Elementary Education Multiple Subjects: Mathematics (5003) Form 3

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

A. 6x-4 (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.)

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?

A, D (The question requires an understanding of how to identify statistical questions. A statistical question is one that can be answered by collecting data and one where there will be variability in the data collected. To answer the question in option (A), one must collect the daily high temperature for each day in August. Such values will vary. To answer the question in option (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.)

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

A. $65,000 (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.)

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

A. -1 5/6 (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.)

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 to 17 B. 17 to 11 C. 17 to 28 D. 28 to 17

A. 11 to 17 (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 peppermints. Therefore, there are 28 minus 1728−17, or 11 caramel chews. The ratio of caramel chews to peppermints is 11 to 17.)

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

A. 11x+2y−4 (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), which is equivalent to 7x−2+4x+2y−2. Adding like terms again yields 11x+2y−4.)

The surface area of a cube is 54 square inches. What is the volume of the cube? A. 27 cubic inches B. 54 cubic inches C. 81 cubic inches D. 108 cubic inches

A. 27 cubic inches (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 inches, then its surface area is 6s squared square inches. Since the surface area is 54 square inches, the length of the side of the cube, in inches, can be found by solving the equation 6s squared, equals 54, which yields s = 3. The volume of the cube can then be found by solving the equation V = s cubed; thus V = 3 cubed. Therefore, the volume is 27 cubic inches.)

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 x 5 B. 34 x 4.75 C. 34.25 x 4.75 D. 35 x 5

A. 34 x 5 (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 34×5.)

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

A. 35 (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 figure n in the pattern can be described by the expression 5+3n, with n=1,2,3,.... Therefore figure 10 of the pattern has 5+3×10, or 35, line segments.)

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

A. Acute (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÷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.)

A certain polygon has the following attributes. 1. There are 2 pairs of parallel sides. 2. It is a quadrilateral. 3. 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

A. Parallelogram (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.)

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

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

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

B. (32)(r)=(r)(32) (The question requires an understanding of how to identify properties of operations. The commutative property of multiplication states that given any two numbers k and m, k×m = m×k; that is, the order of the factors in a multiplication problem does not affect the product.)

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

B. -2 (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 minus, 2 times, open parenthesis, 4 − 2(4×2) + 5 × 2 = 4 − 2 × 8 + 10 = 4 − 16 + 10 = −2.)

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

B. 1/3 (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.)

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

B. 1/4 mile, 3/8 mile, 7/12 mile, 5/6 mile (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 mile, 3/8 mile, 7/12 mile, 5/6 mile.)

2/3 ÷ 4/3 + 3/5 × (5/3)2 (exponent) Which of the following is equivalent to the preceding expression? A. 2/9 B. 13/6 C. 23/9 D. 55/18

B. 13/6 (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 exponent 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.)

In the following figure, all small rectangles contained in the rectangle EFGH shown have the same area. How many of the small rectangles must be shaded so that 38 percent of the area of the rectangle EFGH is shaded? A. 12 B. 19 C. 31 D. 38

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

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

B. 60 (The question requires an understanding of how to find factors and multiples of numbers. The prime factorization of 12 is 2 squared times 3, the prime factorization of 20 is 2 squared times 5, and the prime factorization of 30 is 2 times 3, times 5. Therefore, the least common multiple of the three numbers is 2 squared times 3, times 5, or 60.)

Which phrase describes the solution set to the inequality 18b−5 < 20b+11? A. All numbers that are less than −8 B. All numbers that are greater than −8 C. All numbers that are less than 8 D. All numbers that are greater than 8

B. All numbers that are greater than −8 (The question requires an understanding of how to interpret solutions of multistep one-variable linear equations and inequalities. The first step to find the solution set of the inequality is to use the addition property of inequality to add −20b + 5 to both sides of the inequality. This yields 18b−5−20b+5 < 20b+11−20b+5. The second step is to add like terms. This yields −2b < 16. The third step is to use the multiplication property of inequality to multiply both sides by −1/2. One must not forget to flip the direction of the inequality sign when multiplying by a negative number. This yields (−1/2)(−2b) > (−12)(16), which is equivalent to b > −8. The solution set to the inequality 18b−5 < 20b+11 is the set of all numbers that are greater than −8.)

In the preceding coordinate plane, which point is located in Quadrant 1? A. J B. K C. L D. M

B. K (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 1I is the quadrant above the x-axis and to the right of the y-axis. Point K lies within this quadrant.)

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

B. Meters (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.)

A boxplot for a set of data is shown in the preceding figure. 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.

B. The only outlier is 1,000. (The question requires an understanding of how to describe a set of data. The interquartile range is 500 − 300 = 200. Therefore, any value less than 300 − (200×1.5) = 0 or greater than 500 + (200×1.5) = 800 is an outlier. The only outlier in the data set (that is, a data value less than 0 or greater than 800) is 1,000.)

The preceding figure is a net for which of the following three-dimensional figures? A. Cube B. Triangular prism C. Rectangular prism D. Triangular prism

B. Triangular prism (The question requires an understanding of how to represent three-dimensional figures with nets. The net shown is composed of 2 triangles and 3 rectangles. The triangular prism is the only one of the listed three-dimensional figures that has 2 triangular faces and 3 rectangular faces.)

x/y 1/1 2/4 3/9 4/16 Which of the following functions could be represented by the preceding table? A. y = 2 exponent x B. y = x exponent 2 C. y = 2x D. y = 5x - 4

B. y = x exponent 2 (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 option (B) could be represented by the table because 1 squared equals 1, 2 squared; 4, 3 squared equals 9, and 4 squared equals 16.)

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

C 3/4 can (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 p needed to paint the rest of the room, one can use the proportional relationship that 1 1/2 is to 2/3 as p is to 1/3 to set up the equation 2/3p = (112) × 13. Simplifying the right side of the equation yields 2/3p = 1/2. Therefore, p = 3/2 × 1/2; that is, p = 34.)

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

C. -8x-12 (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); that is, −12+8x-12+8x. Using the commutative property of addition yields 8x−12.)

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

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

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

C. 13,000 (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 = 11,760. The maximum number of pounds of apples picked in one day is 48 × 300 = 14,400. The number in option (C), 13,000 pounds, is the only number of pounds of apples greater than 11,760 and less than 14,400.)

The formula V equals I times RV=IR relates the voltage V, in volts, to the current I, in amperes, 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 amperes B. 2.00 amperes C. 2.25 amperes D. 2.50 amperes

C. 2.25 amperes (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 amperes.)

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

C. 4(x+15)−3 (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). "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)−3.)

1 tablespoon equals = 1/16 cup 1 teaspoon equals = 1/3 tablespoon 1 fluid ounce equals = 2 tablespoons Each of the preceding conversions 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

C. 8 fluid ounces (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 option (A) is already 12 tablespoons. The quantity in option (B) is 7/8 cup, which is equivalent to 7/8 × 16, or 14 tablespoons. The quantity in option (C) is 8 fluid ounces, which is equivalent to 8×2, or 16 tablespoons. Lastly, the quantity in option (D) is 45 teaspoons, which is equivalent to 45 × 1/3, or 15 tablespoons.)

The following table shows the populations of four neighboring counties. County/Population Brookhaven/74,702 Columbus/70,472 Davidson/74,072 Washington/74,720 Quyen lives in the county with a population of 70,000+4,000+70+2. In which county does Quyen live? A. Brookhaven B. Columbus C. Davidson D. Washington

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

In the preceding figure, which two lines form a pair of perpendicular lines? A. Line q and line r B. Line r and line s C. Line s and line t D. Line t and line q

C. Line s and line t (The question requires an understanding of how to use definitions to identify lines, rays, line segments, parallel lines, and perpendicular lines. Two lines in the plane are perpendicular if they form at least one right angle. The figure indicates that lines s and t form a right angle; therefore, line s and line t are perpendicular.)

The following list shows Caleb's scores for the first 6 quizzes in his algebra class. 90, 90, 95, 90, 85, 90 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.

C. The median of the 7 quiz scores is equal to the median of the first 6 quiz scores. (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.)

The preceding figures 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.

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. (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 to 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 to 56, which is equivalent to the ratio 1 to 2. The ratio of the areas of the squares with a side ratio of 1 to 2 will be 1 squared to 2 squared, or 1 to 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 to 196, which is equivalent to the ratio 1 to 4. Thus the perimeter is doubled, and the area is quadrupled.)

The following list shows the first six terms of a sequence. 1, 1, 2, 3, 5, 8,... 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≥2 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

C. a1=1; a2=1; an=an−2+an−1 for n≥3 (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 option (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.)

In a flower shop, there are 5 roses in every bouquet. The following equation gives the number of roses r used to make b bouquets. r=5b Which of the following sentences best describes the variables r and b in the preceding equation? A. b is a dependent variable, and r is a dependent variable. B. b is a dependent variable, and r is an independent variable. C. b is an independent variable, and r is a dependent variable. D. b is an independent variable, and r is an independent variable.

C. b is an independent variable, and r is a dependent variable. (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 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

C. r (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.)

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

D. 1/15 (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.)

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

D. 1/7 (The question requires an understanding of how to recognize concepts of rational numbers and their operations. If the unit square is partitioned into 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 the area of the removed part, the greater 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.)

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

D. 2×2×3×3×3×5×7 (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=2×2×3×3×3×5×7.)

Mary has a rectangular garden in her backyard. The garden measures 5 3/4 feet wide by 7 1/2 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

D. 43 1/8 square feet (The question requires an understanding of how to find the area and perimeters of polygons. If a rectangle has a length of ℓ units and a width of w units, then its area is ℓ×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 x 5 3/4 = 15/2 x 23/4, = 43 1/8 square feet.)

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

D. 700 (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 = 0.7×1,000. Working backward, one can also observe that the decimal point moves three places to the left when finding one-thousandth of a number.)

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

D. A monomial (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.)

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

D. Eight hundred thousand (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 times 10 to the fifth power, or 800,000—that is, eight hundred thousand.)

Which of the preceding figures represents the calculation −7 − (−2)? A. Figure 1 B. Figure 2 C. Figure 3 D. Figure 4

D. Figure 4 (The question requires an understanding of how to represent rational numbers and their operations in different ways, using drawings, models, number lines, and arrays. One must first plot −7 on the number line. Since −(−2) is equivalent to +2, one must next move two steps to the right, which yields an answer of −5.)

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

D. The cost of a membership to Gym G is greater than the cost of a membership to Gym H for any number of months. (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 G and can be represented by the linear equation y = 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 H lasting for x months can be rewritten as y = 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 G is greater than the y-intercept of the line representing Gym H. This can be interpreted to mean that the initial fee for Gym G is greater than the initial fee for Gym H. Since the monthly memberships are the same but Gym G has a greater initial fee, the membership cost for Gym G is always more expensive than the membership cost for Gym H for any number of months.)

The following boxplots 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.

D. The median income for nuclear engineers is greater than the maximum income for police officers. (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.)

(0×10 to the fourth power) + (4×10 cubed) + (0×10 squared) + (5×10 first power) + (2×10 to the zero power) What number is represented by the base-10 expression shown?

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 cubed equals 1,000, 10 squared equals 100, and 10 to the 0 power equals 1, the expression shown is equivalent to (0) + (4×1,000) + (0) + (5×10) + (2×1) = 4,000 + 50 + 2, which equals 4,052.)