Preview/Review Worksheet
Mrs. Britton/Miss Sciandra Supplemental Algebra
Name:______Date:______
1. Which scatterplot most likely has a line of best fit represented by y = 2x + 1?
W. /
X.
Y. /
Z.
/ A. / Z
/ B. / Y
/ C. / W
/ D. / X
2. Select the correct symbol.
/ ? // A.
/ B.
/ C. / =
3. What is the range of the following set of numbers?
30.7, 24.6, 32.8, 29.7, 27.6, 28.7, 26.6, 34.8, 25.6
/ A. / 34.8/ B. / 29.01
/ C. / 10.2
/ D. / 9.2
4. Which statement describes the rate of change of the following function?
f(x) = 2x + 7
/ A. / The function has a varying rate of change when x > 7./ B. / The function has a constant rate of change, increasing for all x at a rate of 7.
/ C. / The function has a constant rate of change, increasing for all x at a rate of 2.
/ D. / The function has a varying rate of change when x > 2.
5. Reid's Hardware discounts all riding lawnmowers 6% to customers paying in cash. If Trey paid $1,176.97 in cash for a riding lawnmower, which of the following equations can be used to determine the original price of the lawnmower?
(Let x represent the original price of the lawnmower and y represent the discounted price.)
/ B. / y = 1.6x
/ C. / y = 1.06x
/ D. / y = 0.94x
6. Solve the following inequalities.
/ A. // B. /
/ C. /
/ D. /
7. Simplify: |6 - 3 • 1| - 16|19 - 18|
/ A. / 319/ B. / -319
/ C. / 13
/ D. / -13
8. Solve the following compound inequality.
-7 < 2x + 3 < 11
/ A. / -6 < x < 4/ B. / -5 < x < 5
/ C. / -5 < x < 4
/ D. / x < 4
9.
Anita sat outside the grocery store selling cookbooks. She kept track of how many cookbooks she sold over a seven day period. She added the number of books sold each day to the previous day and plotted her results on the line graph shown.
When rounded to the nearest whole number, which of the following is closest to the mean number of cookbooks Anita sold each day?
/ B. / 8
/ C. / 6
/ D. / 26
10.
The graph above shows a line of best fit for data collected on the price of a unit in relation to the number of units sold. What is the equation of the line of best fit?
/ B. /
/ C. /
/ D. /
11.
Looking at the graph above showing a line of best fit, what is the correlation between the x and y variables?
/ A. / y increases as x increases/ B. / y is constant
/ C. / y decreases as x decreases
/ D. / y decreases as x increases
12. Simplify the following expression.
/ A. // B. /
/ C. /
/ D. /
13.
/ A. // B. /
/ C. /
/ D. /
14. Erica went shopping for new clothes for school. She bought a pair of jeans for $48.97 and several shirts for $12.47 each. If x represents the number of shirts she bought, which of the following equations should be used to find y, the total cost of Erica's shopping trip?
/ A. / x = $48.97y + $12.47/ B. / x = $12.47y + $48.97
/ C. / y = $12.47x + $48.97
/ D. / y = $48.97x + $12.47
15. Order the following from greatest to least.
/ A. // B. /
/ C. /
/ D. /
Measures of Dispersion & Central Tendency
16. Mike, Shannon, Layla, and Rachel each recorded the grades they received on five tests in their math class in the table below.
Student / Test ScoresTest 1 / Test 2 / Test 3 / Test 4 / Test 5
Mike / 85 / 75 / 72 / 91 / 63
Shannon / 89 / 77 / 76 / 81 / 85
Layla / 84 / 83 / 82 / 75 / 76
Rachel / 86 / 76 / 71 / 82 / 81
What is the range of the student's scores?
/ A. / 29/ B. / 25
/ C. / 28
/ D. / 31
17. Evaluate the following expression when n = -9.
-9|n + 2|
/ A. / 63/ B. / -63
/ C. / -35
/ D. / 119
Answers
1. C
2. B
3. C
4. C
5. D
6. C
7. D
8. D
9. C
10. C
11. C
12. C
13. D
14. B
15. C
16. C
17. C
18. C
19. B
20. C
Explanations
1. The given equation has a positive slope.
Since lines of best fit for X and Y would have negative slopes, they can be ruled out as possible correct answer choices.
A line of best fit for Z has a slope of one and would not represent the given equation.
A line of best fit for W has a slope of two.
Therefore, scatterplot W has a line of best fit which is best represented by the equation y = 2x + 1.
2. In order to compare the two numbers, write both of them in decimal form.
/ / 2.23...../ = / 2.6
So, .
3. The range is the difference between the smallest number and largest number in a set of numbers. To find the range, subtract the smallest number (24.6) from the largest number (34.8).
34.8 - 24.6 = 10.2
The range of this set of numbers is 10.2.
4. The function given represents a linear function. Linear functions have a constant rate of change based on the coefficient of x.
So, the function has a constant rate of change, increasing for all x at a rate of 2.
5. The discounted price is equal to the original price minus the discount.
discounted price / = / original price - discounty / = / x - 0.06x
y / = / (1 - 0.06)x
y / = / 0.94x
6. To solve the inequalities, isolate the x in the middle. Remember that whatever is done to the expression in the middle must also be done to both numbers on the outside of the inequalities.
7. First put the numbers in order:
188, 212, 236, 261, 281, 301, 316
The median (Q2) of the whole set is 261. Then find the median of all numbers greater than 261.
281, 301, 316
So, 301 is the upper quartile (Q3).
Next, find the median of all numbers less than 261.
188, 212, 236
So, 212 is the lower quartile (Q1).
To find the interquartile range, subtract the lower quartile from the upper quartile.
(Q3) - (Q1) = 301 - 212 = 89
Therefore, the interquartile range is 89.
8. Use the order of operations to simplify the expression.
|6 - 3 • 1| - 16|19 - 18| / = / |6 - 3| - 16|1|= / |3| - 16
= / -13
9.
To find the mean growth per week, calculate how many centimeters the herb grew per week and then find the average of those measurements.
First, list the points from the graph for basil.
Height / 0 cm / 2 cm / 4 cm / 8 cm / 11 cm / 14 cm / 18 cm
Find the growth per week for the basil. Then add these numbers and divide by 6 to find the mean growth per week.
6 weeks
/ = / 18 cm
6 weeks
/ =3 cm/week
Next, list the points from the graph for mint.
Height / 0 cm / 1 cm / 2 cm / 4 cm / 7 cm / 9 cm / 12 cm
Find the growth per week for the mint. Then add these numbers and divide by 6 to find the mean growth per week.
6 weeks
/ = / 12 cm
6 weeks
/ =2 cm/week
Now, subtract the two mean growths per week to find the difference.
3 cm/week - 2 cm/week = 1 cm/week
10. When given a double inequality to solve, focus on solving for the x in the middle. Remember that whatever is done to the expression in the middle must also be done to both the numbers on the outside of the inequalities.
-7 / 2x + 3 / 11-10 / 2x / 8
-5 / x / 4
11. To find the mean, divide the total number of cookbooks sold by the total number of days Annita sold cookbooks outside the grocery store.
41 ÷ 7 = 5.8571428571
The answer that is closest to the mean when rounded to the nearest whole number is 6.
So, Annita sold approximately 6 cookbooks each day.
12.
13. The x-axis values are increasing to the right and the y values are decreasing.
Therefore, y decreases as x increases
14. When an exponential expression is raised to a power, multiply the exponents.
15.
16. The total cost of Erica's shopping trip is equal to the cost of each shirt, $12.47, times the number of shirts purchased, x, plus the price of the jeans, $48.97. Therefore, the linear equation which represents the total cost of Erica's shopping trip is shown below.
y = $12.47x + $48.97
17. To order the numbers, first change the fractions to decimals and the percentages to decimals. Round to two decimal places, if needed.
Then, compare the decimals.
Therefore, the numbers from greatest to least are shown below.
18. The range of data in a population is the difference between the largest and smallest value in the population. In this case, the population is the test scores for all four students.
Subtract the lowest test score, 63, from the highest test score, 91.
91 - 63 = 28
19. Absolute value is the magnitude of a number irrespective of its sign.
Evaluate the given expression piece-by-piece, using order of operations:
|n + 2| = |-9 + 2| = |-7| = 7
-9 × 7 = -63
20. The variable n represents the number of products that the employee sells.
n / $1,500 + $225n1 / $1,300 + $300(1) = $1,600
2 / $1,300 + $300(2) = $1,900
3 / $1,300 + $300(3) = $2,200
4 / $1,300 + $300(4) = $2,500
5 / $1,300 + $300(5) = $2,800
As n increases by 1, the employee's earnings increase by $300. Therefore, the correct statement is shown below.
For every product sold, the employee's earnings increase by $300.