Welcome to Form 2!
This packet reviews the basic concepts covered in your Form 1 year at K-O. We
expect that you will be able to do all the material in this packet. The three main
areas that you should be comfortable with are:
1.) Integers – Accentuate the Negative
2.) Solving Equations
3.) Linear Equations – Moving Straight Ahead
If you have difficulty remembering how to solve some of these problems you may
look back at your notes from the past school year. If you encounter difficulty with
the majority of this review packet, you should seek extra help at the beginning of
the school year from your math teacher.
Please complete these worksheets and return them to your math teacher in
September. I would suggest working on them towards the end of the summer.
Please do not use your calculator and show all of your work.
Thanks, have a great summer and see you in September!
Ms. Sciglimpaglia
Middle School Math Coordinator
Accentuate the Negative
Solve the Problem:
1. 7 – 10 =
2. -7 + 10 =
3. -12 - -11 =
4. 11 - -8 =
5.
−24
−6
=
6. 25(-6) =
7. (-12)(-5) =
8. -27 ÷ 3 =
9. -15 – 7 =
10. 15 + -7 =
11. -1.5 + -8.5 =
12. 11 – 23 =
13. Cassidy wrote the equation n + 11 = 24. Using what you know about fact
families, rewrite the equation so that Cassidy could figure out the value of
n.
14. A. Below is a grid with four quadrants. Plot the following points, and
connect them with line segments.
Point A (1, 0)
Point B (3, 4)
Point C (4, 0)
b. On the same grid paper, transform your figure ABC using the rule (-2x, 2y).
Write the new coordinate points here:
Point A:
Point B:
Point C:
c. On the same grid paper, transform your figure ABC using the rule (2x, -2y).
Write the new coordinate points here:
Point A:
Point B:
Point C:
d. Without drawing, predict what will happen to ABC using the rule (3x, 3y).
e. Without drawing, predict what will happen to ABC using the rule (-3x, -3y).
15. Barry plays fullback on his high school football team. Sometimes he
gains yardage (+5 means a 5-yard gain). Sometimes he loses yardage (-3
means a 3-yard loss). Determine Barry’s total yardage in each game
below.
a. Game 1: +4
+6
+7
+1
-8
b. Game 2: +6
-3
0
+15
-1
+8
+11
-6
16. Suppose the Rocky Mountains have 72 centimeters of snow. Warmer
weather is melting the snow at a rate of 5.8 centimeters a day. If the snow
continues to melt at this rate, after seven days of warm weather, how
much snow will be left?
17. Please answer the following questions using the Order of Operations. Be
sure to show all your work.
a. (5 + -3)(4 – 2)
b. 32(-7 + 2)
c.
4 – 4 ∙ 2 + 2 ∙ -1
d. 2 ∙ (3 + -10) - 22
e. 10 – (50 ÷ (-2 ∙ 25) + 7) ∙ 22
18. Use the distributive property to write an equivalent expression and then
simplify the expression. Please show all steps.
a. -2(-8 + 5)
b. (-7 ∙ -2) - (-7 ∙ -12)
c.
X(9 + -5)
19. Use the distributive property to write each of these calculations in an
equivalent form.
a. (56 ∙ 115) + (56 ∙ -15)
b. 10( -6 – 3)
20. In the school’s Future Investment Club stock market game, the following
gains/losses in stock prices were earned over 10 days.
Companies often plot stock price gains/losses to display the changes over
time. Plot a graph of the (day, gain/loss) data from the Future Investors
Club.
Find the missing values:
21. ? ● 8 = 56
22. 12 ● ? = -36
23. ? ● – 10 = 90
24. 7 ● ? = -147
25. ? ÷ 18 = -54
26. 64 ÷ ? = 8
27. Find each missing value.
a. 13 – (8 – 2) = 13 – 8 - ?
b. -6 – (5 – 3) = -6 – 5 - ?
c.
12 – (6 - -1) = 12 – 6 - ?
d. -22 – (-11 – -4) = -22 - - 11 - ?
e. What patterns do you notice in these four problems?
28. Use the order of operations to simplify these expressions.
a. – 5 ● 7 + 10 ÷ 2
b. (2 + 4)2 ● 5 – 2
c.
-9 ● 8 ÷ 23 + -5
d. 6 ● (3 – 5)2 + 8
29. Use the distributive property to write an expression equal to each of the
following. Please be to simplify fully and show all work.
a. -3(4 + -7)
b. (-5 ● 3) – (-5 ● -13)
c.
10(-3 + 5)
d. (-12x) + (4x)
Solving Equations: Solve each equation for the variable. Remember to show all
your work! Remember you can do a check for any of these problems to make
sure you are correct.
1.
3(2x + 1) = 21
2.
3n + 2 = 4n – 5
3.
5p – 2p + 10 = 19
4.
-3(y – 4) = 15
5.
11x – 15 = 4x – 1
6.
5r + 6 + 2r = 48
7.
13 – 6y = -5 + 3y
8.
-24 = -8(-6c + 27)
9.
7(a – 2) – 6 = 2a + 8 + a
10.
8(5 – n) = 2n
11.
3x = 5(x – 6)
12.
27 + r = 3(1 – r)
Moving Straight Ahead
1.
Given one of the representations below, find the other two.
a.
Find the y-intercept for each representation above.
b.
Find the slope for each representation above.
2.
Use the graph below to answer parts a-d.
a.
List the coordinates of three points on the line.
b.
Which equation below is the equation for the line?
i. 𝑦 = 𝑥 + 4
ii. 𝑦 = 0.5𝑥 + 2
iii. 𝑦 = 0.5𝑥 − 5
iv. 𝑦 = 4 − 0.5𝑥
c.
Does the point (56, 35) line on the line? Explain your reasoning.
d.
Does the point (-20, -8) lie on the line? Explain your reasoning.
3.
Here is a graph of two lines:
a.
What is alike about these lines? What is different?
b.
The equation for line A is y = x + 3. What do you think would have to
change in order to make the equation for line B?
c,
Write the equation for line B.
d.
Imagine a line halfway between lines A and B. What do you think its
equation is? Explain your thinking.
4.
Here is a graph of a line:
a.
Complete this table and explain your thinking for the last three rows.
5.
Each table in i-v below represents a linear relationship. Do parts a-c for
each table.
a.
b.
c.
Find the slope of the line that represents the relationship.
Find the y-intercept for the graph of the relationship.
Determine which of the following equations represents the relationship.
6.
Write an equation for each of the four lines shown on the graph below.
7.
Do parts a-d for each pair of points below.
i.
(2, 8) and (4, 12)
a.
Plot the points on a coordinate grid, and draw a line through the points.
b.
Find the slope of the line through the points.
c.
Find the y-intercept from the graph.
ii.
(-3, 5) and (3, 1)
d.
Using your answers from parts a and b, write an equation for the line
through the points.
8.
On Saturdays, Jim likes to go to the mall to play video games or pinball.
Round-trip bus fare to and from the mall is $1.80. Jim spends $0.50 for each
video or pinball game.
a.
Write an equation for the amount of money, M, it costs Jim to go to the
mall and play n video or pinball games. Explain your reasoning.
b.
What is the slope of the line your equation represents? What does the
slope tell you about this situation?
c.
What is the y-intercept of the line? What does the y-intercept tell you
about the situation?
d.
How much will it cost Jim to travel to the mall and play 8 video or pinball
games?
e.
If Jim has $6.75, how many video or pinball games can he play at the
mall?
9.
In parts a-e, write an equation for the line that satisfies the given
conditions.
a.
the slope is 7 and the y-intercept is -2.
b.
the slope is 0 and the y-intercept is 9.18.
c.
the line passes through the points (3,1) and (6,4)
d.
the line passes through the points (-24,-11) and (-8,-3)
e.
the slope is − 3 and the line passes through the point (5,0)
2
10.
Here are some possible descriptions of a line:
A.
B.
C.
D.
E.
F.
G.
H.
I.
J.
positive slope
slope equals 0
negative slope
positive y-intercept
y-intercept equals 0
negative y-intercept
passes through the origin: (0, 0)
crosses the x-axis to the right of the origin
crosses the x-axis to the left of the origin
never crosses the x-axis
For each equation below, list ALL of the properties that describe the graph of the
equation.
a.
y=x
b.
y = 2x + 1
c.
d.
y = 4 – 3x
e.
y = -3 – x
11.
Circle the graph that matches the equation 𝑦 = 2 𝑥 − 1
3
y = -5