SAT 8/7/20 Math Test – Calculator

Math Test – Calculator
55 MINUTES, 38 QUESTIONS

Directions: For questions 1-30, solve each problem, choose the best answer from the choices
provided, and fill in the corresponding circle on your answer sheet. For questions 31-38,
solve the problem and enter your answer in the grid on the answer sheet. Please refer to
the directions before question 31 on how to enter your answers in the grid. You may use
any available space in your test booklet for scratch work.

1. 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(x) is a real number.

1.

2 / 41
2 / 25
7 / 41
2 / 7

2. ( x² – 3 ) – ( -3x² + 5 )
Which of the following expressions is equivalent to the one above?

4x² – 8
4x² – 2
-2x² – 8
-2x² – 2

3. A certain package requires 3 centimeters of tape to be closed securely. What is the maximum number of packages of this type that can be secured with 6 meters of tape? (1 meter = 100 cm)

100
150
200
300

4. A market researcher selected 200 people at random from a group of people who indicated that they liked a certain book. The 200 people were shown a movie based on the book and then asked whether they liked or disliked the movie. Of those surveyed, 95% said they disliked the movie. Which of the following inferences can appropriately be drawn from this survey result?

At least 95% of people who go see movies will dislike this movie.
At least 95% of people who read books will dislike this movie.
Most people who dislike this book will like this movie.
Most people who like this book will dislike this movie.

5. Which of the following ordered pairs ( x, y ) satisfies the inequality 5x − 3y < 4 ?
I. (1, 1)
II. (2, 5)
III. (3, 2)

I only
II only
I and II only
I and III only

6. In the equation ( ax + 3 )² = 36, a is a constant. If x = −3 is one solution to the equation, what is a possible value of a ?

-11
-5
-1
0

7. According to the scatterplot, which of the following statements is true about the relationship between a planetoid’s average distance from the Sun and its density?

Planetoids that are more distant from the Sun tend to have lesser densities.
Planetoids that are more distant from the Sun tend to have greater densities.
The density of a planetoid that is twice as far from the Sun as another planetoid is half the density of that other planetoid.
The distance from a planetoid to the Sun is unrelated to its density.

8. An astronomer has discovered a new planetoid about 1.2 AU from the Sun. According to the line of best fit, which of the following best approximates the density of the planetoid, in grams per cubic centimeter?

3.6
4.1
4.6
5.5

9. 9ax + 9b – 6 =21
Based on the equation above, what is the value of ax + b ?

3
6
8
12

10. Lani spent 15% of her 8-hour workday in meetings. How many minutes of her workday did she spend in meetings?

1.2
15
48
72

11. A software company is selling a new game in a standard edition and a collector’s edition. The box for the standard edition has a volume of 20 cubic inches, and the box for the collector’s edition has a volume of 30 cubic inches. The company receives an order for 75 copies of the game, and the total volume of the order to be shipped is 1,870 cubic inches. Which of the following systems of equations can be used to determine the number of standard edition games, s, and collector’s edition games, c, that were ordered?

75 -s = c

20s + 30c = 1,870
75 -s = c

30s + 20c = 1,870
s – c = 75

25(s + c) = 1,870
s – c = 75

30s + 20c = 1,870

12. A customer paid $53.00 for a jacket after a 6 percent sales tax was added. What was the price of the jacket before the sales tax was added?

$47.60
$50.00
$52.60
$52.84

13.

Theresa ran at a constant speed for five minutes.
Theresa’s speed was increasing for a longer period of time than it was decreasing.
Theresa’s speed decreased at a constant rate during the last five minutes.
Theresa’s speed reached its maximum during the last ten minutes.

14.

45
90
100
105

15. If 50 one-cent coins were stacked on top of each other in a column, the column would be approximately 3 and 7/8 inches tall. At this rate, which of the following is closest to the number of one-cent coins it would take to make an 8-inch-tall column?

75
100
200
390

16. If a − b = 12 and b / 2 = 10, what is the value of a + b ?

2
12
32
52

17. y = 19.99 + 1.50x
The equation above models the total cost y, in dollars, that a company charges a customer to rent a truck for one day and drive the truck x miles. The total cost consists of a flat fee plus a charge per mile driven. When the equation is graphed in the xy-plane, what does the y-intercept of the graph represent in terms of the model?

A flat fee of $19.99
A charge per mile of $1.50
A charge per mile of $19.99
Total daily charges of $21.49

18.

10%
7%
4%
1%

19. Based on Current’s formula, what is w in terms of A ?

w = 30A − 4
w = 30A + 4
w = 30(A − 4)
w = 30(A + 4)

20. If Mosteller’s and Current’s formulas give the same estimate for A, which of the following expressions is equivalent to √hw ?

(4 + w) / 2
(4 + w) / 1,800
2( 4 + w )
(4 + w)² / 2

21.

2.5
2.0
1.5
1.0

22.

0.05%
0.95%
1.22%
7.45%

23. A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of 75 cm² , and the height of the can is 10 cm. If 110 cm³ of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?

7.5cm³
185 cm³
640 cm³
750 cm³

24. h(t) = −16t² + 110t + 72
The function above models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?

The initial height, in feet, of the object
The maximum height, in feet, of the object
The initial speed, in feet per second, of the object
The maximum speed, in feet per second, of the object

25. If x food calories is equivalent to k kilojoules, of the following, which best represents the relationship between x and k ?

k = 0.24x
k = 4.2x
x = 4.2k
xk = 4.2

26. If the 180 food calories in a granola bar come entirely from p grams of protein, f grams of fat, and c grams of carbohydrate, which of the following expresses f in terms of p and c ?

f = 20 + (4/9)(p + c)
f = 20 – (4/9)(p + c)
f = 20 – (4/9)(p – c)
f = 20 + (9/4)(p + c)

27. The world’s population has grown at an average rate of 1.9 percent per year since 1945. There were approximately 4 billion people in the world in 1975. Which of the following functions represents the world’s population P, in billions of people, t years since 1975 ? (1 billion = 1,000,000,000)

P( t ) = 4 (1.019)^t
P( t ) = 4(1.9)^t
P( t ) = 1.19t + 4
P( t ) = 1.019t + 4

28.

1 to 3
1 to 2
2 to 1
3 to 1

29. A circle in the xy‑plane has equation (x + 3)² + (y − 1)² = 25. Which of the following points does NOT lie in the interior of the circle?

( -7, 3 )
( -3, 1 )
( 0, 0 )
( 3, 2 )

30.

6,020
6,027
6,440
6,468

Directions: For questions 31-38, solve the problem and enter your answer in the blank space below.

31. In 1854, during the California gold rush, each ounce of gold was worth $20, and the largest known mass of gold found in California was worth $62,400 in that year. What was the weight, in pounds, of this mass of gold? (16 ounces = 1 pound)

The weight, in pounds, of this mass of gold was

32.

The slope of line t is .

33. The score on a trivia game is obtained by subtracting the number of incorrect answers from twice the number of correct answers. If a player answered 40 questions and obtained a score of 50, how many questions did the player answer correctly?

The player answered questions correctly.

34.

The shaded area of the circle is of the circle.

35.

One possible value of x is .

36.

The length of DE is

37. What was the mean score of the contestants on Day 1 ?

The mean score of the contestants on Day 1 was

38. No contestant received the same score on two different days. If a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days?

SAT 8/7/20 Math Test – Calculator

SAT 8/7/20 Math Test – Calculator

Good Luck!

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