Praxis 2 math
(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?
4150
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 forn≥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
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=11,760. The maximum number of pounds of apples picked in one day is 48×300=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.
(2x+5x−2)−(x+y−3y−5x+2) Which of the following is equivalent to the expression shown? A.11x+2y−4 B.3x−2y−4 C.11x−2y D. x−2y
a
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
a
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
a
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
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
a
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.34×5 B.34×4.75 C.34.25×4.75 D. 35×5
a
The surface area of a cube is 54 in2. What is the volume of the cube? A. 27 in3 B. 54 in3 C. 81 in3 D. 108 in3
a
Three figures are shown. From left to right the figures are labeled, first figure, second figure, and third figure. The pattern of the first figure is a triangle connected to a square, which is connected to a triangle. The figure is composed of 8 line segments. The pattern of the second figure is a triangle connected to a square, which is connected to a square, which is connected to a triangle. The figure is composed of 11 line segments. The pattern of the third figure is a triangle connected to a square, which is connected to a square, which is connected to a square, which is connected to a triangle, all connected together. The figure is composed of 14 line segments. 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
a
Which of the following inequalities is equivalent to the inequality 4x+4≤9x+84x+4≤9x+8? A.x≥−4/5 B.x≤−4/5 C.x≥−12/5 D. x≤−12/5
a
Which of the following is an algebraic expression? a.6x−46x-4 b.6y<46y<4 c.6z=46z=4 d.6+4
a
Which word describes each angle in an equilateral triangle? A.Acute B.Obtuse C.Right D.Straight
a
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 and d
2/3÷4/3+3/5×(5/3)^2 Which of the following is equivalent to the expression shown? 2/9 13/6 23/9 55/18
b
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
If y=2 , what is the value of 4−2(4y)+5y? A.−22 B. −2 C. 22 D. 26
b
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
b
The figure presents a coordinate plane with four plotted points. The number 1 is indicated on both axes. The coordinates of the four points are as follows: A, negative 4 comma 2; B, 4 comma 5; C, 2 comma negative 3; D, negative 3 comma negative 3. In the coordinate plane shown, which point is located in Quadrant I? A.A B.B C.C D.D
b
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
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=2x D. y=5x−4
b
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 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.
r=5br=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 a .... r is a....
b is an independent variable r is a dependent variable 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.
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+15−3 B.3−4x+15 C.4(x+15)−3 D. 3−4(x+15)
c
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.
c
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
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
The figure presents two squares. The first square is labeled Figure 1 and is smaller than the second square, which is labeled Figure 2. 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.
c
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
c
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
c
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
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 78×16, or 14 tablespoons. The quantity in (C) is 8 fluid ounces, which is equivalent to 8×28×2, or 16 tablespoons. Lastly, the quantity in (D) is 45 teaspoons, which is equivalent to 45×13, or 15 tablespoons.
Answer the question below by clicking on the correct response. Question: County Population Brookhaven 74,702 Columbus 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?
c. davidson
0.7 is 1/1,000 of what number? A. 0.0007 B. 0.007 C. 70 D.700
d
4x(3x+2y) What does 2y epresent in the expression shown? A.A binomial B.A factor C.A coefficient D.A monomial
d
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
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
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.
d
The figure presents a graph of two boxplots. The horizontal axis is labeled "Annual Income, in thousands of dollars," and the numbers 0 through 140, in increments of 20, are indicated. The vertical axis is labeled "Profession," and the following two categories are indicated from top to bottom; Nuclear Engineer, Police Officer. The data for each category are as follows. Note that all values are approximate. Nuclear Engineer. The whiskers range from $50,000 to $60,000, and from $94,000 to $119,000. The box ranges from $60,000 to $94,000, with an interior vertical line segment at $70,000. Police Officer. The whiskers range from $12,000 to $21,000, and from $42,000 to $60,000. The box ranges from $21,000 to $42,000, with an interior vertical line segment at $30,000. 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.
d
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
Which of the following expressions is equivalent to −4(3−2x) ? A.−2x−12 B.2x−12 C.−8x−12 D. 8x−12
d
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 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 115115.
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 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 = 2×2×3×3×3×5×7
2 lines in a plane are considered perpendicular if
they form at least one right angle
