Praxis Elementary Education: Math (7003)

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Carlos makes an annual salary of $65,295. Which of the following is Carlos' salary rounded to the nearest thousand?

$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.

If r is a real number, which of the following illustrates the commutative property of multiplication?

(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 ?

-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, 4−2(4×2)+5×2=4−2×8+10=4−16+10=−2.

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?

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.

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?

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 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?

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

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?

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.

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?

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 28−17, 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?

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.

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?

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.

2/3 divided by 4/3 plus 3/5 times (5/3) to the power of 2 Which of the following is equivalent to the preceding expression?

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 can be simplified to 2/3 x 3/4 + 3/5 x 25/9, which yields 1/2 + 5/3 which is equivalent to 13/6

The cost to rent a bus for a field trip is $134.25 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?

134 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 $134, 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 134×5.

There are 50 small squares contained in a rectangle. How many of the small rectangles must be shaded so that 38 percent of the area of rectangle E F G HEFGHEFGH is shaded?

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

What is the prime factorization of 3,780 ?

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.

The formula V=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?

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.

The surface area of a cube is 54 square inches. What is the volume of the cube?

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. 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=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.

3 less than 4 times the sum of the number x and 15 Which of the following expressions best represents the preceding verbal phrase?

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.

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

4052

What is the least common multiple of 12, 20, and 30 ?

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

Which of the following is an algebraic expression?

6w - 4: The question requires an understanding of the difference between algebraic expressions and equations. An algebraic expression is a mathematical statement that can include numbers, variables, and operations (for example, plus++ and times×× ) but does not include comparison symbols (for example, equals== and greater than>> ). Only option (A) is an expression, since it is the only option with a statement that does not contain a comparison symbol.

0.7 is 1/1,000 of what number?

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.

1 tablespoon = 1/16 cup 1 teaspoon = 1/3 tablespoon 1 fluid ounce = 2 tablespoons Each of the preceding conversions shows equivalent measurements. Based on the equivalent measurements, which of the following quantities is greatest?

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.

Which of the following expressions is equivalent to −4(3−2x) ?

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. Using the commutative property of addition yields 8x−12.

4x(3x+2y) What does 2y represent in the expression shown?

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.

Which word describes each angle in an equilateral triangle?

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.

Which phrase describes the solution set to the inequality 18b−5<20b+11?

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)>(−1/2)(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.

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?

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=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?

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.

Which of the following inequalities is equivalent to the inequality 4x+4≤9x+8 ?

x≥−4/5: 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.

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 2y−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?

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.

A square had a length of 7, and another square has side lengths that are double the first square. How do the perimeter and area of the first square compare with the perimeter and area of the second square?

The perimeter of the second square is double the perimeter if the first square, and the area of the second square is four times the area of the first square. 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.

Which TWO of the following are statistical questions?

What is the daily high temperature for an August day in Cheyenne, Wyoming? and What was the average number of miles a week run by the members of the Hereford High School cross-country team last month?: 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.

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?

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.


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