Math Praxis IPT

The figure above is composed of 5 equal-sized squares. If the perimeter of the figure is 96 inches, what is the area of the figure, in square inches?

180

If 9x=18+3y and y=3, what is the value of x ?

3

In the isosceles triangle above, angle A is congruent to angle B. If angle A has a measure of 53°, what is the measure of angle C ?

37 degrees

In a sequence of numbers the first term is x, and each term thereafter is twice the previous term. The fifth term is 160. What is the value of x?

5

During a 5-day sale at a certain car dealership, 5 salespeople sold a total of 140 cars. The pictograph above represents the number of cars sold by each salesperson. How many cars does each represent?

8

In the coordinate plane shown, which point is located in Quadrant I? A.A B.B C.C D.D

Correct Answer: B Option (B) is correct. The question requires an understanding of how to identify the x-axis, the y-axis, the origin, and the four quadrants in the coordinate plane. The x-axis and the y-axis intersect at the origin and divide the coordinate plane into four quadrants. Quadrant I is the quadrant above the x-axis and to the right of the y-axis. Point B is the only point that lies within this quadrant.

The formula V=IRV=IR relates the voltage V, in volts, to the current I, in amps, and the resistance R, in ohms, in a circuit. What is the current produced by a 9-volt battery in a circuit with 4 ohms of resistance? A.1.50 amps B.2.00 amps C.2.25 amps D.2.50 amps

Correct Answer: C Option (C) is correct. The question requires an understanding of how to use formulas to determine unknown quantities. Since V=9 volts and R=4 ohms, I=V/R=9/4=2.25 amps.

Brookhaven 74,702Columbus 70,472 Davidson 74,072 Washington 74,720 The chart shows the populations of four neighboring counties. Quyen lives in the county with a population of 70,000+4,000+70+2. In which county does Quyen live?

Davidson Option (C) is correct. The question requires an understanding of how to compose and decompose multidigit numbers. The expanded form 70,000+4,000+70+270,000+4,000+70+2 corresponds to the number 74,072, which is the population of Davidson County.

What is the range of all integers greater than 40 and less than 99 that are multiples of 3 ?

59

The figure above shows rectangle ABCD. Which of the following must be true?

∠AEB≅∠BEC

At a fruit stand Jacob bought 12 apples for $0.45 each, 9 oranges for $0.55 each, 8 bananas for $0.32 each, and a watermelon for $3.00. What was the total cost for these purchases?

$15.91

A local government spent 82 percent of the $12,500 budgeted for snow removal. How much of the budgeted money for snow removal was not spent?

$2250

(0×10^4)+(4×10^3)+(0×10^2)+(5×10^1)+(2×10^0)(0×10^4)+(4×10^3)+(0×10^2)+(5×10^1)+(2×10^0) What number is represented by the base-10 expression shown?

Correct Answer: 4052 The correct answer is 4,052. The question requires an understanding of how to write numbers using base-10 numerals, number names, and expanded form. Since 10^3=1,000, 10^2=100, and 10^0=1, the expression shown is equivalent to (0)+(4×1,000)+(0)+(5×10)+(2×1)=4,000+50+2(0)+(4×1,000)+(0)+(5×10)+(2×1)=4,000+50+2, which equals 4,052.

(2x+5x−2)−(x+y−3y−5x+2)(2x+5x−2)−(x+y−3y−5x+2) Which of the following is equivalent to the expression shown? A.11x+2y−411x+2y−4 B.3x−2y−43x−2y−4 C.11x−2y11x−2y D.x−2y

Correct Answer: A Option (A) is correct. The question requires an understanding of how to add and subtract linear algebraic expressions. Adding like terms in the given expression yields the equivalent expression (7x−2)−(−4x−2y+2)(7x−2)−(−4x−2y⁢+2), which is equivalent to 7x−2+4x+2y−27x−2+4x+2y−2. Adding like terms again yields 11x+2y−411x+2y−4.

In a bag there are 28 candies, of which 17 are peppermints and the rest are caramel chews. What is the ratio of the number of caramel chews to the number of peppermints in the bag? A.11:17 B.17:11 C.17:28 D.28:17

Correct Answer: A Option (A) is correct. The question requires an understanding of how to apply the concepts of ratios and unit rates to describe relationships between two quantities. The total number of candies is 28, and 17 of them are peppermint. Therefore, there are 27−1727−17, or 11 caramel chews. The ratio of caramel chews to peppermints is 11:1711:17.

Which word describes each angle in an equilateral triangle? A.Acute B.Obtuse C.Right D.Straight

Correct Answer: A Option (A) is correct. The question requires an understanding of how to classify angles based on their measure. An equilateral triangle is also equiangular; that is, all its angles have the same measure. Therefore, each angle has a measure of 180÷3180÷3, or 60 degrees. An acute angle is an angle that measures less than 90 degrees. Therefore, the angles of an equilateral triangle are all acute.

Which of the following is an algebraic expression? A.6x−46x-4 B.6y<46y<4 C.6z=46z=4 D.6+4

Correct Answer: A Option (A) is correct. The question requires an understanding of how to differentiate between algebraic expressions and equations. An algebraic expression is made of constants, variables, and algebraic operations. While (A) is an algebraic expression, (B) is an algebraic inequality, (C) is an algebraic equation, and (D) is a numerical expression.

The first three figures in a pattern are shown. The 1st figure is composed of two triangles and one square. Each figure after the 1st figure is composed of two triangles and one square more than the preceding figure. How many line segments are in the 10th figure of the pattern? A.35 B.38 C.41 D.44

Correct Answer: A Option (A) is correct. The question requires an understanding of how to identify and extend a pattern. The first figure has 8 line segments. Adding a square to each figure is equivalent to adding 3 line segments. So the number of line segments of the nthnth figure can be described by the equation f(n)=5+3nf(n)=5+3n, with n=1,2,3,...n=1,2,3,... Therefore the 10th figure of the pattern has f(n)=5+3×10f(n)=5+3×10, or 35 line segments.

Carlos makes an annual salary of $65,295. Which of the following is Carlos' salary rounded to the nearest thousand? A.$65,000 B.$65,300 C.$66,000 D.$70,000

Correct Answer: A Option (A) is correct. The question requires an understanding of how to round multidigit numbers to any place value. To round to the nearest thousand, one must look at the digit in the hundreds place first. The digit in the hundreds place is 2, which is less than 5. Therefore, the digit in the thousands place is not changed when rounding to the nearest thousand.

Which of the following inequalities is equivalent to the inequality 4x+4≤9x+84x+4≤9x+8? A.x≥−45x≥−45 B.x≤−45x≤−45 C.x≥−125x≥−125 D.x≤−125

Correct Answer: A Option (A) is correct. The question requires an understanding of how to solve multistep one-variable linear equations and inequalities. Using the addition property of inequality, the given inequality is equivalent to 4x+4+(−9x−4)≤9x+8+(−9x−4)4x+4+(−9x−4)≤9x+8+(−9x−4). Simplifying like terms yields −5x≤4−5x≤4. Using the multiplication property of inequality and taking into account the sign, −5x≤4−5x≤4 is equivalent to (−1/5)(−5x)≥(−1/5)(4). Simplifying yields x≥−45x≥−45.

The surface area of a cube is 54 in254 in2. What is the volume of the cube? A. 27 in3 B. 54 in3 C. 81 in3 D.108 in3

Correct Answer: A Option (A) is correct. The question requires an understanding of how to solve problems involving elapsed time, money, length, volume, and mass. If the length of the side of the cube is s in, then its surface area is 6s26s2 in2. Since the surface area is 54 in2, then the length of the side of the cube, in inches, can be found by solving the equation 6s2=54, which yields s=3. The volume of the cube can then be found by solving the equation V=s3, thus V=33. Therefore the volume is 27 in3.

A certain polygon has the following attributes. There are 2 pairs of parallel sides. It is a quadrilateral. One pair of parallel sides has length 2, and the other pair of parallel sides has length 4. Which of the following types of polygons has all of the attributes listed? A.Parallelogram B.Rhombus C.Triangle D.Square

Correct Answer: A Option (A) is correct. The question requires an understanding of how to use attributes to classify or draw polygons and solids. A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral with two pairs of parallel sides. A rhombus is a parallelogram with all sides of the same length. A square is a rhombus with at least one right angle. For attributes 1 and 2, the polygon is not a triangle. For attribute 3, the polygon is neither a rhombus nor a square. Therefore, the polygon must be a parallelogram.

The cost to rent a bus for a field trip is $34.25 per hour, and the duration of the trip is 4 hours and 45 minutes. Which of the following expressions is best for doing a mental calculation to closely estimate the total cost, in dollars, of renting the bus for the trip? A.34×534×5 B.34×4.7534×4.75 C.34.25×4.7534.25×4.75 D.35×5

Correct Answer: A Option (A) is correct. The question requires an understanding of how to use mental math, estimation, and rounding strategies to solve problems and determine reasonableness of results. The total cost of the trip can be calculated by multiplying the hourly rate by trip duration, in hours. The cost of the bus per hour is best estimated as $34, and the duration of the trip is best estimated as 5 hours. Therefore, the best expression to estimate the total cost using a mental calculation is 34×534×5.

1−2 5/6 What is the value of the expression shown? A. −1 5/6 B. −1/6 C. 1/6 D. 1 5/6

Correct Answer: A Option (A) is correct. The question requires an understanding of various strategies and algorithms used to perform operations on rational numbers. The given expression is equivalent to 6/6−17/6, that is −11/6, or −1 5/6.

Which of the following is a statistical question? Select all that apply. A.What is the daily high temperature for an August day in Cheyenne, Wyoming? B.How many speeches did George Washington make during his life? C.How many minutes did Hannah spend talking on her phone on August 28, 2016 ? D.What was the average number of miles a week run by the members of the Hereford High School cross-country team last month?

Correct Answer: A, D Options (A) and (D) are correct. The question requires an understanding of how to identify statistical questions. A statistical question is one that can be answered by collecting data and where there will be variability in the data collected. To answer the question in (A), one must collect the daily high temperature for each day in August. Such values will vary. To answer the question in (D), one must collect the number of miles a week run by each of the members of the team during the past month. Such values will vary. The questions in (B) and (C) can be answered simply by counting.

Lilly, Madelyn, Natalie, and Olivia each walked from their houses to the mall. Lilly walked 1/4 mile, Madelyn walked 3/8 mile, Natalie walked 5/6 mile, and Olivia walked 7/12 mile. Which list shows these distances in order from least to greatest? A.1/4 mi, 3/8 mi, 5/6 mi, 7/12 mi B.1/4 mi, 3/8 mi, 7/12 mi, 5/6 mi C.1/4 mi, 5/6 mi, 3/8 mi, 7/12 mi D.7/12 mi, 3/8 mi, 5/6 mi, 1/4 mi

Correct Answer: B Option (B) is correct. The question requires an understanding of how to compare, classify, and order rational numbers. The distances can be ordered by rewriting all fractions as equivalent fractions with the common denominator 24. Since 1/4=6/24, 3/8=9/24, 5/6=20/24, and 7/12=14/24, the correct order from least to greatest distance is 1/4 mi, 3/8 mi, 7/12 mi, 5/6 mi.

A boxplot for a set of data is shown. Which of the following is true? A.The only outlier is 200. B.The only outlier is 1,000. C.The only outliers are 200, 700, and 1,000. D.All values greater than 500 or less than 300 are outliers.

Correct Answer: B Option (B) is correct. The question requires an understanding of how to describe a set of data. The interquartile range is 500−300=200500−300=200. Therefore, any value less than 300−(200×1.5)=0300−(200×1.5)=0 or greater than 500+(200×1.5)=800500+(200×1.5)=800 is an outlier. The only outlier in the data set, i.e., a data value less than 0 or greater than 800, is 1,000.

If y=2, what is the value of 4−2(4y)+5y? A.−22 B. −2 C. 22 D. 26

Correct Answer: B Option (B) is correct. The question requires an understanding of how to evaluate simple algebraic expressions. The first step is to substitute 2 in place of the variable y, which yields the arithmetic expression 4−2(4×2)+5×2. Using the order of operations, 4−2(4×2)+5×2=4−2×8+10=4−16+10=−24−2(4×2)+5×2=4−2×8+10=4−16+10=−2.

What is the least common multiple of 12, 20, and 30? A. 2 B. 60 C.240 D.360

Correct Answer: B Option (B) is correct. The question requires an understanding of how to find factors and multiples of numbers. The prime factorization of 12 is 2^2×3, the prime factorization of 20 is 2^2×5, and the prime factorization of 30 is 2×3×5. Therefore, the least common multiple of the three numbers is 2^2×3×5, or 60.

If r is a real number, which of the following illustrates the commutative property of multiplication? A.(32)(r)=(3)(2r)(32)(r)=(3)(2r) B.(32)(r)=(r)(32)(32)(r)=(r)(32) C.(32)(r)=(30)(r)+(2)(r)(32)(r)=(30)(r)+(2)(r) D.(32)(r)=(32)(r)(1)

Correct Answer: B Option (B) is correct. The question requires an understanding of how to identify properties of operations. The commutative property of multiplication states that given any two numbers A and B, A×B=B×AA×B=B×A; that is, the order of the factors in a multiplication problem does not affect the product.

x y 1 1 2 4 3 9 4 16 Which of the following functions could be represented by the table shown? A. y=2^x B. y=x^2 C. y=2^x D. y=5x−4

Correct Answer: B Option (B) is correct. The question requires an understanding of how to identify relationships between the corresponding terms of two numerical patterns. To find out which function could be represented by the table, one must substitute the values of x given in the table and verify which function gives the corresponding values of y. The function in (B) could be represented by the table because 1^2=1, 2^2=4, 3^2=9, and 4^2=16. The functions in (A) and (C) could not be represented by the table because for x=1, each yields y=2. The function in (D) could not be represented by the table because for x=2, it yields y=6.

Two friends went out for lunch and decided to share the dessert. One of them ate 1/2 of the dessert, and the other ate 1/3 of the remaining part. What fraction of the dessert was left over? A.1/6 B.1/3 C.2/3 D.5/6

Correct Answer: B Option (B) is correct. The question requires an understanding of how to solve multistep mathematical and real-world problems. The first friend ate 1/2 of the dessert, while the second friend ate 1/3 of the remaining part; that is, 1/3(1−1/2), or 1/6. Altogether they ate 1/2+1/6=4/6, or 2/3 of the dessert. Therefore, the fraction left over is 1−2/3, or 1/3 of the dessert.

2/3÷4/3+3/5×(5/3)^2 Which of the following is equivalent to the expression shown? A.2929 B.136136 C.239239 D.5518

Correct Answer: B Option (B) is correct. The question requires an understanding of how to solve problems using the order of operations. By using the order of operations and the fact that dividing is equivalent to multiplying by the inverse, the expression 2/3÷4/3+3/5×(5/3)^2 can be simplified to 2/3×3/4+3/5×25/9. Performing both multiplications yields 1/2+5/3, which is equivalent to 13/6.

All small rectangles contained in rectangle ABCD shown have the same area. How many of the small rectangles must be shaded so that 38 percent of the area of rectangle ABCD is shaded? A.12 B.19 C.31 D.38

Correct Answer: B Option (B) is correct. The question requires an understanding of percent as a rate per 100. There are 50 congruent small rectangles in ABCD. If 38% of the area of ABCD is shaded, then 38/100×50, or 19 small rectangles, must be shaded.

A window's size is 8 feet by 4 feet. Which of the following units is most appropriate to use to convert the dimensions to metric units? A.Kilometers B.Meters C.Millimeters D.Nanometers

Correct Answer: B Option (B) is correct. The question requires an understanding of relative sizes of United States customary units and metric units. Since 1 meter is approximately 3.28 feet, meters are the most appropriate unit to use to convert 8 feet and 4 feet to metric units.

r=5b In a flower shop, there are 5 roses in every bouquet. The equation shown gives the number of roses r used to make b bouquets. Select the appropriate choices to correctly complete each sentence. b is (i) B.an independent variable.r is (ii) A.a dependent variable.

Correct Answer: B, A Options (B) and (A) are correct. The question requires an understanding of how to differentiate between dependent and independent variables in formulas. In the given formula, there are two variables, b and r. Since the formula investigates how the number of roses r used increases depending on the number of bouquets b, the dependent variable is r and the independent variable is b.

The figures shown are squares. Each side in Figure 1 has length 7, and Figure 2 has side lengths that are double those in Figure 1. How do the perimeter and area of Figure 1 compare with the perimeter and area of Figure 2 ? A.The perimeter and area of Figure 2 are double the perimeter and area of Figure 1. B.The perimeter and area of Figure 2 are four times the perimeter and area of Figure 1. C.The perimeter of Figure 2 is double the perimeter of Figure 1, and the area of Figure 2 is four times the area of Figure 1. D.The perimeter of Figure 2 is four times the perimeter of Figure 1, and the area of Figure 2 is eight times the area of Figure 1.

Correct Answer: C Option (C) is correct. The question requires an understanding of how changes to dimensions change area and volume. If the dimensions of a figure double, the ratio of corresponding sides will be 1:2. This same ratio will apply to the perimeter. In the figures shown, the perimeter of the smaller square is 28, and the perimeter of the larger square is 56. This results in a ratio of 28:56, which can be simplified to 1:2. The ratio of the areas of the squares with a side ratio of 1:2 will be 1^2:2^2, or 1:4. The area of the smaller square is 49, and the area of the larger square is 196. This results in a ratio of 49:196, which can be simplified to 1:4. Thus the perimeter is doubled, and the area is quadrupled.

1 tablespoon 1/16 cup 1 teaspoon 1/3 tablespoon 1 fluid ounce 2 tablespoons Each row of the table shows equivalent measurements. Based on the equivalent measurements, which of the following quantities is greatest? A.12 tablespoons B.7/8 cup C.8 fluid ounces D.45 teaspoons

Correct Answer: C Option (C) is correct. The question requires an understanding of how to convert units within the U.S. customary system. To answer the question, one can convert all measurements to the same unit, for example, tablespoons. The quantity in (A) is already 12 tablespoons. The quantity in (B) is 7/8 cup, which is equivalent to 7/8×16, or 14 tablespoons. The quantity in (C) is 8 fluid ounces, which is equivalent to 8×2, or 16 tablespoons. Lastly, the quantity in (D) is 45 teaspoons, which is equivalent to 45×1/3, or 15 tablespoons.

90, 90, 95, 90, 85, 90 Caleb's scores for the first 6 quizzes in his algebra class are shown above. If he receives a score of 95 on the 7th quiz, which of the following statements will be true? A.The average (arithmetic mean) of the 7 quiz scores is less than the average of the first 6 quiz scores. B.The mode of the 7 quiz scores is greater than the mode of the first 6 quiz scores. C.The median of the 7 quiz scores is equal to the median of the first 6 quiz scores. D.The range of the 7 quiz scores is greater than the range of the first 6 quiz scores.

Correct Answer: C Option (C) is correct. The question requires an understanding of how to determine how changes in data affect measures of center or range. Placing the first 6 quiz scores in order gives 85, 90, 90, 90, 90, and 95. Since the two middle numbers are both 90, it is easy to see that the median is 90. The mode and the mean are also 90, and the range is 10. After adding 95 to the list, the median remains 90, the mode remains 90, and the range remains 10. Only the mean is affected by adding 95 to the list. Since 95 is greater than 90, that is, the mean of the first 6 quiz scores, the mean of the 7 quiz scores is greater than the mean of the first 6 quiz scores. Therefore, of the given statements, the only true statement is that the two medians are equal.

a=5,000(1+r)a=5,000(1+r) The formula shown can be used to find the amount of money in dollars, a, in an account at the end of one year when $5,000 is invested at simple annual interest rate r for the year. Which of the following represents the independent variable in the formula? A.a B.5,000 C.r D.1+r

Correct Answer: C Option (C) is correct. The question requires an understanding of how to differentiate between dependent and independent variables in formulas. In the given formula, there are two variables, a and r. The formula can be used to investigate how the amount of money a varies depending on the interest rate r. Therefore, the dependent variable is a and the independent variable is r.

1,1,2,3,5,8,... The first six terms of a sequence are shown. Which of the following formulas can be used to find the terms of the sequence? A.a1=1 an=an−1 for n≥2 B.a1=1 an=an−1+1 for n≥3 C.a1=1 a2=1 an=an−2+an−1 for n≥3 D.a1=1 a2=1 an=an−2+an−1+n−3 for n≥3

Correct Answer: C Option (C) is correct. The question requires an understanding of how to make conjectures, predictions, or generalizations based on patterns. The only formula that yields a sequence whose terms are those shown is the one in (C), in which the first two terms are defined as 1 and each subsequent term is the sum of the two terms immediately preceding it. The formula in (A) yields a sequence in which every term is 1. The formula in (B) yields a sequence in which the first two terms are 1 and 2. The formula in (D) yields a sequence in which the first four terms are 1, 1, 2, and 4.

At an apple orchard, between 280 and 300 bushels of apples are picked each day during peak harvest season. There are between 42 and 48 pounds of apples in each bushel. Which of the following could be the number of pounds of apples picked at the orchard in one day during peak harvest season? A. 9,000 B.11,000 C.13,000 D.15,000

Correct Answer: C Option (C) is correct. The question requires an understanding of how to recognize the reasonableness of a solution within the context of a given problem. The minimum number of pounds of apples picked in one day is 42×280=11,76042×280=11,760. The maximum number of pounds of apples picked in one day is 48×300=14,40048×300=14,400. The number in (C), 13,000 pounds, is the only number of pounds of apples greater than 11,760 and less than 14,400.

A machine that works at a constant rate processes 18 pounds of fruit every 3 hours. At this rate, how many hours does it take the machine to process 72 pounds of fruit? A. 4 B.10 C.12 D.15

Correct Answer: C Option (C) is correct. The question requires an understanding of how to solve unit-rate problems. One must first find the unit rate by dividing 18 pounds (lbs) by 3 hours, resulting in 6 lbs/hour. Then one must divide 72 lbs by 6 lbs/hour to determine how many hours it will take to process 72 lbs of fruit. Since 72÷6=1272÷6=12, it will take 12 hours to process 72 lbs of fruit.

3 less than 4 times the sum of the number x and 15 Which of the following expressions best represents the verbal phrase shown? A.4x+15−34x+15−3 B.3−4x+153−4x+15 C.4(x+15)−34(x+15)−3 D.3−4(x+15)

Correct Answer: C Option (C) is correct. The question requires an understanding of how to translate between verbal statements and algebraic expressions or equations. The product of a number and a sum requires parentheses around the sum. Therefore, "4 times the sum of the number x and 15" can be represented by the expression 4(x+15)4(x+15). "Less than" can be translated as subtraction, where what comes before "less than" is taken away from what comes after it. Therefore, the verbal phrase can be represented by the expression 4(x+15)−34(x+15)−3.

A painter used 1 1/2 cans of paint to paint 2/3 of a room. At this rate, how much more paint does the painter need to paint the remainder of the room? A.1/3 can B.1/2 can C.3/4 can D.1 can

Correct Answer: C Option (C) is correct. The question requires an understanding of how to use proportional relationships to solve ratio and percent problems. Since the painter has already painted 2/3 of the room, the painter still needs to paint 1−2/3, or 1/3 of the room. To determine the amount of paint x needed to paint the rest of the room, one can set up the proportion 1 1/2:2/3=x:1/3, which yields the equation 2/3x=(1 1/2)×1/3. Simplifying the right side of the equation yields 2/3x=1/2. Therefore, x=3/2×1/2; that is, x=3/4.

Mary has a rectangular garden in her backyard. The garden measures 534534 feet wide by 712712 feet long. What is the area of the garden? A.26 1/2 square feet B.35 3/8 square feet C.36 1/8 square feet D.43 1/8 square feet

Correct Answer: D Option (D) is correct. The question requires an understanding of how to find the area and perimeters of polygons. If a rectangle has a length of ℓℓ units and a width of w units, then its area is ℓ×wℓ×w square units. Since the garden has a length of 7 1/2 feet and a width of 5 3/4 feet, the area is 7 1/2×5 3/4=15/2×23/4=345/8 square feet, that is, 43 1/8 square feet.

What is the prime factorization of 3,780? A.2×5×6×7×92×5×6×7×9 B.3×4×5×7×93×4×5×7×9 C.2×3×6×7×152×3×6×7×15 D.2×2×3×3×3×5×7

Correct Answer: D Option (D) is correct. The question requires an understanding of how to identify and use prime and composite numbers. The prime factorization of a number is that number written as a product of its prime factors. The prime factors of 3,780 are 2, 3, 5, and 7, and 3,780 = 2×2×3×3×3×5×73,780 = 2×2×3×3×3×5×7.

What value does the 8 represent in the number 5,836,303 ? A.Eight hundred B.Eight thousand C.Eighty thousand D.Eight hundred thousand

Correct Answer: D Option (D) is correct. The question requires an understanding of how to identify the place a digit is in and its value in that place. The digit 8 is in the fifth place to the left of the ones place, so its value is 8×1058×105 or 800,000, that is, eight hundred thousand.

At a flower shop, there are 5 different kinds of flowers: tulips, lilies, daisies, carnations, and roses. There are also 3 different colors of vases to hold the flowers: blue, green, and pink. If one kind of flower and one color of vase to hold them are to be selected at random, what is the probability that the selection will be lilies held in a pink vase? A. 2/8 B.2/15 C. 1/8 D.1/15

Correct Answer: D Option (D) is correct. The question requires an understanding of how to interpret probabilities relative to likelihood of occurrence. There are 15 possibilities (5 different kinds of flowers times 3 different colors of vases), so the probability of selecting lilies held in a pink vase is 1/15.

The boxplots shown compare the incomes of two professions. Based on the boxplots, which of the following statements is true? A.All nuclear engineers earn more than all police officers. B.Exactly 50% of nuclear engineers earn more than all police officers. C.The range of incomes for nuclear engineers is the same as that for police officers. D.The median income for nuclear engineers is greater than the maximum income for police officers.

Correct Answer: D Option (D) is correct. The question requires an understanding of how to interpret various displays of data. The top boxplot shows that the annual income of a nuclear engineer ranges from a minimum of approximately $50,000 to a maximum of approximately $120,000, with a median annual income of approximately $70,000. The bottom boxplot shows that the annual income of a police officer ranges from a minimum of approximately $15,000 to a maximum of approximately $60,000, with a median annual income of approximately $50,000. Therefore, the median income for nuclear engineers is greater than the maximum income for police officers.

A unit square is partitioned into identical parts having equal areas. One of the parts is removed from the square, and a shape is formed by the parts that remain after the removal. For which of the following areas of the removed part will the shape that is formed have the greatest area? A.1/4 B.1/5 C.1/6 D.1/7

Correct Answer: D Option (D) is correct. The question requires an understanding of how to recognize concepts of rational numbers and their operations. If the unit square is partitioned in n parts having equal area, the area of each part is 1/n. Therefore the area of the shape that is formed when removing one of the identical parts is 1−1/n. The smaller is the area of the removed part, the greater is the area of the shape that is left. Since 1/7 is the smallest of the four fractions listed, the shape that has the greatest area is the one that is left by removing a part with area 1/7 .

Membership Length ,in months Cost, in dollars 1 75 3 125 6 200 12 350 24 650 The table shows the cost of a membership to Gym B for the five possible membership lengths. Gym A has the same possible membership lengths, and the cost, y, in dollars, of a membership to Gym A for x months is given by the equation 2y−50x=852y−50x=85. Which of the following is true about the cost, in dollars, of a membership to Gym A compared with the cost of a membership to Gym B? A.The cost of a membership to Gym B is greater than the cost of a membership to Gym A for membership lengths of 6 months or less but is greater for membership lengths of greater than 6 months. B.The cost of a membership to Gym A includes the same initial membership fee as the cost of a membership to Gym B but a greater monthly fee. C.The cost of a membership to Gym A includes a greater initial membership fee than the cost of a membership to Gym B but a lower monthly fee. D.The cost of a membership to Gym B is greater than the cost of a membership to Gym A for any number of months.

Correct Answer: D Option (D) is correct. The question requires an understanding of how to use linear relationships represented by equations, tables, and graphs to solve problems. The table describes the costs of varying lengths of membership to Gym B and can be represented by the linear equation y=25x+50y=25x+50, where y is the cost of a membership lasting x months. The equation that describes the cost y of a membership to Gym A lasting for x months can be rewritten as y=25x+42.50y=25x+42.50. The monthly fees, represented by the slopes of the two linear equations, are equal for the two memberships. However, the y-intercept of the equation representing Gym B is greater than the y-intercept of the line representing Gym A. This can be interpreted to mean that the initial fee for Gym B is greater than the initial fee for Gym A. Since the monthly memberships are the same but Gym B has a greater initial fee, the membership cost for Gym B is always more expensive than the membership cost for Gym A for any number of months.

4x(3x+2y)4x(3x+2y) What does 2y2y represent in the expression shown? A.A binomial B.A factor C.A coefficient D.A monomial

Correct Answer: D Option (D) is correct. The question requires an understanding of how to use mathematical terms to identify parts of expressions and describe expressions. A monomial is an algebraic expression that consists of one term that is a number, a variable, or a product of a number and a variable, where all exponents are whole numbers.

Which of the following expressions is equivalent to −4(3−2x)−4(3−2x) ? A.−2x−12−2x−12 B.2x−122x−12 C.−8x−12−8x−12 D.8x−12

Correct Answer: D Option (D) is correct. The question requires an understanding of how to use the distributive property to generate equivalent linear algebraic expressions. Using the distributive property of multiplication over addition, −4(3−2x)=−4(3)−4(−2x)−4(3−2x)=−4(3)−4(−2x); that is, −12+8x−12+8x. Using the commutative property of addition yields 8x−128x−12.

0.7 is 1/1,000 of what number? A. 0.0007 B. 0.007 C. 70 D.700

Correct Answer: D Option (D) is correct. The question requires an understanding of place value by recognizing that a digit in one place represents ten times what it represents in the place to its right and one-tenth of what it represents in the place to its left and the ability to extend this concept several places to the right or left. If 0.7 is 1/1,000 of a number n, then 0.7=1/1,000n. Therefore, n=0.7×1,000n. Working backward, one can also observe that the decimal point moves three places to the left when finding one-thousandth of a number.