OGT Review Worksheet Patterns, Functions, and Algebra – Part One

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OGT Review Worksheet
Patterns, Functions, and Algebra – Part One
1.
The table above represents what type of function?
A. nonlinear
B. neither linear nor nonlinear
C. linear
D. linear and nonlinear
x
y
-2
-20
-1
-5
0
0
1
-5
2
-20
2. June wants to plant a vegetable garden. The graph below shows the area of the garden based
on the length of the garden.
Which equation below represents the area of the garden, A, based on its length, x?
A.
B.
C.
D.
3.
4. The graph above represents what type of function?
A. both linear and nonlinear
B. linear
C. neither linear nor nonlinear
D. nonlinear
5. Solve the inequality below for n.
15n - 7 > 9n - 61
6.
Which graph corresponds to the equation above?
W.
X.
Y.
Z.
7.
y = -14x + 9
Is the equation above linear, nonlinear, both linear and nonlinear, or neither linear nor nonlinear?
8.
9. A chemist is conducting an experiment which involves a certain chemical reaction. He begins
the experiment with 741 milliliters of the chemical, which is consumed by the reaction at a
varying rate that is no more than 16 milliliters per minute. Partway through the experiment, the
chemist measures the amount of chemical remaining. If there are 645 milliliters of the chemical
left, what is the smallest number of minutes that could have passed?
10. Which of the following patterns is determined from the expression below?
7n2 - 2n
A. 5, 6, 3, -4, -15, ...
B. 5, 10, 15, 20, 25, ...
C. 5, 24, 57, 104, 165, ...
D. -5, -6, -3, 4, 15, ...
11. The city of Cartesianville is sponsoring an event to collect food for those in need in their
community. A local church has already donated 357 pounds of food. The event is expecting
102 attendees. Based on the inequality below, how many pounds of food, f, should each attendee
donate in order to collect at least 1,071 pounds of food?
357 + 102f > 1,071
12. What is the value of the 8th term in the sequence?
1 , -3 , -7 , -11 , -15 , ...
13.
W.
X.
Y.
Z.
14.
y = -6x + 7
Is the equation above linear, nonlinear, both linear and nonlinear, or neither linear nor nonlinear?
15. Jason borrowed money from his father, interest free, to purchase computer equipment for a
start-up business.
The equation below shows the amount of the loan, y, he has left to pay after x months of
repayment.
y = $4,500 - $250x
Which graph represents the given equation?
W.
X.
Y.
Z.
16. Look at the pattern below.
12, 19, 26, 33, ...
Which number sentence can be used to determine n, the 10th number in the pattern?
A. n = 7 ÷ 10
B. n = 7 × 10 + 5
C. n = 7 × 10 - 5
D. n = 7 × 10
17. The first five terms of a sequence are given below.
69 , 66 , 63 , 60 , 57 , ...
18. Which equation corresponds to the graph above?
19. The first three patterns of a sequence of dots is shown below.
If the pattern continues indefinitely, which of the following expressions can be used to determine
the number of dots in the nth term of the sequence?
A. n(n + 1)
B. n(n + 3)
C. n2 + 3
D. 3n
20. Solve the following inequality for x.
10 + 10x < 9x
21. What is the sixth term in the pattern below?
13, 32, 57, 88, ...
22.
23. Jamie is trying to lose weight. She starts a diet and workout regimen and records her weight
(y) every week (x) at her gym. Her initial weight was 188 lbs.
Week (x)
1
2
3
4
Weight (y)
185
182
179
176
If Jamie continues to lose weight at the same rate, how many more weeks will it take her to reach
her goal of 161 lbs?
24. The table below shows how many people have purchased coffee at a local coffee shop each
day since its grand opening.
Days Since Grand Opening 2
Number of People
5
7
10
14
10 34 60 114 214
Which equation represents p, the number of people who purchased coffee, after the shop had
been open d days?
A. p = d2 - d + 8
B. p = d2 + 0.5d + 5
C. p = d2 + d + 4
D. p = d2 + 6
25.
26. Which of the following situations describes a nonlinear relationship?
A.
B.
C.
D.
The number of graduates with a mathematics degree increases by 20 graduates each year.
The cost of tuition increases by $150 for each credit hour a student is enrolled.
For every question missed on an exam, a student's score decreases by six points.
The number of students enrolled in a local college increases by 5% each semester.
27. Solve the following inequality for x.
4.1x + 7 > 43.9
28.
The table above represents what type of function?
A. neither linear nor nonlinear
B. linear and nonlinear
x
y
-2
12
-1
9
0
6
1
3
2
0
C. linear
D. nonlinear
29. Laura retired from her job recently, and she has saved about $413,373.00 over the course of
her career. She plans to withdraw $1,228.00 each month to pay for living expenses. After a
certain amount of time, the balance in Laura's account is $377,761.00. How many months have
passed since Laura retired?