# 7th grade prealgebra final review

Document Sample

```					Pre-Algebra Final review

Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.

Evaluate each expression.

____    1. 6g – q if g = 10 and q = 10
a. 540                                             c. 70
b. 50                                              d. 590

Solve each equation mentally.

____    2. a – 18 = 29
a. 47                                              c. 10
b. 11                                              d. 48

Name the property shown by each statement.

____    3. 4  (3 + c) = 4  3 + 4  c
a. Associative Property of Multiplication
b. Commutative Property of Multiplication
c. Distributive Property
d. Identity Property of Multiplication

The line plot shows the grades earned on Mr. Johnson’s science quiz.

____    4. What is the range of the data?
a. 25                                              c. 35
b. 30                                              d. 60

Find the mean for each set of data. Round to the nearest tenth if necessary.

____    5. \$100, \$120, \$94, \$111, \$156, \$160, \$138, \$104, \$99, \$132
a. \$121.40                                    c. \$114.70
b. \$135.25                                    d. \$129.50

Find the mode for each set of data. If there is no mode, select or write none.

____    6. 7, 3, 4, 6, 9, 10, 6, 4, 5, 3, 6, 8, 1, 8
a. 4                                               c. 8
b. 6                                               d. 3

Write an integer for each situation.
____   7. a deposit of \$245
a. –245                                          c. 245
b. 2450                                          d. 24.50

Subtract.

____   8. 9 – 22
a. 13                                            c. –31
b. –13                                           d. 31

Write each sentence as an algebraic equation.

____   9. A number less 12 equals       .
a.                                               c.
b.                                               d.

Solve each equation. Check your solution.

____ 10.
a.      1                                       c. 50
2
b. 2                                            d. 5

Write each fraction as a percent.

2
____ 11.   5
a. 40%                                          c. 8%
b. 160%                                         d. 0.4%
1
____ 12. 5 2
a. 55%                                          c. 5.5%
b. 550%                                         d. 0.055%

Add or subtract. Write in simplest form.

9             8
____ 13. 1 13 1 13
a.      1                                       c. 1 1
13                                          21
b. 2 124                                        d. 3 4
169                                            13

Multiply. Write in simplest form.

4        6
____ 14. 1 9           17
a.      54                                      c. 4 5
221                                         54
b.   26                                 d. 1 25
51                                      26

Find the perimeter of each figure.

____ 15.

16 ft

5 ft

a. 21 ft                                c. 160 ft
b. 42 ft                                d. 80 ft
____ 16.

cm
5.3

cm
10.6

a. 31.8 cm                              c. 63.6 cm
b. 56.18 cm2                            d. 15.9 cm

Find the area of each rectangle.
____ 17.

yd
14.3
yd
6.7

a. 93.8 yd                                      c. 98 yd2
b. 42 yd                                        d. 95.81 yd2

Find the circumference of each circle. Use 3.14 or     for . Round to the nearest tenth if necessary.

____ 18.

35 in.

a. 55.0 in.                                     c. 109.9 in.
b. 108.5 in.                                    d. 219.8 in.

Find each unit rate. Round to the nearest tenth if necessary.

____ 19. \$253 for 20 hours
a. 1 hour/\$15.50                                  c. \$25.30/hour
b. \$12.65/hour                                    d. 1 hour/\$12.65
____ 20. \$316 for 4 VCRs
a. 1 VCR/\$79                                      c. \$85/VCR
b. \$62.50/VCR                                     d. \$79/VCR

Solve each problem.
____ 21. A map has a scale of 3.5 inches = 20 kilometers. If the distance between two cities on the map is 4.9 inches,
what is the actual distance between the cities?
a. 28 km                                        c. 14.3 km
b. 30.6 km                                      d. 0.9 km

Write each percent as a fraction in simplest form.

1
____ 22. 61 2 %
a.       123                                    c.     1
200                                           5
b.        61                                    d.     123
1000                                          20

Find each number. Round to the nearest tenth if necessary.

____ 23. 16.2% of 180 is what number?
a. 18                                              c. 38.5
b. 29.2                                            d. 9

Find the percent of discount to the nearest percent.

____ 24. cereal: regular price, \$4.50
sale price, \$2.00
a. 44%                                             c. 125%
b. 56%                                             d. 225%

For each situation, make a tree diagram to show the sample space. Then give the total number of outcomes.

____ 25. picking a number from 1 to 4 and choosing the color red, green, or yellow
a. 6                                           c. 12
b. 9                                           d. 24

A group of commuters from a large urban city was polled to study how people get to work each day. The
results of the poll are shown in the circle graph.

____ 26. What is the least popular method of commuting to work among those polled?
a. Other                                      c. Drive Alone
b. Public Transit                             d. Carpool
Find the best name to classify each quadrilateral.

____ 27.

a. rhombus                                      c. trapezoid

____ 28.

10 yd
5 yd

6 yd
14 yd

a. similar                                      b. not similar

Determine which figures have line symmetry. If a figure has line symmetry, tell how many unique lines of
symmetry there are.

____ 29.

a. 1 line of symmetry                           c. 3 lines of symmetry
b. 2 lines of symmetry                          d. no line symmetry
____ 30.

a. 1 line of symmetry                          c. 3 lines of symmetry
b. 2 lines of symmetry                         d. no line symmetry

Write an integer for each situation.

31. 60 seconds before liftoff

Complete.

32. 196 oz = ____ lb

Find the perimeter of each figure.

33.

15 ft               15 ft

18 ft

Write an equation for each problem. Then solve. Round to the nearest tenth if necessary.

34. 84 is 28% of what number?

Determine whether each statement is sometimes, always, or never true.

35. A rectangle is a square.

Essay

36. Use the table of ordered pairs to answer the following questions.
x            y
4            2
–5            2
4           –4

a.   Plot the ordered pairs in the table on a coordinate plane.
b.   In which quadrant is a point on the graph not represented?
c.   Connect the points on the graph. What special kind of triangle do they form?
d.   How would you double the size of the figure you drew in step c?
e.   Add four more columns to the table. Label the columns x + y, x – y, xy and x ÷ y. Complete the table.

37. Emi delivers newspapers in her neighborhood. She receives a flat rate of \$10 and an additional \$0.25 for each
newspaper she delivers.
a. Write an equation to represent the total pay Emi receives. Use p for the total pay and n for each
newspaper she delivers.
b. If Emi delivers 15 newspapers, how much money does she receive?
38. Stephen is researching the value of his car.
a. The value of his car decreased from \$1,600 to \$1,328. What is the percent of decrease?
b. The current value of the car, \$1,328, will increase by 8% if Stephen purchases new tires. What will be the
value of the car with new tires?
39.

50 ft

40 ft

A goat is tied to the corner of a square outbuilding with a 40 ft rope as pictured above.
a. What is the measure of the partial circumference created as the goat walks at the full
length of the rope?
b. Since the goat is trimming the grass from part of the outbuilding, how much of the
perimeter of the outbuilding will the building owner have to trim?
40. A deli offers sub sandwiches on wheat or rye bread, with a choice of ham, salami, or turkey. The deli also
offers customers a choice of American, Provolone, or Cheddar cheese. Suppose a sandwich is chosen at
random.
a. Make a tree diagram that shows all of the possible outcomes.
b. What is the probability that a randomly selected sandwich will be ham on rye with American
cheese?
c. What is the probability that a randomly selected sandwich will contain Provolone cheese or
salami?
Pre-Algebra Final review

MULTIPLE CHOICE

1. ANS: B
You can evaluate an algebraic expression by replacing the variables with numbers and then finding the value
of the numerical expression.

DIF: Average         OBJ: 1-4.1 Evaluate simple algebraic expressions.
STO: MA.D.1.3.1-3, MA.D.1.3.1-4, MA.D.1.3.2-1, MA.D.1.3.2-2, MA.D.2.3.1-3
TOP: Evaluate simple algebraic expressions.
KEY: Evaluating expressions, Algebraic expressions
NOT: /A/ Do multiplication before addition. /B/ Correct! /C/ Watch addition and subtraction signs. /D/
Watch the order of operations.
2. ANS: A
Some equations can be solved mentally by using basic facts or arithmetic skills you know.

DIF: Basic             OBJ: 1-5.1 Solve equations using mental math.
STO: MA.A.3.3.3-1, MA.D.1.3.2-2, MA.D.2.3.1-3, MA.D.2.3.1-4
TOP: Solve equations using mental math.                           KEY: Mental math, Solving equations
NOT: /A/ Correct! /B/ Use basic facts or arithmetic skills you know. /C/ Use basic facts or arithmetic skills
you know./D/ Use basic facts or arithmetic skills you know.
3. ANS: C
Distributive Property: a  (b + c) = a  b + a  c

DIF: Average           OBJ: 1-6.2 Name properties of addition and multiplication shown in statements.
STO: MA.A.3.3.1-3, MA.A.3.3.2-4, MA.D.2.3.2-2
TOP: Name properties of addition and multiplication shown in statements.
NOT: /a/ That is a x (b x c) = (a x b) x c. /b/ That is a x b = b x a. /c/ Correct! /d/ That is a x 1 = a.
4. ANS: C
The range of the data is 95 – 60 = 35.

DIF: Average            OBJ: 2-3.2 Interpret line plots.               STO: MA.E.1.3.1-2, MA.E.1.3.1-3
TOP: Interpret line plots.                       KEY: Line plots, Analyzing data
NOT: /a/ The range is the difference between the greatest number and the least number. /b/ Remember, the
range is the total spread of the data. It is the difference between the highest and lowest data points. /c/
Correct! /d/ Subtract the least number from the greatest number.
5. ANS: A
Divide the sum of the numbers by the number of items in the set.

DIF: Average           OBJ: 2-4.1 Find the mean of a set of data.
STO: MA.E.1.3.2-1, MA.E.1.3.2-2, MA.E.1.3.3-1                      TOP: Find the mean of a set of data.
KEY: Mean, Analyzing data
NOT: /a/ Correct! /b/ Remember, the mean is the sum of the numbers in the data set divided by the number
of items. /c/ Double check your work and try again. /d/ What is the sum of the numbers? Divide this by the
number of items in the set.
6. ANS: B
The mode is 6 because it occurs most often.

DIF: Basic             OBJ: 2-4.3 Find the mode of a set of data.
STO: MA.E.1.3.2-1, MA.E.1.3.2-2, MA.E.1.3.3-1                         TOP: Find the mode of a set of data.
KEY: Mode, Analyzing data
NOT: /a/ Is there a number that occurs more often than 4? /b/ Correct! /c/ Remember, the mode is the number
that occurs most often in a set of data. /d/ Is there a number that occurs more often than 3?
7. ANS: C
A deposit indicates a positive value, so 245 is the correct integer.

DIF: Average         OBJ: 3-1.1 Write integers.
STO: MA.A.1.3.1-1, MA.A.1.3.2-1, MA.A.1.3.4-2, MA.A.1.3.4-3
TOP: Write integers.                       KEY: Integers, Numbers
NOT: /a/ Does a deposit represent a negative or a positive amount? Think in terms of a bank deposit. /b/
What integer can be used to represent \$245? /c/ Correct! /d/ 24.50 is not an integer.
8. ANS: B
Sample:
–22 – 15

–22 + (–15)
–37

DIF: Average           OBJ: 3-5.1 Subtract positive integers.
STO: MA.A.1.3.3-3, MA.A.3.3.1-1, MA.A.3.3.1-2, MA.A.3.3.1-4, MA.A.3.3.2-1
TOP: Subtract positive integers.              KEY: Subtraction, Integers
NOT: /A/ Be careful with your signs and try again. /B/ Correct! /C/ What is the additive inverse of the
integer bring subtracted? Add this to the first integer./D/ To subtract an integer, add its additive inverse.
9. ANS: A
Subtract the number from the variable. Then set the expression equal to the remaining number.

DIF: Average          OBJ: 4-1.2 Write verbal sentences as simple algebraic equations.
STO: MA.D.1.3.2-2, MA.D.2.3.1-1               TOP: Write verbal sentences as simple algebraic equations.
KEY: Verbal sentences, Algebraic equations
NOT: /a/ Correct! /b/ Subtract the number from the variable. /c/ Check the sign of each number. /d/ Less
means subtraction.
10. ANS: B
Divide both sides by the coefficient of the variable.

DIF: Basic             OBJ: 4-3.1 Solve multiplication equations.
STO: MA.A.3.3.1-3, MA.D.2.3.1-1, MA.D.2.3.1-4, MA.D.2.3.2-1
TOP: Solve multiplication equations.         KEY: Multiplication, Solving equations
NOT: /A/ Divide the right-hand side by the coefficient of the variable. /B/ Correct! /C/ Division undoes
multiplication. /D/ Division undoes multiplication.
11. ANS: A
Divide the numerator by the denominator. Then move the decimal two places to the right.

DIF: Basic             OBJ: 5-5.2 Write fractions as percents.
STO: MA.A.1.3.1-1, MA.A.1.3.4-1, MA.A.1.3.4-2, MA.A.1.3.4-4
TOP: Write fractions as percents.        KEY: Percent, Fractions
NOT: /A/ Correct! /B/ Remember to divide not multiply by the denominator. /C/ Remember to divide by the
denominator. /D/ Remember to move the decimal place.
12. ANS: B
Sample:

Write the mixed number as a decimal. Then multiply the number by 100 to write it as a percent.

DIF: Average          OBJ: 7-6.4 Write fractions as percents greater than 100% and percents less than 1%.
STO: MA.A.1.3.4-1, MA.A.1.3.4-2, MA.A.1.3.4-4
TOP: Write fractions as percents greater than 100% and percents less than 1%.
KEY: Fractions, Percent
NOT: /A/ Remember the definition of a percent. What should you multiply the decimal by in order to write it
as a percent? /B/ Correct! /C/ A percent is a ratio that compares a number to what other number? /D/ The
number 1 represents 100%. Should your answer be greater than or less than 100%?
13. ANS: A
To subtract mixed numbers with like denominators, subtract the whole numbers and subtract the fractions.
Rewrite the first mixed number if necessary to subtract the fractions. Simplify.

DIF: Average         OBJ: 6-3.2 Subtract mixed numbers.
STO: MA.A.3.3.1-1, MA.A.3.3.1-2, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.3.3.2-2
TOP: Subtract mixed numbers.              KEY: Subtraction, Mixed numbers
NOT: /A/ Correct! /B/ Did you multiply? /C/ Did you divide?/D/ Did you add?
14. ANS: B
To multiply mixed numbers, convert both factors to improper fractions. Then multiply the numerators and
denominators. Simplify.

DIF: Basic             OBJ: 6-4.2 Multiply mixed numbers.
STO: MA.A.3.3.1-1, MA.A.3.3.1-2, MA.A.3.3.1-3, MA.A.3.3.2-1, MA.A.4.3.1-1
TOP: Multiply mixed numbers.                 KEY: Multiplication, Mixed numbers
NOT: /A/ Did you multiply the reciprocals after converting to improper fractions? /B/ Correct! /C/ Is that the
product or the quotient? /D/ Did you multiply the second fraction by the reciprocal of the first?
15. ANS: B
The perimeter of a rectangle is the sum of the measures of the sides. It can also be expressed as two times the
length (l) plus two times the width (w).

DIF: Basic             OBJ: 6-8.1 Find the perimeters of figures.
STO: MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.1-3, MA.B.1.3.3-3, MA.B.2.3.2-3
TOP: Find the perimeters of figures.         KEY: Perimeter, Measurement
NOT: /A/ Did you consider all four sides? /B/ Correct! /C/ Is your answer reasonable?/D/ How do you find
the perimeter?
16. ANS: A
The perimeter of a rectangle is the sum of the measures of the sides. It can also be expressed as two times the
length (l) plus two times the width (w).
DIF: Average           OBJ: 6-8.1 Find the perimeters of figures.
STO: MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.1-3, MA.B.1.3.3-3, MA.B.2.3.2-3
TOP: Find the perimeters of figures.         KEY: Perimeter, Measurement
NOT: /A/ Correct! /B/ Did you find the area? /C/ What is the formula for perimeter of a rectangle?/D/ Did
you consider all four sides?
17. ANS: D
The area of a rectangle equals the product of its length and width.

DIF: Average          OBJ: 6-8.2 Find the areas of figures.
STO: MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.1-3, MA.B.1.3.3-3, MA.B.2.3.2-3
TOP: Find the areas of figures.               KEY: Area, Measurement
NOT: /A/ Be careful with multiplication and units./B/ That is the perimeter. /C/ How do you find the area of
a rectangle? /D/ Correct!
18. ANS: C
The circumference of a circle is equal to  times its diameter or times twice the radius.

DIF: Average           OBJ: 6-9.1 Find the circumference of circles.
STO: MA.B.1.3.1-3, MA.B.1.3.3-3, MA.C.1.3.1-6                    TOP: Find the circumference of circles.
KEY: Circumference, Circles
NOT: /A/ Did you use the correct formula for circumference? /B/ What did you use for pi? /C/ Correct! /D/ Is
19. ANS: B
The unit rate is the amount earned for 1 hour.
\$253 ÷ 20 = \$12.65/hour

DIF: Average           OBJ: 7-2.1 Determine unit rates.             STO: MA.A.1.3.1-1, MA.A.1.3.4-2
TOP: Determine unit rates.                    KEY: Unit rate, Ratios
NOT: /a/ Double check your computation to be sure you have the correct unit rate. Also, remember that the
terms of the ratio should be written in the same order as the problem statement. /b/ Correct! /c/ Double check
your computation to be sure you have the correct unit rate. /d/ The terms of the ratio should be written in the
same order as the problem statement.
20. ANS: D
The unit cost is the cost of 1 VCR.
\$316 ÷ 4 = \$79/VCR

DIF: Basic            OBJ: 7-2.1 Determine unit rates.             STO: MA.A.1.3.1-1, MA.A.1.3.4-2
TOP: Determine unit rates.                   KEY: Unit rate, Ratios
NOT: /a/ The terms of the ratio should be written in the same order as the problem statement. /b/ Double
check your computation to be sure you have the correct unit rate. /c/ Did you divide out the common factor
from both terms? /d/ Correct!
21. ANS: A
Set up a proportion and solve for the distance.
DIF: Average          OBJ: 7-4.1 Solve problems involving scale drawings.
STO: MA.B.1.3.4-1, MA.B.1.3.4-2, MA.B.1.3.4-3, MA.B.2.3.1-3
TOP: Solve problems involving scale drawings.                      KEY: Scale drawings, Proportions
NOT: /a/ Correct! /b/ Double check your computation and try again. /c/ Be careful when solving your
proportion. What are the cross products of the proportion? /d/ Be careful when setting up your proportion. Be
sure you order the terms correctly.
22. ANS: A
Sample:
%

Write the percent over 100 and simplify.

DIF: Average           OBJ: 7-5.1 Write percents as fractions.
STO: MA.A.1.3.4-1, MA.A.1.3.4-2, MA.A.1.3.4-4                        TOP: Write percents as fractions.
KEY: Percent, Fractions
NOT: /A/ Correct! /B/ Be careful when writing the fraction in simplest terms. /C/ Double check your work
and try again./D/ Should the fraction be greater than or less than 1?
23. ANS: B
Set up a proportion to find the number.

DIF: Average            OBJ: 7-8.1 Solve problems using the percent proportion.
STO: MA.A.3.3.2-3                             TOP: Solve problems using the percent proportion.
KEY: Percent proportion, Problem solving
NOT: /a/ Write a proportion where one of the ratios is the percent over 100. Then solve for the number. /b/
Correct! /c/ Double check your work and try again. /d/ Be careful when setting up your proportion. The terms
in the ratios must be consistent.
24. ANS: B
Subtract the sale price from the regular price.Use the percent proportion to determine what percent the
difference is of the regular price.

DIF: Average            OBJ: 8-5.2 Solve problems involving discounts.
STO: MA.A.3.3.2-3                              TOP: Solve problems involving discounts.
KEY: Discounts, Problem solving
NOT: /a/ Do not divide the sale price by the regular price. /b/ Correct! /c/ Do not divide the differenceby the
sale price. /d/ Do not divide the regular price by the sale price.
25. ANS: C
There are twelve possible outcomes: 1R, 1G, 1Y, 2R, 2G, 2Y, 3R, 3G, 3Y, 4R, 4G, and 4Y.

DIF: Average           OBJ: 9-2.1 Use tree diagrams to count outcomes and find probabilities.
STO: MA.E.3.3.1-1, MA.E.3.3.1-2, MA.E.3.3.1-3
TOP: Use tree diagrams to count outcomes and find probabilities.
KEY: Probability, Tree diagram
NOT: /a/ List all of the possible outcomes for the number. Then branch off each number to list all of the
possible outcomes for the color. /b/ Double check your work and try again. /c/ Correct! /d/ List all of the
possible outcomes to make sure they are all unique.
26. ANS: D
Carpool has the smallest section, so it is the least popular method.

DIF: Basic             OBJ: 10-2.2 Interpret circle graphs.           STO: MA.E.1.3.1-3
TOP: Interpret circle graphs.                  KEY: Circle graph, Analyzing data
NOT: /a/ Is there a section that is smaller than the Other section? /b/ Would the least popular method of
travel have the smallest or the largest section of the circle graph? /c/ Which section of the circle graph is the
smallest? /d/ Correct!
27. ANS: B
The figure is simply a quadrilateral.

DIF: Average            OBJ: 10-5.1 Identify quadrilaterals.
STO: MA.C.1.3.1-3, MA.C.1.3.1-4, MA.C.1.3.1-6                         TOP: Identify quadrilaterals.
NOT: /a/ A rhombus is a parallelogram with four congruent sides. /b/ Correct! /c/ Does the figure have a pair
of opposite sides that are parallel? /d/ Are the pairs of opposite sides parallel to each other?
28. ANS: B
Find the ratios of the corresponding sides to see if they are in proportion.

The corresponding sides are not in proportion, so the figures are not similar.

DIF:    Average         OBJ: 10-6.1 Determine whether figures are similar.
STO:    MA.A.3.3.2-5, MA.B.2.3.1-3            TOP: Determine whether figures are similar.
KEY:    Similarity, Similar figures
NOT:    /a/ Are the corresponding sides of the rectangles in proportion? /b/ Correct!
29. ANS:    B
Sketch all lines that will produce identical figures when reflected over the line.

The figure has 2 lines of symmetry.

DIF: Basic               OBJ: 10-9.1 Identify figures with line symmetry.
STO: MA.C.2.3.1-5, MA.C.2.3.2-3                TOP: Identify figures with line symmetry.
KEY: Line symmetry, Symmetry
NOT: /a/ Copy the figure onto your paper and sketch the line of symmetry. Are there any other lines that will
produce identical figures when you fold along the line? /b/ Correct! /c/ Copy the figure onto your paper to
verify that all three lines of symmetry will produce identical figures. /d/ Are there any lines that will produce
identical figures when you fold along the line?
30. ANS: A
Sketch all lines that will produce identical figures when reflected over the line.

The figure has 1 line of symmetry.

DIF: Average            OBJ: 10-9.1 Identify figures with line symmetry.
STO: MA.C.2.3.1-5, MA.C.2.3.2-3               TOP: Identify figures with line symmetry.
KEY: Line symmetry, Symmetry
NOT: /a/ Correct! /b/ Copy the figure onto your paper and verify that there are two lines that divide the figure
into equal halves. /c/ Double check your answer by sketching the figure and any lines of symmetry on your
paper. /d/ Are there any lines that will produce identical figures when you fold along the line?

31. ANS:
–60

Rationale:
The time is given in relation to liftoff. Since it has not occurred yet, the value should be negative. –60 is the
correct integer.

DIF: Average         OBJ: 3-1.1 Write integers.
STO: MA.A.1.3.1-1, MA.A.1.3.2-1, MA.A.1.3.4-2, MA.A.1.3.4-3
TOP: Write integers.                     KEY: Integers, Numbers
32. ANS:

When changing from a smaller unit to a larger unit, divide. Since there are 16 ounces in one pound, divide
196 by 16.

DIF: Average           OBJ: 6-7.1 Change units in the customary system.
STO: MA.A.3.3.3-1, MA.B.2.3.1-1               TOP: Change units in the customary system.
KEY: Measurement, Customary units
33. ANS:
48 ft
The perimeter of a triangle is the sum of the measures of the sides.

DIF: Average       OBJ: 6-8.1 Find the perimeters of figures.
STO: MA.B.1.3.3-1, MA.B.1.3.3-2, MA.B.1.3.1-3, MA.B.1.3.3-3, MA.B.2.3.2-3
TOP: Find the perimeters of figures.   KEY: Perimeter, Measurement
34. ANS:
base = 300

DIF: Average        OBJ: 8-2.1 Solve problems by using the percent equation.
STO: MA.A.3.3.2-3                       TOP: Solve problems by using the percent equation.
KEY: Percent equation, Problem solving
35. ANS:
sometimes

When a rectangle has four congruent sides, it is a square.

DIF: Average        OBJ: 10-5.2 Classify quadrilaterals.
STO: MA.C.1.3.1-3, MA.C.1.3.1-4, MA.C.1.3.1-6                         TOP: Classify quadrilaterals.

ESSAY
36. ANS:
a.                                y
5

4

3

2

1

–5   –4   –3   –2   –1         1   2   3   4   5    x
–1

–2

–3

–4

–5

c.                                y
5

4

3

2

1

–5   –4   –3   –2   –1         1   2   3   4   5    x
–1

–2

–3

–4

–5

right triangle
d. double the sides of the triangle.
e.
x          y          x+y                        x–y    xy   x÷y
4          2           6                          2      8      2
–5           2          –3                         –7    –10   –2.5
4        –4            0                          8    –16    –1

Rationale:
a. Plot the ordered pairs as directed.
b. There are no points in the third quadrant.
c. Connect the points as directed. They form a right triangle.
d. The triangle’s size can be doubled by doubling the lengths of its sides.
e. Perform the addition, subtraction, multiplication, and division using the properties of integers.

DIF: Advanced     OBJ: 3-8.1 Solve problems and show solutions.
TOP: Solve problems and show solutions.                   KEY: Problem solving, Solutions
37. ANS:
a.
Emi will receive \$10 regardless of the number of papers she delivers. For each paper delivered, Emi will
receive an additional \$0.25 per paper. In the equation, the variable p represents the total pay that Emi will
receive, and n represents the number of newspapers delivered.
b. \$13.75

The equation from part a can be used to solve this equation. Since Emi delivers 15 newspapers, fifteen is
substituted for the variable n.

DIF: Advanced     OBJ: 4-8.1 Solve problems and show solutions.
TOP: Solve problems and show solutions.                   KEY: Problem solving, Solutions
38. ANS:
a. 17%

b. \$1,434.24

DIF: Advanced      OBJ: 8-7.1 Solve problems and show solutions.
TOP: Solve problems and show solutions.                           KEY: Problem solving, Solutions
39. ANS:
a. You need to find three fourths of the circumference of a circle with radius 40 feet.

b.    The perimeter of the building is 200 ft. The goat is trimming 40 ft of two of the sides
leaving                  .

DIF: Advanced     OBJ: 6-10.1 Solve problems and show solutions.
TOP: Solve problems and show solutions.                   KEY: Problem solving, Solutions
40. ANS:
a.

There are 18 possible outcomes: WHA, WHP, WHC, WSA, WSP, WSC, WTA, WTP,
WTC, RHA, RHP, RHC, RSA, RSP, RSC, RTA, RTP, and RTC.
b.

There is only 1 favorable outcome (RHA) out of 18 possible outcomes.
c.

There are 10 outcomes that contain either Provolone cheese or salami (WHP, WSA,
WSP, WSC, WTP, RHP, RSA, RSP, RSC, RTP). Write this over the total number of
outcomes and simplify.

DIF: Advanced     OBJ: 9-8.1 Solve problems and show solutions.
TOP: Solve problems and show solutions.                   KEY: Problem solving, Solutions

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