Download Geometry - Blue Valley Schools

Geometry
Algebra Review Summer
Packet
Blue Valley Northwest
Page 1
Fractional Review
Add, Subtract, Multiply or Divide and then write answer in simplified form.
MULTIPLY
1)
1
5
3
2)
2 3

5 5
3)
7 2

8 3
4)
x 7

5 8
5)
7 3

a b
6)
4 2y

9
y
DIVIDE
7)
2
5
7
8)
3 1

8 8
9)
5 3

4 8
10)
x 1

9 3
11)
z 3

12 4
12)
a 3

b c
13)
6 1

7 14
14)
2
15)
3 1

4 9
16)
w 7

5 10
17)
a b

3 10
18)
1 1

x 12
20)
12 3

13 26
21)
9 1

10 4
23)
y z

4 6
24)
3 4

a b
ADD
3
5
SUBTRACT
5
7
19)
6
22)
x 6

10 5
Page 2
Order of Operations
Show all work!
Evaluate each expression.
1) 3 + 8  2 + 72
3) 5(13 – 9 )2 + 4
2) –1 + (3 – 7 4) + 8
3
3) 24 +
5)
7) 3 + –7
7) 8
9) –8 + 16  2 - 7.4
5
17  5
– 13
3
5) 3(0.5 + 6 ) – 2( 21  3)
2–5
8
+3
2
3 – 12  4
10) 17 –
3(27  3)
+ 14.5
22
Page 3
Solving Equations
Show all work!
Solve for the unknown.
1) –12 = 9w – 30
2) – 10 =
3(w  9)  4
4
3)
2  3x  1
 8
4
4) –3(5x – 4) = – 21
5)
x
– 8 = 12
5
6)
15  8  x  6 
 2.25
4
7) 11 = 6m – 7
8) 8(p – 3 ) – 9 = – 25
9) 15x – 6 –3x + 5 = 11
10) –18(y + 0.5) = 27
Rewrite the equation in slope-intercept form.
11) 3x + 2y = 16
12) 4x + 5y = 20
13) 6x – 2y = 13
14) x – 5y = 25
Page 4
Slope Intercept Form
Show all work!
1) Erin opened a savings account with $15. Then, every week she deposited $5. Write an equation in slopeintercept form that represents the data.
2) Graph the data for #1 on the coordinate axis on the following page.
3) Jenny has a jar of 20 jelly beans. Each hour she eats 5 of them. Write an equation in slope-intercept form
that represents the data.
4) Graph the data for #3 on the coordinate axis on the following page.
4
5) Write the equation of a line with a y-intercept of 6 and a slope of  .
5
6) Given the equation, y 
1
x  3 , find the slope and the y-intercept.
2
7) Graph the equation in #6 on the coordinate axis on the following page.
8) Given the equation, y  2 x  3 , find the slope and the y-intercept.
9) Graph the given equation in #8 on the coordinate axis on the following page.
10) Given the following data, find the equation in slope-intercept form.
Time (sec)
5
10
15
25
Distance (ft)
11
22
33
55
11) Write the equation of a line that has a slope of 3 and contains the point (4, -2) in slope intercept form.
12) Write the equation of a line that contains the points (6, 9) and (7, 5) in slope intercept form.
Page 5
Graph 1)
Graph 6)
Graph 3)
Graph 8)
Page 6
Writing Equations of Lines - Equations of lines passing through 2 points
For each problem, determine the slope of the line and write the equation of the line in both
y  y1  m  x  x1  and y = mx + b form.
1) (-2,-5) (-1,-1)
2) (11,6) (12,-2)
Slope:
Slope:
Point-slope:
Point-slope:
Slope-intercept form:
Slope-intercept form:
3) (5,5) (-1,8)
4) (2,3) (5,-2)
Slope:
Slope:
Point-slope:
Point-slope:
Slope-intercept form:
Slope-intercept form:
5) (6,8) (3,6)
Slope:
Point-slope:
Slope-intercept form:
Page 7
Parallel and Perpendicular Lines
Show all work!
1) Given AB , with the equation 10x  2y  8 , the slope of any line parallel to AB is ________.
2) With the equation 2x  6y  9 , write an equation of a line that would be parallel.
3) Given CD , with the equation 2x  5y  10 , the slope of any line perpendicular to CD is ______.
4) With the equation 3x  4y  16 , write an equation of a line that would be perpendicular.
5) What is the relationship between the graphs of these two linear equations?
2x  y  10
2x  y  10
6) What is the relationship between the graphs of these 2 linear equations?
-6x – 4y = 10
3x + 2y = 10
7) Out of these 3 lines, which two are perpendicular?
2
3
A. y  x  6
B. y  x  2
3
2
C. 3x  2y  6
8) Out of these 3 lines, which two are parallel?
A.
2x + 3y = 6
B.
4x + 6y = 5
C.
x – 2y = 10
C.
6x – 9y = 9
9) Out of these 3 lines, which two are parallel?
A.
-2x + 3y = 6
B.
6x + 4y = 12
Page 8
10) Write an equation of a line parallel to y = 2x – 7
11) Write an equation of a line perpendicular to y  5x  9
12) The slope of a line parallel to the line passing through the points (3, 4) and (7, -2) is ____________.
13) The slope of a line perpendicular to the line passing through the points (-3, 4) and (7, 2) is __________.
14) The slope of a line parallel to the line passing through the points (-2, 4) and (-5, -2) is ___________.
15) The slope of a line perpendicular to the line passing through the points (-6, -4) and (-1, 2) is ________.
16) The equations y = 2x + 5 and y = 2x – 5 describe lines that are parallel.
The lines are parallel because ______________________________________
1
x – 7 describe lines that are perpendicular.
4
The lines are perpendicular because __________________________________
17) The equations y = -4x – 7 and y =
Page 9
Slope-Intercept Form
Show all work!
1) What is the slope-intercept form of 4x + 5y = 20?
2) What does the slope of a line represent?
3) What is the y-intercept of the line that is described by the equation –x = -y?
4) Graph a line with a slope of 2/3
and passes through point (4, 1).
6)
5) Graph a line with a slope of 0
and passes through point (2, -3).
A can of pop in a vending machine sells for 50¢. The cost (y) of buying (x) cans of pop can be
represented by the linear equation y = 0.50x. Find the cost of 2, 4, and 5 cans of pop. Write the results in
coordinate form (x, y). Graph the points you find in the graph. Using this graph visually, determine the
slope of the line.
Page 10
7) Which graph shows the equation y = -3x + 6?
A)
B)
8) Write the equation of the line displayed in the graph. ___________________________
9) Write the equation of the line displayed in the graph. ___________________________
10) Write the equation of the line displayed in the graph. ___________________________
Page 11
Solving Systems of Equations by Substitution
Solve each equation by substitution. Show all work.
State the point of intersection as an ordered pair. Remember to check all work.
1)
y 3
3x  2y  8
2)
x  y 5
3x  2y  3
3)
y  2x  3
y  x 2
4)
x y 3
3y  12
5)
y  2x
x y 3
6)
y  x 3
4 x  y  32
7)
y 5x
x  5y  7
8)
y  x  13
2x  3y  1
9)
1  2x  y
1
3
x  3 y
4
4
10) The school that Krystal goes to sold tickets to a choral performance. The adult ticket price was $8, and a
student ticket was $5. On the first night they made $1196 and sold 190 tickets. How many adult and
student tickets were sold on the first night?
Page 12
Solving Systems of Equations by Elimination
Solve each equation by elimination. Show all work.
State the point of intersection as an ordered pair. Remember to check all work.
1)
2x  y  0
3x  y  10
2)
2x  y  3
3x  2y  22
3)
x y 8
2x  3y  20
4)
6x  y  31
4 x  3y  17
5)
x y  8
5x  3y  12
6)
2x  y  3
3x  2y  8
7)
2x  3y  18
x  y 5
8)
10 x  14 y  6
9x  8 y  26
9)
14 x  3 y  12
6 x  5 y  32
10) The school that Dan goes to is selling tickets to a play. On the first day of ticket sales the school sold 6
adult tickets and 16 student tickets for a total of $312. The school took in $189 on the second day by
selling 7 adult tickets and 7 student tickets. Find the price of an adult ticket and the price of a student
ticket.
Page 13
Quadratics
Multiply using the distribution property.
1) ( x  7)( x  4)
2) ( x  9)( x  8)
4) (4 x  5)(6 x  7)
5)  x  7   x  8 
7) ( x  5)2
8) ( x  7)2
3) (2 x  1)(3x  4)


6)  3x  4  2x  9 
9) 5( x  2)2
Factor each by finding the greatest common factor.
10) 9x – x2
11) x2 + 10x
12) 2x2 + 8x
13) 3x2 – 1x
14) 5ab2 + 25ab – 15b2
15) 12y + 24x – 18w
Factor each quadratic trinomial completely.
16) x2 + 10x + 16
17) m2 - 5m + 6
18) x2 - 6x - 40
19) x2 + 4x - 60
20) x2 + 2x + 1
21) x2 - 20x + 100
22) x2 - 12x + 35
23) b2 + 4b - 21
24) 2g2 + 16g + 30
Page 14