
3.
15 – 2x ≥ -18
4.
5.
-18 > 14 – 2x
6.
24 > -9 – x – 3x – 15
18 – 7x ≥ -5( x – 10 )
Concept 4: Solve absolute value equations and inequalities.
Solve each equation for x.
1.
| 4x – 2 | = 24
2.
15 + | 4 – 3x | = 25
3.
| x + 4 | = -20
4.
| 2x – 5 | ≤ 10
5.
| 3x – 4 | ≥ -5
6.
18 + | 3x – 6 | < 24
Concept 5: Find the Slope given two points.
Find the slope of the line containing the given points.
1. ( -3, 5 ) and ( 5, -6 )
2.
( 4, 12 ) and ( -4, -4 )
3.
( 4, 7 ) and ( 3, 11 )
4.
5.
( 6, 10 ) and ( -9, 10 )
6.
( -5, -8 ) and ( -3, - 7 )
( -5, 6 ) and ( -5, 9 )
Concept 6: Write equations for lines.
Write the equation for the line with the given information.
1.
With slope = and y-intercept ( 0, -3 )
2. Containing the two points ( 3, 8 ) and ( 1, 4 )
3. Parallel to y = -3x + 4 that also contains the point ( 2, -8 )
4. Perpendicular to y =
5. With slope =
6.
7.
8.
9.
10.
11.
that also contains the point ( -1, 4 )
that also contains the point ( -12, 4 )
Containing the points ( 4, -7 ) and ( 4, 8 )
Parallel to y = 7 + x that contains the point ( 4, -8 )
With slope = -4 that also contains the points (3, 7 )
With an undefined slope that contains the point ( 6, 10 )
That contains the point ( 1,1 ) and has a slope of 0
Perpendicular to y = -4x – 2 that contains the point ( 7, -2 )
Concept 7: Graph and write linear equations.
1.
y = x–6
2.
slope:_____ y int: _____
4.
y = 4
slope:_____ y int: _____
7.
y + 2x = 7
slope:_____ y int: _____
Y = -
3.
slope:_____ y int: _____
5.
Y =
slope:_____ y int: _____
8.
y > 2x - 5
slope:_____ y int: _____
Y = -2x
slope:_____ y int: _____
6.
X = -2
slope:_____ y int: _____
9.
Y ≥ 6x – 9
slope:_____ y int: _____
10.
Y < 6
11.
slope:_____ y int: _____
X ≥ 4
12.
slope:_____ y int: _____
3x - Y > -9
slope:_____ y int: _____
Concept 8: Multiply Polynomials
Multiply. Write your answer in standard form.
1. ( x + 8 )2
2.
( 3x – 4 )2
3.
( 4 –x )( 4 + x )
4.
( x- 6 )( x – 4 )
5. ( x + 3 )( x + 8 )
6.
( x – 11 )( x + 8 )
7.
( 2x – 3 )( x + 5 )
8.
( x + 5)( x2 – 3x – 5 )
(
)
Concept 9: Simplify Expressions
Simplify each expression.
1.
4. (
(
)
)
(
2.
)
5.
3.
( 80 – 125 ) – ( -40 + 28 )
6.
6x – 4y + 16x + 12y
7. 12x – ( 5 – 3x )
8.
-3xy3( x – 2y )
9.
10. 3( x + 2 )2 – 3( x – 4 )
11.
115 – [ 80 – ( 9 – 2 )2] + 112
12.
Concept 10: Factor polynomials
Factor each polynomial. (Be sure to first factor out the GCF)
2.
X2 – 13x – 30
3.
5x2 – 8x – 4
4. 9x2 – 49
5.
X2 + 16x + 64
6.
5x2 + 35x – 40
6. 3x2 + 5x
8.
2x2 + 5x -7
9.
12x3 – 52x2- 40
1.
X2 – 19x + 48
Concept 11: Write a linear model to represent a word problem.
1.
Each night after dinner, a family goes to the cookie jar and eats 6 cookies. The cookie jar holds 214 cookies
when it is completely full. Write a linear model to represent the number of cookies in the jar, y, in terms of the
number of days since the jar has been full, x.
b. Use the above equation to determine the number of cookies left 10 days after it had been filled.
c. Use the above equation to find the number of days it will take to empty the jar if the family continues to eat them
at the same rate.
2.
Joe goes to the store and buys x pounds of jelly beans that cost $8 per pound and y pounds of chocolate that
costs $10 per pound. Write an equation which can be used to find all combinations of jelly beans and chocolate
that will cost exactly $56.
3.
Last summer Ben purchased materials to build model airplanes and then sold the finished models. He sold each
model for the same amount of money. The table below shows the relationship between the number of model
airplanes sold and the running total of Ben’s profit.
Ben’s Model Airplane Sales
Model planes sold
12
15
20
22
A.
Total profit
$63
$135
$255
$303
Write a linear equation, in slope-intercept form, to represent the amount of Ben’s total profit (y) based on the
number of model airplanes (x) he sold.
B. Use your equation to find how much did Ben spend on his model – building materials?
C. Use your equation to find the fewest number of model airplanes Ben needed to sell in order to make a profit?