Math - F2, Math - F3
2 lines in a plane are considered perpendicular if...
They form at least one right angle
(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
Answer is 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
Answer is A.
462,359 In the number shown, the value represented by the digit 6 is 6×b, where b is a constant. Which of the following equals b? A. 10^3 B. 10^4 C. 10^5 D. 10^6
Answer is B. 10^4 Option (B) is correct. The question requires an understanding of how to use whole-number exponents to denote powers of 10. The number 462,359 can be written as 4x10^5 + 6x10^4 + 2x10^3 + 3x10^2 + 5x10^1 + 9x10^0
The function f(x)=x^2+3 is represented by which table of values?
(-2, 7), (-1,4), (0,3), (3,12)
Rodrigo left his workplace at 4:50 P.M., and it took him 3/4 of an hour to get home. At what time did Rodrigo get home? A. 5:35 P.M. B. 5:45 P.M. C. 5:55 P.M. D. 6:05 P.M.
Answer is A.5:35 P.M. Option (A) is correct. The question requires an understanding of elapsed time. Since there are 60 minutes in an hour, it took Rodrigo 60 x3/4 , or 45 minutes, to get home. Since 50 minutes after 4:00 P.M. plus 45 minutes more is 95 minutes after 4:00 P.M., and 95 minutes is 1 hour and 35 minutes, Rodrigo got home at 5:35 P.M
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
Answer is B.
Which of the following is the expanded form of 3,056.45?
(3×1,000)+(5×10)+(6×1)+(4×1/10)+(5×1/100) 3,056.45=3,000+50+6+0.4+0.05
Which of the following is an algebraic equation? A. 3x − 5 = 2 B. 4x − 2y + 8 C. 3(9 − 4) = 5 (4 − 1) D. 7 + 5 − 12/3
Answer is A. 3x−5 = 2
A family of 5 consumes 1/2 gallon of milk a day. How many 1-gallon jugs of milk must the family buy to have enough milk for a week?
4 jugs
Drag each net onto the most specific corresponding name for its three-dimensional figure. Cube - Triangular pyramid - Triangular prism - Rectangular prism -
Correct Answer: C, D, A, B The net order third, fourth, first, and second is correct. The question requires an understand-ing of how to represent three-dimensional figures with nets. The net of a cube is made of 6 squares, so it must be the third net in the row. The net of a triangular pyramid is made of 4 triangles, so it must be the fourth net in the row. The net of a triangular prism is made of 2 triangles and 3 rectangles, so it must be the first net in the row. The net of a rectangular prism is made of either 6 rectangles or 4 rectangles and 2 squares, so it must be the second net in the row.
What is the area, in square inches, of the polygon shown?
1080
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
Answer is 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 = 12, it will take 12 hours to process 72 lbs of fruit.
Tasha has T books, and Aisha has A books. Aisha has twice as many books as Tasha, and altogether they have 30 books. Which of the following proportions can be used to find out how many books Aisha has? A. A : T = 2 : 3 B. T : A = 2 : 3 C. A : (T + A) = 2 : 3 D. T : (T + A) = 2 : 3
Answer is C. A : (T+A) =2 : 3 Option (C) is correct. The question requires an understanding of ratios and unit rates to describe relationships between quantities. Since Aisha has twice as many books as Tasha, the ratio of T:A is equal to 1:2 ; that is, Tasha has one-third of the books, while Aisha has two-thirds. Therefore, the ratio of Aisha's books, A, and the total T+A is 2:3.
2y^2 + 17x^2 + 14x^2 y + 8xy^2 + 1 Which THREE of the following statements are correct about the algebraic expression shown? A. The coefficients are 2, 17, 14, 8, and 1. B. The variables are x and y. C. There are like terms. D. There are 4 terms. E. The degree of the expression is 3.
Answers are A, B, E.
−12x−6>4−3x Which of the following is the graph of the solutions to the inequality shown?
x>4 (white dot)
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
Answer is 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 nth figure can be described by the equation f(n) = 5 + 3n , with n = 1, 2, 3, ... Therefore the 10th figure of the pattern has f(n) = 5 + 3 × 10, or 35 line segments.
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
Answer is 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). Simplifying like terms yields −5x ≤ 4. Using the multiplication property of inequality and taking into account the sign, 5x ≤ 4 is equivalent to (− ) (−5x) ≥ (− ) (4) . Simplifying yieldsx ≥ − 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)
Answer is 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×A; that is, the order of the factors in a multiplication problem does not affect the product.
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
Answer is 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 equivalent to 1/4÷1/8? A. 1/4 x 1/8 B. 1/4 x 8 C. 4 x 1/8 D. 4 × 8
Answer is B. 14×8
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
Answer is 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.
Which of the following represents the calculation -7-(-2) on the number line? A. B. C. D.
Answer is D. Option (D) is correct. 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.
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
Answer is 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.
The digit 5 is in what place in the number 3.141593? A. Thousands place B. Thousandths place C. Hundredths place D. Ten-thousandths place
Answer is D. Ten-thousandths place
Click on the answer box and type in a number. Backspace to erase. (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?
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, which equals 4,052.
3×2+7×2 The expression shown results when the distributive property of multiplication over addition is applied to which of the following expressions?
(3+7) x 2
25x2+6y3+4x−25y+3x2−4y2 Which of the following shows all like terms of the expression above?
25x^2 and 3x^2
Activity Time Dance class 15 minutes Running 8 minutes Walking 20 minutes The table shows the time it takes Larissa to burn 100 calories while performing each of three activities. Larissa's workout routine includes a 30-minute dance class, 10 minutes of running, and 15 minutes of walking. How many calories did Larissa burn to complete her workout?
400
The figure presents a line. The points A, B, and C are indicated from left to right. Which of the following can be used to name the ray that has endpoint A and goes in the direction of C in the figure shown?
AC and AB
Click on the answer box and type in a number. In a set of number cubes, the length of the edge of each number cube is 2/3 inch. It takes 27 of these number cubes to completely fill a box in the shape of a cube. What is the volume, in cubic inches, of the box?
Answer is 8 The correct answer is 8. The question requires an understanding of how to find the volume of a right rectangular prism. If 27 number cubes fit in the cubical box, there must be 3 layers of number cubes, with each layer consisting of 3 rows of 3 number cubes. With 3 number cubes, each having edge length 2/3 inch, along one edge of the box, each edge of the box is3 x 2/3 = 2 inches in length. The volume of the box is thus 2^3 = 8 cubic inches. Another approach is to find the volume of each number cube first. The volume of each number cube is (2/3)^3, or 8/27 or cubic inches. Since there are 27 number cubes in the box, the volume of the box is 8/27 x 27 , or 8 cubic inches.
Which of the following is an algebraic expression? A. 6x − 4 B. 6y < 4 C. 6z = 4 D. 6 + 4
Answer is 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 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
Answer is 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 6s^2 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 6s^2 = 54, which yields s = 3 . The volume of the cube can then be found by solving the equation V=s^3, thus V=3^3 . Therefore the volume is 27 in3 .
Which list of numbers is ordered from least to greatest? A. 9/25, 0.35, 2/5, 0.35 B. 0.35, 0.35, 9/25, 2/5 C. 2/5, 9/25, 0.35, 0.35 D. 0.35, 0.35, 9/25, 2/5
Answer is B. 0.35, 0.35¯ ,9/25 , 2/5 Option (B) is correct. The question requires an understanding of how to compare and order rational numbers. One way to compare the four numbers is by finding the decimal equivalent of the fractions.
A certain polygon has the following attributes. I. There are 2 pairs of parallel sides. II. It is a quadrilateral. III. 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
Answer is 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.
Which word describes each angle in an equilateral triangle? A. Acute B. Obtuse C. Right D. Straight
Answer is 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 180/3, 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 salesperson records data consisting of total sales each day for one year. If the least and greatest total sales values are deleted from the data set, which of the following is most likely true about the effect of the deletion? A. The range and mean of the data set will change, but not the median. B. The range and median of the data set will change, but not the mean. C. The median and mean of the data set will change, but not the range. D. The mean, median, and range of the data set will all change.
Answer is A. Option (A) is correct. The question requires an understanding of how to determine how changes in data affect measures of center or range. The range is the difference between the greatest and the least values. Removing the greatest and least values will decrease the range. The mean is the sum of the daily values divided by the number of days. Removing the greatest and the least values will likely affect the mean by shifting it toward the value of the two that was closer to the mean before the removal. The median is the value of the data point that is in the middle when the values in the data set are arranged in numerical order. Since the least value is at the left of the median and the greatest value is at the right of the median, removing those values will not affect the median.
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
Answer is 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.
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
Answer is 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 34x5.
In the xy-plane, point A has coordinates (2,1) and point B has coordinates (5,1). Which of the following could be the coordinates for point C so that the area of triangle ABC is equal to 9 square units? A. (5, 7) B. (5, 4) C. (3, 4) D. (4, 6)
Answer is A. (5,7) A=1/2×b×h
(2a − a + 3) − (−5a + 6a + 2) Which of the following is equivalent to the expression shown? A. 1 B. 5 C. 2a + 1 D. 12a + 5
Answer is A. 1 Option (A) is correct. The question requires an understanding of how to add and subtract linear algebraic expressions. In fact, (2a − a + 3) − (−5a + 6a + 2) = a + 3 - a - 2 = 1
Tony made 1,500 milliliters of lemonade for a party. Which of the following represents the amount of lemonade, in liters, that Tony made? A. 1.5 B. 15 C. 150 D. 15,000
Answer is A. 1.5L Option (A) is correct. The question requires an understanding of how to convert units within the metric system. Since 1 liter is equivalent to 1,000 milliliters, it follows that 1 milliliter is equivalent to 0.001 liter. Therefore, 1,500 milliliters are equivalent to 1.500 x 0.001, or 1.5 liters.
The net shown above forms a right triangular prism. Which of the following represents the surface area of the right triangular prism? A. 84 B. 92 C. 96 D. 120
Answer is A. 84 (72+12)? Option (A) is correct. The question requires an understanding of how to use nets to determine the surface area of three-dimensional figures. The surface area of the three dimensional figure is the sum of the areas of its faces. The faces of the right triangular prism are a 6-by-5 rectangle, a 6-by-4 rectangle, a 6-by-3 rectangle, and two congruent right triangles, each of which has sides of lengths 4 and 3. The areas of the rectangular faces are, respectively, 6x5, or 30; 6x4, or 24; and 6x3, or 18. The area of each of the triangular faces is 1/2x3x4, or 6. Therefore, the surface area of the figure is 30+24+18+2x6, or 84.
Which of the following statements must be true about the two non-right angles of a right triangle? A. Both angles are acute. B. One angle is acute and one is obtuse. C. The angles are congruent. D. Both angles are obtuse.
Answer is A. Both angles are acute. Option (A) is correct. The question requires an understanding of how to classify angles based on their measure. The sum of the measures of the angles in a triangle is 180°. Since the right angle measures 90°, the other two angles must add up to the remaining 90°. Since both together make 90°, each individually must be less than 90° and therefore be acute.
Which of the following addition sentences represents the model shown? A. −5 + 1 = −4 B. −3 + (−1) = −4 C. 5 + (−1) = 4 D. 6 + (−2) = 4
Answer is A. −5 + 1 = −4 Option (A) is correct. The question requires an understanding of how to represent rational numbers and their operations in different ways. The first box shows 5 counters with a minus sign and 1 counter with a plus sign; that is, −5 + 1. The middle box shows that −5 + 1 is equivalent to −4 + (−1 + 1) and that −1 + 1 can be removed as it is equivalent to 0. The last box shows that −4 + 0 is equivalent to −4.
Answer the question below by clicking on the correct response. 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.
Answer is B. Option (B) is correct. 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, 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
Answer is 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 = −2
Answer the question below by clicking on the correct response. What is the least common multiple of 12, 20, and 30? A. 2 B. 60 C. 240 D. 360
Answer is 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 x 3, the prime factorization of 20 is 2^2 x 5, and the prime factorization of 30 is 2 x 3 x 5. Therefore, the least common multiple of the three numbers is 2^2 x 3 x 5, or 60.
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
Answer is 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.
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
Answer is 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.
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
Answer is 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 1/4mi, 3/8mi, 7/12mi, 5/6mi.
x y 1 1 2 4 3 9 4 16 Which of the following functions could be re-presented by the table shown? A. y = 2 ^x B. y = x^2 C. y = 2x D. y = 5x−4
Answer is 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 correspond-ing 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.
2/3 ÷ 4/3 + 3/5 × (5/3)^2 Which of the following is equivalent to the expression shown? A. 2/9 B. 13/6 C. 23/9 D. 55/18
Answer is 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 x 3/4 + 3/5 x 25/9. Performing both multiplications yields 1/2 + 5/3, which is equivalent to 13/6.
The figure presents a sequence of figures in a 3 column table, with 4 rows of data. The heading for column 1 is "Term." The heading for column 2 is "Figure." The heading for column 3 is "Lines Needed." The 4 rows of data are as follows. Row 1. Term 1: 1 square, 4 lines. Row 2. Term 2: 1 square, 1 cross, 1 square, 10 lines. Row 3. Term 3: 1 square, 1 cross, 1 square, 1 cross, 1 square, 16 lines. Row 4: All three columns indicate that the table continues In the sequence of figures shown, the first term is made of a single square and each successive term is made by adding one cross and one square to the preceding term. To form each square, 4 line segments are needed, and to form each cross, 2 line segments are needed. Which of the following expressions can be used to find the number of line segments needed to form the nth term in the sequence of figures? A. n + 6 B. 6n − 2 C. n^2 + 3n D. (n + 1)^2
Answer is B. 6n−2 Option (B) is correct. The question requires an understanding of how to identify, extend, describe, or generate number and shape patterns. The nth figure includes n squares made up of 4 line segments n - 1 and crosses made up of 2 line segments. Therefore, the number of line segments required for the nth figure is equal to 4n + 2(n-1), which simplifies to 6n-2 .
{9, 11, 1, 4, 7, 12, 10, 4, 9, 2, 5, 9, 8 } The figure presents a box plot. 15 equally spaced tick marks are indicated on a number line. The letters A, B, C, D, and E are indicated at some of the tick marks on the number line. A is indicated at the third tick mark, B is indicated at the sixth tick mark, C is indicated at the seventh tick mark, D is indicated at the ninth tick mark, and E is indicated at the twelfth tick mark. The whiskers range from point A to point E, and the box ranges from point B to point D, with an interior vertical line segment at point C. The list shows the number of books each of the 13 students in a class read over the summer. The teacher wants to summarize the data using the boxplot shown. What is the value of C on this boxplot? A. 7 B. 8 C. 9 D. 10
Answer is B. 8 (the median is the 7th point) Option (B) is correct. The question requires an understanding of how to identify, construct, and complete a boxplot that correctly represents given data. Point C on the boxplot is the median of the data. To find the median, the data points must be reordered from least to greatest, which yields 1, 2, 4, 4, 5, 7, 8, 9, 9, 9, 10, 11, 12. The median is the 7th data point, which is 8.
On a major league roster of 25 players, three players have a yearly salary of $15 million each, two players have a yearly salary of $10 million each, and the remaining players have yearly salaries of $1 million each. Which of the following best represents a typical player's yearly salary? A. Mean B. Median C. Mode D. Range
Answer is B. Median Option (B) is correct. The question requires an understanding of how to recognize which measure of center best describes a set of data. The median salary is $1 million and represents nearly all (80%) of the players' salaries on the team. The mean is $3.4 million and does not represent a typical yearly salary since the five salaries that are very high cause the mean to be far from the typical player salary. The mode is not unique, and the range is not a measure of center.
−3(x − 4) ≥ 9 Which of the following inequalities is equivalent to the inequality shown? A. x ≤ −1 B. x ≤ 1 C. x ≥ −1 D. x ≥ 1
Answer is B. x≤1 Option (B) is correct. The question requires an understanding of how to solve multistep one-variable linear inequalities. Using the distributive property of multiplication over addition yields −3x + 12 ≥ 9. Adding −12 to both sides of the inequality and adding like terms yields −3x ≥ −3. Dividing both sides by −3 yields x ≤ 1 , as the inequality sign must be reversed when multiplying or dividing by a negative number.
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
Answer is 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.
Answer is 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) 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
Answer is 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.
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)
Answer is 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). "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.
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
Answer is 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) x 1/3. Simplifying the right side of the equation yields 2/3x =1/2. Therefore, x=3/2x1/2; that is, x=3/4.
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.
Answer is 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.
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? A. Brookhaven B. Columbus C. Davidson D. Washington
Answer is C. 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 + 2 corresponds to the number 74,072, which is the population of Davidson County.
The formula V=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
Answer is 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.
Rosa left a 20% tip on a restaurant bill of $47.30. What amount did Rosa leave for the tip? A. $0.95 B. $4.73 C. $9.46 D. $14.19
Answer is C. $9.46 Option (C) is correct. The question requires an understanding of percent as a rate per 100. The tip is 20% of $47.30, and it can be found by multiplying 47.30 by 20/100 , which yields $9.46. Alternatively, to find 20% of $47.30, 0.2 x 47.30 = 9.46 could be calculated.
5 1/4% is equivalent to which of the following? A. 5.25 B. 0.525 C. 0.0525 D. 0.00525
Answer is C. 0.0525 Option (C) is correct. The question requires an understanding of how to convert between fractions, decimals, and percents. The fraction 1/4 can be converted to 0.25 so that the original percent can be written as 5.25%. Since 5.25% is equivalent to 45.25/100, to convert 5.25% to a decimal number, one must divide 5.25 by 100. This means that 5.25% is equivalent to 0.0525.
What is the prime factorization of 180 ? A. 3^2 × 4 × 5 B. 2^2 × 5 × 9 C. 2^2 ×3^2 × 5 D. 2 × 3^2 × 10
Answer is C. 2^2 x 3^2 x 5
30M + 15R = 900 In a certain year, Rodney earned a total of $900 mowing lawns and raking leaves for his neighbors. He received $30 for each lawn he mowed and $15 for each job raking leaves he had. In the formula above, M represents the number of lawns Rodney mowed for his neighbors and R represents the number of jobs raking leaves he had during the year. If Rodney mowed 15 lawns that year, how many jobs raking leaves did he have? A. 15 B. 20 C. 30 D. 90
Answer is C. 30 Option (C) is correct. The question requires an understanding of how to use formulas to determine unknown quantities. Since Rodney mowed 15 lawns, M=15. Plugging the number in the formula yields 30 x 15 + 15R = 900. Solving for R yields R=900-450/15 .
Color Probability Red 1/3 Blue x Green 1/6 Yellow 1/12 A spinner is divided into 12 congruent sections. Each section is either red, blue, green, or yellow. The table shows the theoretical probability of landing on a color when spinning the spinner once. How many sections are blue? A. 2 B. 4 C. 5 D. 9
Answer is C. 5 Option (C) is correct. The question requires an understanding of probability. The sample space consists of the possible outcomes of a spin, which are red, blue, green, or yellow. The sum of the probabilities of the possible outcomes in the sample space is 1; that is, 1/3 + x + 1/6 + 1/12 = 1, which is equivalent to 7/12 + x = 12/12. It follows that the probability x of landing on blue is 5/12. Therefore, 5 out of 12 sections of the spinner are blue.
Alireza has been reading a 600-page novel at a constant rate. The graph shows the number of pages y he has read after x days of reading. If he continues reading at the same rate, how many days will it take him to read the novel from beginning to end? A. 4 B. 6 C. 8 D. 10
Answer is C. 8 (read graph) Option (C) is correct. The question requires an understanding of how to use linear relationships represented by a graph to solve problems. The graph shows that Alireza has read 150 pages in 2 days and that he has read 300 pages in 4 days. Therefore, Alireza has been reading the novel at a constant rate of 75 pages per day. If he continues to read at the same rate, he will finish reading the novel in 600/75 , or 8 days.
Jamal bought a pair of headphones priced at $17.99. If the sales tax rate is 8%, which of the following proportions can be used to find the amount of sales tax x, in dollars, for the headphones? A. 8/17.99 = x/100 B. 8/17.99 = 100/x C. 8/100 = x/17.99 D. 8/100 = 17.99/x
Answer is C. 8/100=x/17.99 Option (C) is correct. The question requires an understanding of how to use proportional relationships to solve ratio and percent problems. The taxes are 8% of the price; that is, the ratio x : 17.99 is equal to 8 : 100. Therefore, 8/100 = x/17.99.
A basket contains A apples and P pears, and there are two fewer apples than three times the number of pears. Which of the following equations can be used to represent algebraically the relationship between the number of apples and the number of pears in the basket? A. A = 2 − 3P B. A − 2 = 3P C. A + 2 = 3P D. 3A = P − 2
Answer is C. A + 2 = 3P Option (C) is correct. The question requires an understanding of how to translate between verbal statements and algebraic equations. The basket contains two fewer apples than three times the number of pears, so if there were two more apples, there would be as many apples as three times the number of pears.
Ms. Gupta is making 3 batches of chocolate chip cookies for a picnic. Each batch requires 1 and 1/2 cups of sugar and 3 and 1/4 cups of flour. Which of the following is the best estimate of the total amount of sugar and flour Ms. Gupta uses for the cookies? A. Less than 9 cups B. Between 9 and 12 cups C. Between 12 and 15 cups D. More than 15 cups
Answer is C. Between 12 and 15 cups Option (C) is correct. The question requires an understanding of how to use mental math and estimation to solve problems and determine the reasonableness of results. Each batch of cookies requires a total of 1 1/2 + 3 1/4 = 4 3/4 cups of sugar and flour. This number is between 4 and 5, so three batches would require between 3x4 and 3x5 cups of flour and sugar, so the total is between 12 and 15 cups.
Into how many equilateral triangles can a regular hexagon be decomposed? A. 3 B. 4 C. 5 D. 6
Answer is 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
Answer is 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
Answer is 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 l units and a width of w units, then its lxw area is 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 3/5 = 15/2 x 23/4 =345/8 square feet, that is, 43 1/8 square feet.
0.7 is 1/1,000 of what number? A. 0.0007 B. 0.007 C. 70 D. 700
Answer is 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 = 1/1,000 n. Therefore, n=0.7 x 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.
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
Answer is 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
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.
Answer is 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.
Membership Length, Cost in in months 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=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.
Answer is 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 + 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 + 42.50 . 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) What does 2y represent in the expression shown? A. A binomial B. A factor C. A coefficient D. A monomial
Answer is 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.
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
Answer is 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.
Which of the following expressions is equivalent to −4(3−2x) ? A. −2x−12 B. 2x−12 C. −8x−12 D. 8x−12
Answer is 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); that is, −12 + 8x. Using the commutative property of addition yields 8x− 12
In a certain number, a and b represent digits, and a represents 10^4 times what b represents. Which of the following could be the place value of a and b? A. a is in the thousandths place, & b is in the tens place. B. a is in the tenths place, & b is in the hundreds place. C. a is in the ones place, & b is in the hundredths place. D. a is in the tens place, & b is in the thousandths place.
Answer is D. Option (D) is correct. The question requires an understanding of place value and how a digit in one place represents ten times what it represents in the place to its right and one-tenth what it represents in the place to its left. A digit in the tens place is 10^4 times what a digit in the thousandths place represents. In option (A), a would be 10^2 what b represents. In option (B), a would be 1/10^3 times what b represents. In option (C), a would be 10^2 what b represents.
Item Cost of Each Package Utensils $1.50 Cups $2.00 Plates $2.00 Tablecloths $4.50 The table shows the costs of supplies for a birthday party. Anton buys 6 packages of utensils, 4 packages of cups, 2 packages of plates, and 2 packages of tablecloths. Anton's total purchase is subject to a 7.5% sales tax. How much will the party supplies cost Anton?
Answer is D. $32.25 30 × 1.075 = 32.25.
8+24÷4×(6−4) A. 5 B. 11 C. 16 D. 20
Answer is D. 20 Option (D) is correct. The question requires an understanding of how to solve problems using the order of operations. Using the order of operations, the first step is performing the subtraction within the parentheses, which yields 8 + 24 ÷ 4 × 2. The second step is performing the division, which yields 8+6x2. The third step is performing the multi-plication, which yields . Finally, the fourth step is performing the addition, which yields 20.
(x−2)(y+1) + (y−1)(x−2) Which of the following expressions is equivalent to the expression shown? A. 2y B. (x-2) C. 2(x-2) D. 2y(x-2)
Answer is D. 2y(x-2) Option (D) is correct. The question requires an understanding of how to use the distributive property to generate equivalent linear expressions. The expression shown can be simplified using the distributive property of multiplication over addition in two different approaches.
Which of the following pairs of numbers estimates the number 3.274613 point 2 7 4 6 1 to the nearest tenth and to the nearest thousandth, respectively? A. 3.2 and 3.274 B. 3.2 and 3.275 C. 3.3 and 3.274 D. 3.3 and 3.275
Answer is D. 3.3 and 3.275 Option (D) is correct. The question requires an understanding of how to round multidigit numbers to any place value. The tenths place is the first digit after the decimal and would be rounded to 3 based on the next digit,7,which is in the hundredths place. The thousandths place is the third digit after the decimal and would be rounded to 5 based on the next digit, 6, which is in the ten-thousandths place.
8a − 3b What is the value of the expression shown when a=2 and b=−5? A. -46 B. -31 C. 1 D. 31
Answer is D. 31 Option (D) is correct. The question requires an understanding of how to evaluate simple algebraic expressions. Substituting a = 2 and b = -5 into the expression yields 8(2) - 3(-5) = 16 - (- 15) = 16 + 15 = 31.
Cube A has a volume of 1 cubic inch. The length of each side of cube B is 1 inch greater than the length of each side of cube A. The volume of cube B is how many times the volume of cube A? A. 2 times B. 3 times C. 4 times D. 8 times
Answer is D. 8 times Option (D) is correct. The question requires an understanding of how changes to dimensions change area and volume of three-dimensional shapes. Since the volume of cube A is 1 cubic inch, its sides must have a length of 1 inch. The length of each side in cube B is 1 inch greater than the 1 inch length of each side in cube A, so each side in cube B has length 2 inches. The volume of cube B is thus 8 cubic inches, which is 8 times the volume of cube A.
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 .............. variable. r is ............... variable.
Answer is listed as B, 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.
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?
Answers are 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.
1,2,4 ... The first three terms of a certain sequence are shown. Which of the following mathematical relationships could describe the terms of the sequence? Select all that apply. A. The first term is 1. Each subsequent term of the sequence is obtained by multiplying a constant quantity by the preceding term. B. The first term is 1. Each subsequent term of the sequence is obtained by adding a constant quantity to the preceding term. C. The first term is 1. Each subsequent term of the sequence is obtained by adding the preceding term and a quantity that increases by 1 with each new term. D. The first term is 1. Each subsequent term of the sequence is obtained by adding 1 to the square of the preceding term. E. The first term is 1. Each subsequent term of the sequence is obtained by squaring a number that is one greater than the number that was squared to obtain the preceding term.
Answers are A, C. Options (A) and (C) are correct. The question requires an understanding of how to make conjectures, predictions, or generalizations based on patterns. In the pattern described in option (A), the first term is 1, and if the constant described in the pattern is 2, then the first 3 terms of the sequence are 1, 2, and 4. Hence, the pattern described in option (A) could produce the three terms 1, 2, and 4, and, if extended, the fourth term would be 8. In the pattern described in option (C), the first term is 1, and if the quantity that is added is initially 1, then the first three terms of the sequence are 1, 2, and 4. Hence the pattern described in option (C) could produce the three terms 1, 2, and 4, and, if extended, the fourth term would be 7. In option (B), the quantity that would add to the first term, 1, to produce the second term, 2, must be 1. Hence the first three terms produced by the pattern are 1, 2, and 3. The third term is 3, not 4, as required. In option (D), the terms produced by the pattern would be 1, 2, and 5. The third term is 5, not 4, as required. In option (E), the first three terms are 1, 4, and 9. The second and third term values, respectively, are not 2 and 4, as required.
7, 9, 10, 11, 14, 15, 15, 15, 17, 18, 18, 20, 26, 26, 27, 28, 30 The list shows the times spent eating lunch for the 17 students in Ms. Begay's class. Which of the following statements about the times must be true? Select all that apply. A. The mode is 17 minutes. B. The median is 17 minutes. C. The mean is 18 minutes. D. The range is 37 minutes.
Answers are B. The median is 17 minutes. C. The mean is 18 minutes. Options (B) and (C) are correct. The question requires an understanding of solving problems involving measures of center (mean, median, and mode) and range. The list is already ordered and contains 17 numbers, so the ninth number, which is 17, is the median since it has 8 numbers above it and 8 numbers below it in the ordered list. The sum of all 17 numbers is 306, and the mean is found by dividing 306 by 17. This yields a mean of 18. Hence both options (B) & (C) are correct. The mode is the value that occurs most frequently in the list, so that is 15, & hence option (A) is incorrect. The range is 30-7=23 , so option (D) is incorrect.
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.
Which of the following lists shows all the factors of 24 ?
D.1, 2, 3, 4, 6, 8, 12, 24