Chapter 1 Practice Test Simplify each expression. If not possible, write simplified. 1. 7a + 7a 2 + 14b 2 Simplified, although a better format would be: 7a 2 + 7a +14b 2 Write an algebraic expression for each verbal expression. 2. the sum of the square of a number and 15 n 2 + 15 3. 34 decreased by triple some number 34 – 3n 4. Write a verbal expression for 5 times the cube of a number divided by 4 The product of 5 and the cube of a number divided by 4 The quotient of 5 times the cube of a number and 4 5. Evaluate Evaluate each expression if x = -2, y = 3, z = -1, and w = -4. 6. xy 3 + z(w 2 – x) 2 3 2 3 1 4 2 2 27 1 16 2 54 18 72 7. 3xw – w 2 + z 3 3 2 (3)( 2)( 4) ( 4) ( 1) 24 16 1 7 + 11. 4 2 10 2 3 15 11 11 4 3 2 10 16 34 11 16 6 10 4 11 15 10
Transcript
Chapter 1 Practice Test
Simplify each expression. If not possible, write simplified.
1. 7a + 7a2
+ 14b2
Simplified, although a better format would be:
7a2 + 7a +14b2
Write an algebraic expression for each verbal expression.
2. the sum of the square of a number and 15
n2 + 15
3. 34 decreased by triple some number 34 – 3n
4. Write a verbal expression for 5 times the cube of a number divided by 4 The product of 5 and the cube of a number divided by 4 The quotient of 5 times the cube of a number and 4 5. Evaluate
Evaluate each expression if x = -2, y = 3, z = -1, and w = -4.
6. xy3 + z(w
2 – x)
232 3 1 4 2
2 27 1 16 2
54 18 72
7. 3xw – w2 + z
3 32(3)( 2)( 4) ( 4) ( 1)
24 16 1 7
+ 11.
4
2
10 2 3 15 1111
4 3 2
10 16 3 411
16 6
10 411 15
10
Name the property used in each equation. Then find the value of n.
8. 8y - y = 8y - 1y
Identity of multiplication
9. (5 + w)x = 10x
Substitution Property of Equality
10. Evaluate . Name the property used in each step.
11. Rewrite 6y - 2(2x + 3y – 2z) - 4x using the Distributive Property. Then simplify. 6y – 4x -6y +4z -4x = -8x +4z
Simplify each expression. If not possible, write simplified.
12. 4 + 5(6x + 8xy) + 9yx
4 + 30x 40xy +9xy = 30x +49xy + 4
13.
Simplified
14. Solve .
2 2 26 3 2 3 6 9 4 9 54 36 189
5 3 5 3 2 2
2 2 26 3 2 3 6 9 4 9 54 36 189
5 3 5 3 2 2
2 2 26 3 2 3 6 9 4 9 54 36 189
5 3 5 3 2 2
15. Find the solution of
53
4 3 2 324
3 432 32 Substitution
4 3
1 32 32 Multiplicative Inverse
1 0 Additive Inverse
1 Identity of Addition
2 2 26 3 2 3 6 9 4 9 54 36 189
5 3 5 3 2 2
5Solution Set:
3
16. Some warehouse stores charge members an annual fee to shop there. On his first trip to a warehouse store, Mr.
Marsh pays a $75 membership fee. Cases of bottled water cost $3.99 at the warehouse store. Write and solve
an equation to find the total amount Mr. Marsh spent on his first trip before tax if he bought 10 cases of water.
c(b) = 3.99b + 75
c(10) = 3.99(10) + 75
c(10) = $114.90
17. The graph shown represents a puppy exploring a trail. Describe what is happening in the graph. Is the function
discrete or continuous?
The graph is continuous (not separate discrete points) You should be creative with your description! Below is just one possibility: The puppy walked at a constant speed away from the trailhead. He stopped a while to sniff. He saw a squirrel and ran after it. He stopped again when the squirrel ran up a tree and he watched it. He heard his owner calling him and ran quickly back to her at the trailhead. Use the graph that shows the average daily circulation of the Evening Telegraph.
18. Identify the independent and dependent variables.
The independent is the year and the dependent is the number of newspapers sold.
19. Write a description of what the graph displays.
The number of newspapers sold dropped drastically by about 20,000 over the two-year
period from 2006 through 2008. After 2008, the sales leveled out, but are still
decreasing very slowly. It appears they have stabilized at a little less than 60,000.
20. Each day David drives to work in the morning, returns home for lunch, drives back to work, and then goes to a
gym to exercise before he returns home for the evening. Draw a reasonable graph to show the distance David is from his home for a two-day period:
THIS IS JUST A SAMPLE ANSWER! IT ASSUMES THE GYM IS FARTHER AWAY FROM HOME THAN WORK…THAT MAY NOT BE TRUE.
21. Determine whether represents a function. Yes, it’s a function. It passes the vertical line test if you graph it. It will be a slanted line, slanting from bottom left to top right.
The population of Ohio was about 4 million in 1900.
24. Interpret the end behavior of the function. The population of Ohio will approach about 13 million in the future.
25. Identify the function graphed as linear or nonlinear. Then estimate and interpret the intercepts of
the graph, any symmetry, where the function is positive, negative, increasing, and decreasing, the
xcoordinate of any relative extrema, and the end behavior of the graph.
The graph is nonlinear (curved).
The y-intercept is about 10 meters and that is where he started his dive.
The x-intercept is about 1.75 seconds and that is when he reached the water.
There is no symmetry.
The function is positive everywhere since he is above the water.
The graph is increasing to about .3 seconds and that is when he has started his dive
and launches upwards.
At .3 seconds, he reaches the maximum height of his dive of about 10.3 meters, which
is the extrema.
The graph is decreasing the rest of the way, as he dives down to the water.
The left end is the diving board and is also the y-intercept.
The right end is the water and is also the x-intercept, but the diver would continue
going downward into the water for a certain length of time (and then would ultimately
come back up but the graph doesn’t tell you that!)
The dive takes about 1.75 seconds to the water.
26.
The graph is nonlinear (curved).
The y-intercept is about 24 inches at birth.
There is no x-intercept because that would mean the height would go down to 0 inches
or start at 0 inches.
There is no symmetry.
The function is positive everywhere since he always has a positive height.
The graph is increasing everywhere to between 18 and 19 years old and that is where
most boys reach their maximum height (extrema) of about 72 inches according to this
graph. The graph levels out there and so the end behavior assumes that the average
height will remain 6 feet for his lifetime.
Indicate the answer choice that best completes the statement or answers the question.
Determine whether each relation is a function. 27.
Yes, no input repeats
28.
No, the input 1 repeats 29.
Yes, it passes the VLT
30. (1, 4), (2, –2), (3, –6), (–6, 3), (–3, 6)
Yes, no input repeats
31. (6, –4), (2, –4), (–4, 2), (4, 6), (2, 6)
No, the input 2 repeats
32. x = –2 No, this graphs as a vertical line so it fails the VLT.
33. y = 2
Yes, this graphs as a horizontal line so it passes the VLT.
Express each relation as a graph and a mapping. Then determine the domain and range.
34. (3, –4), (1, –2), (3, 5), (3, 0), (1, 5)
The answer is a (it was multiple choice)
D = 1, 3; R = –4, –2, 0, 5
35. Identify the graph that displays the speed of a baseball being pitched and then hit by the batter. The answer is a (it was multiple choice)
If f(x) = 2x – 6 and g(x) = x – 2x2, find each value.
36. g(–1) = -1 – 2(-1)2 = -1 – 2(1) = -1 – 2 = -3
The answer is a (it was multiple choice) 37. Troy drops a pebble from a bridge into the river below. The graph shows the height of the pebble after he drops it. Identify and interpret the x-intercept. drops it.
The answer is b (it was multiple choice)
b. 2; It takes 2 seconds for the pebble to reach the river.
38. The graph shows the average cost, y, of producing x units. Identify and interpret any lines of symmetry.
The answer is c (it was multiple choice)
c. At x = 125 there is the line of symmetry; For n units more or n units less than 125, the average cost will be
the same.
If f(x) = 2x – 6 and g(x) = x – 2x2, find each value.
39. f(7) – 9 = 2(7) – 6 – 9 = 14 – 15 = -1
The answer is c (it was multiple choice)
40. On which interval(s) of x is the function increasing? On which interval(s) of x is the function decreasing?
The graph shows Eric's heart rate in beats per minute (bpm) at different times during a workout. Use the graph to
answer each question.
The answer is c (it was multiple choice)
c. increasing: between 0 and 4, between 17 and 33; decreasing: between 4 and 17, between 33 and 40
41. The graph below shows the number of hits a website has received since it came online 6 months ago. Estimate
where the function is positive, negative, increasing, or decreasing. Then find the x-coordinate(s) of any relative
extrema and determine the end behavior of the graph.
The graph is positive everywhere because you can only have positive hits to your website.
The graph is increasing everywhere so the website’s hits are increasing over time.
The y-intercept is about 1000 hits when the website first went online and there is no x-
intercept because it appears the website is very successful and is continually getting an
increasing number of hits. An x-intercept would mean that the website was getting 0 hits.
Because it is constantly increasing, there is no extrema.
Indicate the answer choice that best completes the statement or answers the question.
If f(x) = 2x – 6 and g(x) = x – 2x2, find each value.
