Math - F1
The function f(x)=x^2+3 is represented by which table of values?
(-2, 7), (-1,4), (0,3), (3,12)
25x2+6y3+4x−25y+3x2−4y2 Which of the following shows all like terms of the expression above?
25x^2 and 3x^2
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.
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
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
−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.
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.
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
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.
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
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
What is the area, in square inches, of the polygon shown?
1080
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
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.
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.
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
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 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.
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.
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.
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.
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.
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.
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.
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.
Which of the following lists shows all the factors of 24 ?
D.1, 2, 3, 4, 6, 8, 12, 24
−12x−6>4−3x Which of the following is the graph of the solutions to the inequality shown?
x>4 (white dot)
