Algebra Final Study Guide—Answer Key
1. Use your pattern-detection skills to find a rule for the table below.
x
y
2
5
–1
–1
a.
Complete the table.
b.
What is the rule?
3
7
0
1
–3
-5
-1.5
–2
2x + 1
2. Examine the pattern of dots below.
Figure 2
Figure 3
Figure 4
a.
Describe the pattern. Can you think of another way to describe the
pattern?
b.
Find the number of dots for Figure 0, Figure 1, and Figure 5.
Fig. 0 = 1 dot; Fig. 1 = 3 dots; Fig. 5 = 11 dots
c.
Make an x  y table and write a rule.
Rule is 2x + 1
d.
Graph your rule on separate graph paper.
3. Angeni stacked some unit tiles to create the pattern shown below.
Figure 1
Figure 2
Figure 3

a.
Cholena predicted that Angeni would need five tiles to make the next
stack in the pattern. Decide with your team whether Cholena is correct.
Justify your answer by drawing the fourth figure.
Cholena is correct.
b.
Cholena decided to challenge Angeni by asking her to determine the
perimeter of Figure # 50. Explain how she could get the answer without
drawing the entire Figure.
104 units
c.
Angeni decided to return the challenge by asking Cholena to determine
which Figure will have a perimeter of 78 units. Find the answer for her.
Explain how you got it.
Figure 37
d.
Write a rule that determines the perimeter of any Figure.
Rule is : 2x + 4
4.
Adrian is in Algebra 2. He solved the equation 2 x 2  5 x  13  20 and got the
answer x  3 , but he’s not feeling very confident. Decide whether or not he
is correct and convince him of your position.
No the answer is x = - 11
5.
Create a tile pattern that grows by 3 tiles for every new figure. Draw figures
0, 1, 2, and 3 of your pattern. Make an x  y table to match your drawings
and write an equation (rule) for the table.
6.
Richard is frustrated. He knows the line to the right
should have a 3 and a 4 in the equation but he can’t
remember if it is y  4x  3 or y  3x  4 .
a.
7.
1
Which equation is correct? How do you know?
4x + 3 is correct
b.
4
• (0, 3)
It is very common for students to get confused like Richard because they do not
understand why the growth is multiplied by x and the y-intercept gets added (or
subtracted) to that. Discuss this as a group and write a clear explanation of why
the growth is multiplied by the x and the y-intercept gets added (or subtracted) to
that.
Molly and Tess like to shop at the mall. Their sister Jessica prefers to play
bocce ball instead. Molly has $280 in her bank account and spends $40
every trip. Tess has $170 in her account and spends half as much as
Molly during each trip. Jessica has $50 in her account and does not spend
any of it.
a.
Find the number of trips it will take for the Molly and Tess to have the
same amount of money in their accounts. Show all of your work and
explain your method for finding the number of trips.
5.5 ( or 6 trips)
b.
When will Jessica have the largest bank account? How do you know?
After 7 trips to the mall
x
8.
For each equation below, solve for x. Show all work.
a.
7x  3  4x  3
x=2
9.
6(2  x)  5(2x  4)
b.
x=-2
Find the mistake in the solution below and explain how to correct it. Find the
correct answer.
Algebra
3x  5  3x  x  8  x  1
6x  5  2x  7
4x  5  7
4x  12
x3
Steps
original problem
combine like terms
subtract 2x from both sides
add 5 to both sides
divide both sides by 4
X=2
10. Find the area of the shaded region in the figure below. Show all work.
11
5
5
2
2
7
77 – 25 – 4 = 48
11. Simply each expression by combining like terms.
a. 2x + 3y –y + 14 + 2y –xy –13
2x + 4y – xy + 1
b. –2xy + x + 4x –2y – (-4x) + 7
-2xy + 9x – 2y + 7
c. 3y - (-2x + 1) + 4xy –xy – y +2x
d. 5y + 3 –2 + x - x + 4 – (2y + 3 – 2x)
2y + 4x + 3xy –1
3y + 2x + 2
12.
Graph the following rules on one set of axes. Label each line with its
equation, the y-intercept, and a growth triangle.
a.
y  4x  3
b.
y  2x  5