sat suite of assessments - math test—calculator · web viewmath test—calculator 38 questions...

Math Test—Calculator38 Questions

Turn to Section 4 of your answer sheet to answer the questions in this section.

DirectionsFor questions 1 through 30, solve each problem, choose the best answer from the choices provided, and indicate your answer choice on your answer sheet. For questions 31 through 38, solve the problem and indicate your answer, which is to be recorded in the spaces provided on the answer sheet. Please refer to the directions before question 31 on how to record your answers in the spaces provided. You may use scratch paper for scratch work.

Notes1. The use of a calculator is permitted.

2. All variables and expressions used represent real numbers unless otherwise indicated.

3. Figures provided in this test are drawn to scale unless otherwise indicated.

4. All figures lie in a plane unless otherwise indicated.

5. Unless otherwise indicated, the domain of a given function f is the set of all real

numbers x for which f of x is a real number

Reference

Begin skippable figure descriptions.

The figure presents information for your reference in solving some of the problems.

Reference figure 1 is a circle with radius r. Two equations are presented below reference figure 1.

A equals pi times the square of r.C equals 2 pi r.

Reference figure 2 is a rectangle with length ℓ and width w. An equation is presented below reference figure 2.

A equals ℓ w.

Reference figure 3 is a triangle with base b and height h. An equation is presented below reference figure 3.

A equals one half b h.

Reference figure 4 is a right triangle. The two sides that form the right angle are labeled a and b, and the side opposite the right angle is labeled c. An equation is presented below reference figure 4.

c squared equals a squared plus b squared.

Special Right TrianglesReference figure 5 is a right triangle with a 30 degree angle and a 60 degree angle. The side opposite the 30 degree angle is labeled x. The side opposite the 60 degree angle is labeled x times the square root of 3. The side opposite the right angle is labeled 2 x.

Reference figure 6 is a right triangle with two 45 degree angles. Two sides are each labeled s. The side opposite the right angle is labeled s times the square root of 2.

Reference figure 7 is a rectangular solid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 7.

V equals ℓ w h.

Reference figure 8 is a right circular cylinder whose base has radius r and whose height is h. An equation is presented below reference figure 8.

V equals pi times the square of r times h.

Reference figure 9 is a sphere with radius r. An equation is presented below reference figure 9.

V equals four thirds pi times the cube of r.

Reference figure 10 is a cone whose base has radius r and whose height is h. An equation is presented below reference figure 10.

V equals one third times pi times the square of r times h.

Reference figure 11 is an asymmetrical pyramid whose base has length ℓ and width w and whose height is h. An equation is presented below reference figure 11.

V equals one third ℓ w h.

End skippable figure descriptions.

Additional Reference InformationThe number of degrees of arc in a circle is 360.The number of radians of arc in a circle is 2 pi.The sum of the measures in degrees of the angles of a triangle is 180.

Question 1.A helicopter, initially hovering 40 feet above the ground, begins to gain altitude at a rate of 21 feet per second. Which of the following functions represents the helicopter’s altitude above the ground y, in feet, t seconds after the helicopter begins to gain altitude?

A. y equals, 40 plus 21B. y equals, 40 plus 21 tC. y equals, 40 minus 21 tD. y equals, 40 t plus 21

Question 2.A text messaging plan charges a flat fee of $5 per month for up to 100 text messages sent plus $0.25 for each additional text message sent that month. Which of the following graphs represents the cost, y, of sending x texts in a month?

Each answer choice presents the graph of one or two line segments in the x y-plane, with the origin labeled O. The number 100 is indicated on the x-axis, and the number 5 is indicated on the y-axis.

A.

Begin skippable figure description.

The graph consists of two line segments. The first line segment begins on the y-axis at the point with coordinates 0 comma 5, and moves horizontally to the right until it ends at the point with coordinates 100 comma 5. The second line segment begins where the first line segment ends, and moves upward and to the right where it ends.

End skippable figure description.

B.


The graph consists of two line segments. The first line segment begins on the y-axis at the point with coordinates 0 comma 5, and moves horizontally to the right until it ends at the point with coordinates 100 comma 5. The second line segment begins where the first line segment ends, and moves downward and to the right where it ends on the x-axis.


C.


The graph consists of one line segment. The line segment begins on the y-axis at the point with coordinates 0 comma 5, and moves upward and to the right where it ends.


D.


The graph consists of one line segment. The line segment begins on the y-axis at the point with coordinates 0 comma 5, and moves downward and to the right until it ends on the x-axis at the point with coordinates 100 comma 0.


Question 3.Jake buys a bag of popcorn at a movie theater. He eats half of the popcorn during the 15 minutes of previews. After eating half of the popcorn, he stops eating for the next 30 minutes. Then he gradually eats the popcorn until he accidentally spills all of the remaining popcorn. Which of the following graphs could represent the situation?

Each answer choice presents a graph consisting of four line segments in a coordinate plane. The horizontal axis is labeled “Time, in minutes,” and the numbers 0 through 90, in increments of 30, are indicated. The vertical axis is labeled “Amount of popcorn in the bag.” Although no numbers are indicated on the vertical axis, the coordinates of each segment with respect to the vertical axis will be described by an approximate fraction that indicates how full the bag of popcorn is.

A.


The first segment begins at 0 minutes with the full bag, and slants downward and to the right until it ends at 20 minutes with half the bag. The second segment begins where the first segment ends, and moves horizontally to the right until it ends at 40 minutes with half the bag. The third segment begins where the second segment ends, and slants downward and to the right until it ends at 75 minutes with one tenth of the bag. The fourth segment begins where the third segment ends, and moves vertically upward until it ends at 75 minutes with three fourths of the bag.


B.


The first segment begins at 0 minutes with the full bag, and slants downward and to the right until it ends at 15 minutes with half the bag. The second segment begins where the first segment ends, and moves horizontally to the right until it ends at 45 minutes with half the bag. The third segment begins where the second segment ends, and slants gradually downward and to the right until it ends at 90 minutes with a quarter of the bag. The fourth segment begins where the third segment ends, and moves vertically downward until it ends at 90 minutes with the empty bag.


C.


The first segment begins at 0 minutes with the full bag, and slants downward and to the right until it ends at 10 minutes with half the bag. The second segment begins where the first segment ends, and moves horizontally to the right until it ends at 45 minutes with half the bag. The third segment begins where the second segment ends, and slants upward and to the right until it ends at 90 minutes with three fourths of the bag. The fourth segment begins where the third segment ends, and moves vertically downward until it ends at 90 minutes with the empty bag.


D.


The first segment begins at 0 minutes with one tenth of the bag, and slants upward and to the right until it ends at 15 minutes with half the bag. The second segment begins where the first segment ends, and moves horizontally to the right until it ends at 40 minutes with half the bag. The third segment begins where the second segment ends, and slants upward and to the right until it ends at 90 minutes with a full bag. The fourth segment begins where the third segment ends, and moves vertically downward until it ends at 90 minutes with one third of the bag.


Question 4.If 20 minus x, equals 15, what is the value of 3 x ?

A. 5B. 10C. 15D. 35

Question 5 is based on the following function.

f of x equals, the fraction with numerator x plus 3, and denominator 2

Question 5.

For the preceding function f, what is the value of f of negative 1 ?

A. negative 2B. negative 1C. 1D. 2

Question 6.

Which of the following is equivalent to 2 x, times, open parenthesis, x squared, minus 3 x, close parenthesis?

A. negative 4 x squared

B. 3 x cubed, minus x squared

C. 2 x cubed, minus 3 x

D. 2 x cubed, minus 6 x squared

Question 7.A retail company has 50 large stores located in different areas throughout a state. A researcher for the company believes that employee job satisfaction varies greatly from store to store. Which of the following sampling methods is most appropriate to estimate the proportion of all employees of the company who are satisfied with their job?

A. Selecting one of the 50 stores at random and then surveying each employee at that store

B. Selecting 10 employees from each store at random and then surveying each employee selected

C. Surveying the 25 highest-paid employees and the 25 lowest-paid employeesD. Creating a website on which employees can express their opinions and then

using the first 50 responses

Question 8 is based on the following figure.


The figure presents two line graphs in the same coordinate plane. The horizontal axis is labeled “Number of weeks,” and the numbers 0 through 7, in increments of 1, are indicated. The vertical axis is labeled “Total amount deposited, in dollars,” and the numbers 0 through 900, in increments of 100, are indicated. The two graphs intersect at the point representing 4 weeks, 500 dollars. One graph is labeled “Ian,” and the other graph is labeled “Jeremy.” There are 8 data points indicated on each graph. The data points for each graph are listed as follows.

Line graph labeled Ian.Point 1. 0 weeks, 100 dollars.Point 2. 1 week, 200 dollars.Point 3. 2 weeks, 300 dollars.Point 4. 3 weeks, 400 dollars.Point 5. 4 weeks, 500 dollars.Point 6. 5 weeks, 600 dollars.Point 7. 6 weeks, 700 dollars.Point 8. 7 weeks, 800 dollars.

Line graph labeled Jeremy.Point 1. 0 weeks, 300 dollars.Point 2. 1 week, 350 dollars.Point 3. 2 weeks, 400 dollars.Point 4. 3 weeks, 450 dollars.Point 5. 4 weeks, 500 dollars.Point 6. 5 weeks, 550 dollars.Point 7. 6 weeks, 600 dollars.Point 8. 7 weeks, 650 dollars.


Question 8.The preceding two graphs show the total amounts of money that Ian and Jeremy each have deposited into their savings accounts for the first seven weeks after opening their accounts. After they made their initial deposits, how much more did Ian deposit each week than Jeremy?

A. $200B. $100C. $50D. $25


h of x equals, 2 to the x power

Question 9.

The function h is defined. What is h of 5, minus, h of 3?

A. 2B. 4C. 24D. 28

Question 10.A researcher surveyed a random sample of students from a large university about how often they see movies. Using the sample data, the researcher estimated that 23% of the students in the population saw a movie at least once per month. The margin of error for this estimation is 4%. Which of the following is the most appropriate conclusion about all students at the university, based on the given estimate and margin of error?

A. It is unlikely that less than 23% of the students see a movie at least once per month.

B. At least 23%, but no more than 25%, of the students see a movie at least once per month.

C. The researcher is between 19% and 27% sure that most students see a movie at least once per month.

D. It is plausible that the percentage of students who see a movie at least once per month is between 19% and 27%.

Question 11 is based on the following table.List A 1 2 3 4 5 6List B 2 3 3 4 4 5

Question 11.The preceding table shows two lists of numbers. Which of the following is a true statement comparing list A and list B ?

A. The means are the same, and the standard deviations are different.B. The means are the same, and the standard deviations are the same.C. The means are different, and the standard deviations are different.D. The means are different, and the standard deviations are the same.

Question 12.A book was on sale for 40% off its original price. If the sale price of the book was $18.00, what was the original price of the book? (Assume there is no sales tax.)

A. $7.20B. $10.80C. $30.00D. $45.00

Questions 13 and 14 are based on the following information.Three colonies of insects were each treated with a different pesticide over an 8-week period to test the effectiveness of the three pesticides. Colonies A, B, and C were treated with Pesticides A, B, and C, respectively. Each pesticide was applied every 2 weeks to one of the three colonies over the 8-week period. The following bar graph shows the insect counts for each of the three colonies 0, 2, 4, 6, and 8 weeks after the initial treatment.


The figure presents a bar graph titled “Insect Count for Three Pesticide Treatments.” The horizontal axis is labeled “Weeks after initial treatment,” and the numbers 0 through 8, in increments of 2, are indicated. There are three bars above each of the numbers. A key indicates that the first bar represents “Colony A,” the second bar represents “Colony B,” and the third bar represents “Colony C.” The vertical axis is labeled “Number of insects,” and the numbers 0 through 160, in increments of 20, are indicated. The data are as follows. Note that all values are approximate.

0 Weeks after initial treatment. Colony A, 80 insects. Colony B, 65 insects. Colony C, 58 insects.2 Weeks after initial treatment. Colony A, 52 insects. Colony B, 60 insects. Colony C, 140 insects.4 Weeks after initial treatment. Colony A, 32 insects. Colony B, 39 insects. Colony C, 110 insects.6 Weeks after initial treatment. Colony A, 26 insects. Colony B, 37 insects. Colony C, 80 insects.8 Weeks after initial treatment. Colony A, 18 insects. Colony B, 10 insects. Colony C, 50 insects.End skippable figure description.

Question 13.Which of the following colonies showed a decrease in size every two weeks after the initial treatment with pesticide?

Colony A

Colony B

Colony C

A. Colony A onlyB. Colony C onlyC. Colony A and colony B onlyD. Colony A, colony B, and colony C

Question 14.Of the following, which is closest to the ratio of the total number of insects in all three colonies in week 8 to the total number of insects at the time of initial treatment?

A. 2 to 5B. 1 to 4C. 3 to 5D. 1 to 2

Question 15.A right circular cone has a volume of 24 pi cubic inches. If the height of the cone is 2 inches, what is the radius, in inches, of the base of the cone?

A. 2 times the square root of 3B. 6C. 12D. 36

Question 16.In 2015 the populations of City X and City Y were equal. From 2010 to 2015, the population of City X increased by 20% and the population of City Y decreased by 10%. If the population of City X was 120,000 in 2010, what was the population of City Y in 2010?

A. 60,000B. 90,000C. 160,000D. 240,000

Question 17.

The volume of a sphere is given by the formula V equals, four thirds pi, r cubed, where r is the radius of the sphere. Which of the following gives the radius of the sphere in terms of the volume of the sphere?

A. the fraction 4 pi over 3 V, end fraction

B. the fraction 3 V over 4 pi, end fraction

C. the cube root of the fraction 4 pi over 3 V, end fraction, end root

D. the cube root of the fraction 3 V over 4 pi, end fraction, end root

Question 18 is based on the following table.Survey Results

Answer PercentNever 31.3%Rarely 24.3%Often 13.5%Always 30.9%

Question 18.The preceding table shows the results of a survey in which tablet users were asked how often they would watch video advertisements in order to access streaming content for free. Based on the table, which of the following is closest to the probability that a tablet user answered “Always,” given that the tablet user did not answer “Never”?

A. 0.31B. 0.38C. 0.45D. 0.69

Question 19 is based on the following equation.

y equals, negative, open parenthesis, x minus 3, close parenthesis, squared, plus a

Question 19.In the preceding equation, a is a constant. The graph of the equation in the x y-plane is a parabola. Which of the following is true about the parabola?

A. Its minimum occurs at the point with coordinates negative 3 comma a.

B. Its minimum occurs at the point with coordinates 3 comma a.

C. Its maximum occurs at the point with coordinates negative 3 comma a.

D. Its maximum occurs at the point with coordinates 3 comma a.

Question 20.The maximum value of a data set consisting of 25 positive integers is 84. A new data set consisting of 26 positive integers is created by including 96 in the original data set. Which of the following measures must be 12 greater for the new data set than for the original data set?

A. The meanB. The medianC. The rangeD. The standard deviation


0.10 x, plus 0.20 y, equals, 0.18, times, open parenthesis, x plus y, close parenthesis

Question 21.Clayton will mix x milliliters of a 10% by mass saline solution with y milliliters of a 20% by mass saline solution in order to create an 18% by mass saline solution. The preceding equation represents this situation. If Clayton uses 100 milliliters of the 20% by mass saline solution, how many milliliters of the 10% by mass saline solution must he use?

A. 5B. 25C. 50D. 100

Question 22.The first year Eleanor organized a fund-raising event, she invited 30 people. For each of the next 5 years, she invited double the number of people she had invited

the previous year. If f of n is the number of people invited to the fund-raiser n years after Eleanor began organizing the event, which of the following statements best describes the function f?

A. The function f is a decreasing linear function.B. The function f is an increasing linear function.C. The function f is a decreasing exponential function.D. The function f is an increasing exponential function.

Question 23 is based on the following table.x a 3 a 5 ay 0 negative a negative 2 a

Question 23.Some values of x and their corresponding values of y are shown in the preceding table, where a is a constant. If there is a linear relationship between x and y, which of the following equations represents the relationship?

A. x plus 2 y, equals aB. x plus 2 y, equals 5 aC. 2 x, minus y, equals negative 5 aD. 2 x minus y, equals 7 a



The figure presents a scatterplot in the coordinate plane. The horizontal axis is labeled “Number of registered voters,” and the numbers 120 through 300, in increments of 20, are indicated. The vertical axis is labeled “Number of people who voted,” and the numbers 60 through 150, in increments of 10, are indicated. There are 7 data points in the scatterplot. Note that all values are approximate. The data points begin at the point with coordinates 130 comma 63, and trend upward and to the right until they end at the point with coordinates 290 comma 140.

A line of best fit for the data is shown. The line begins at the point with coordinates 120 comma 60, and slants upward and to the right. It passes through the point with coordinates 200 comma 100, and through the point with coordinates 280 comma 140.


Question 24.The preceding scatterplot shows the number of registered voters, x, and the number of people who voted in the last election, y, for seven districts in a town. A line of best fit for the data is also shown. Which of the following could be the equation of the line of best fit?

A. y equals, negative 0.5 xB. y equals, 0.5 xC. y equals, negative 2 xD. y equals, 2 x

Question 25 is based on the following two equations.

Equation 1: 2.4 x, minus 1.5 y, equals 0.3. Equation 2: 1.6 x, plus 0.5 y, equals negative 1.3.

Question 25.The preceding system of equations is graphed in the x y-plane. What is the

x-coordinate of the intersection point with coordinates x comma y of the system?

A. negative 0.5B. negative 0.25C. 0.8D. 1.75

Question 26.Keith modeled the growth over several hundred years of a tree population by estimating the number of the trees’ pollen grains per square centimeter that were deposited each year within layers of a lake’s sediment. He estimated there were 310 pollen grains per square centimeter the first year the grains were deposited, with a 1% annual increase in the number of grains per square centimeter thereafter.

Which of the following functions models P of t, the number of pollen grains per square centimeter t years after the first year the grains were deposited?

A. P of t equals, 310 to the t power

B. P of t equals, 310 raised to the 1.01 t power

C. P of t equals, 310 times, open parenthesis, 0.99, close parenthesis, to the t power

D. P of t equals, 310 times, open parenthesis, 1.01, close parenthesis, to the t power


two thirds times, open parenthesis, 9 x minus 6, close parenthesis, minus 4, equals, 9 x minus 6

Question 27.Based on the preceding equation, what is the value of 3 x minus 2 ?

A. negative 4

B. negative four fifths

C. negative two thirds

D. 4


f of x equals, open parenthesis, x plus 3, close parenthesis, times, open parenthesis, x minus k, close parenthesis

Question 28.The function f is defined. If k is a positive integer, which of the following could

represent the graph of y equals, f of x in the x y-plane?

Each answer choice presents the graph of a parabola in the x y-plane, with the origin labeled O. The numbers negative 4 through 4, in increments of 2, are indicated on the x-axis. The numbers indicated on the y-axis vary by answer choice.

A.


The numbers negative 2 through 6, in increments of 2, are indicated on the y-axis. The parabola opens downward. It crosses the x-axis at negative 3 and 2, and crosses the y-axis at 6.


B.


The numbers negative 2 through 6, in increments of 2, are indicated on the y-axis. The parabola opens downward. It crosses the x-axis at negative 2 and 3, and crosses the y-axis at 6.


C.


The numbers negative 6 through 2, in increments of 2, are indicated on the y-axis. The parabola opens upward. It crosses the x-axis at negative 2 and 3, and crosses the y-axis at negative 6.


D.


The numbers negative 6 through 2, in increments of 2, are indicated on the y-axis. The parabola opens upward. It crosses the x-axis at negative 3 and 2, and crosses the y-axis at negative 6.


Question 29 is based on the following formula. H equals, 1.88 L, plus 32.01

Question 29.The preceding formula can be used to approximate the height H, in inches, of an adult male based on the length L, in inches, of his femur. What is the meaning of 1.88 in this context?

A. The approximate femur length, in inches, for a man with a height of 32.01 inches

B. The approximate increase in a man’s femur length, in inches, for each increase of 32.01 inches in his height

C. The approximate increase in a man’s femur length, in inches, for each one-inch increase in his height

D. The approximate increase in a man’s height, in inches, for each one-inch increase in his femur length



The figure presents quadrilateral A B C D with side A D horizontal and vertex D to the right of vertex A. Vertex C is vertically above vertex D, and angle C is marked with a right angle symbol. Side B C is horizontal and shorter than side A D.


Question 30.

In preceding quadrilateral A B C D, line segment A D is parallel to line

segment B C and the length of side C D, equals, one half times the length of side A B. What is the measure of angle B ?

A. 150 degreesB. 135 degreesC. 120 degreesD. 90 degrees

DirectionsFor questions 31 through 38, solve the problem and record your answer in the spaces provided on the answer sheet, as described in the following directions and examples.

1. Although not required, it is suggested that your answer be recorded in the boxes at the top of the columns to help fill in the bubbles accurately. You will receive credit only if the bubbles are filled in correctly.

2. Mark no more than one bubble in any column.

3. No question has a negative answer.

4. Some problems may have more than one correct answer. In such cases, indicate only one answer.

5. Mixed numbers such as three and one half must be recorded as 3.5 or

seven slash two. (If three, one, slash, two, is recorded in the

spaces provided on the answer sheet, it will be interpreted as thirty one

halves, not three and one half.)

6. Decimal answers: If you obtain a decimal answer with more digits than the spaces on the answer sheet can accommodate, it may be either rounded or truncated, but it must fill all four spaces.

The following are four examples of how to record your answer in the spaces provided. Keep in mind that there are four spaces provided to record each answer.

Examples 1 and 2


Example 1: If your answer is a fraction such as seven twelfths, it should be recorded as follows. Enter 7 in the first space, the fraction bar (a slash) in the second space, 1 in the third space, and 2 in the fourth space. All four spaces would be used in this example.

Example 2: If your answer is a decimal value such as 2.5, it could be recorded as follows. Enter 2 in the second space, the decimal point in the third space, and 5 in the fourth space. Only three spaces would be used in this example.


Example 3


Example 3: Acceptable ways to record two thirds are: 2 slash 3, .666, and .667.


Example 4

Note: You may start your answers in any column, space permitting. Columns you don’t need to use should be left blank.


Example 4: It is not necessary to begin recording answers in the first space unless all four spaces are needed. For example, if your answer is 201, you may record 2 in the second space, 0 in the third space, and 1 in the fourth space. Alternatively, you may record 2 in the first space, 0 in the second space, and 1 in the third space. Spaces not needed should be left blank.


Question 31.Lynne has $8.00 to spend on apples and oranges. Apples cost $0.65 each, and oranges cost $0.75 each. If there is no tax on this purchase and she buys 5 apples, what is the maximum number of whole oranges she can buy?



The figure presents a triangle. One angle is labeled a degrees, one angle is labeled b degrees, and one angle is labeled c degrees. A note indicates that the figure is not drawn to scale.


Question 32.In the preceding triangle, a, equals 34. What is the value of b plus c?

Question 33 is based on the following five numbers.700, 1200, 1600, 2000, x

Question 33.If the mean of the preceding five numbers is 1600, what is the value of x ?

Question 34.The relationship between x and y can be written as y equals, m x, where m is a constant. If y equals 17 when x equals a, what is the value of y when x equals, 2 a ?


a, times, open parenthesis, x plus b, close parenthesis, equals, 4 x, plus 10

Question 35.In the preceding equation, a and b are constants. If the equation has infinitely many solutions for x, what is the value of b ?

Question 36.In the x y-plane, a line that has the equation y equals c for some constant c intersects a parabola at exactly one point. If the parabola has the equation

y equals, negative, x squared, plus 5 x, what is the value of c ?

Questions 37 and 38 are based on the following information.The peregrine falcon can reach speeds of up to 200 miles per hour while diving to catch prey, making it the fastest animal on the planet when in a dive.

Question 37.What is a peregrine falcon’s maximum speed while diving to catch prey, in feet per second? (Round your answer to the nearest whole number. 1 mile equals 5280 feet)

Question 38.If a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take? (Round your answer to the nearest second.)

Stop.If you finish before time is called, you may check your work on this section only. Do not go on to any other section.

sat suite of assessments - math test—calculator · web viewmath test—calculator 38 questions...

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