SAT Practice Test Mathematics Test
Mathematics Test – No Calculator
25 MINUTES, 20 QUESTIONS
Turn to Section 3 of your answer sheet to answer the questions in this section.
DIRECTION
For questions 1-15, solve each problem, choose the best answer from the choices provided, and fill in the corresponding circle on your answer sheet. For questions 16-20, solve the problem and enter your answer in the grid on the answer sheet. Please refer to the directions before question 16 on how to enter your answers in the grid. You may use any available space in your test booklet for scratch work.
NOTES
.The use of a calculator is not permitted.
.All variables and expressions used represent real numbers unless otherwise indicated.
.Figures provided in this test are drawn to scale unless otherwise indicated.
.All figures lie in a plane unless otherwise indicated.
.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.If x-1
=k and k=3, what is the value of x ?
3
A) 2
B)4
C) 9
D) 10
2. For i= -1, what is the sum (7+3i) + (?8+9i) ?
A) ?1 + 12i
B) ?1?6i
C) 15 + 12i
D) 15?6i
3.On Saturday afternoon, Armand sent m text messages each hour for 5 hours, and Tyrone sent p text messages each hour for 4 hours. Which of the following represents the total number of messages sent by Armand and Tyrone on Saturday afternoon?
A) 9mp
B) 20mp
C) 5m+4p
D) 4m+5p
4.Kathy is a repair technician for a phone company. Each week, she receives a batch of phones that need repairs. The number of phones that she has left to fix at the end of each day can be estimated with the equation P = 108 ? 23d, where P is the number of phones left and d is the number of days she has
worked that week. What is the meaning of the value 108 in this equation?
A) Kathy will complete the repairs within 108 days.
B) Kathy starts each week with 108 phones to fix.
C) Kathy repairs phones at a rate of 108 per hour.
D) Kathy repairs phones at a rate of 108 per day.
5.(x2y ? 3y2 + 5xy2) ?(?x2y + 3xy2 ? 3y2) Which of the following is equivalent to the expression above?
A) 4x2y2
B) 8xy2?6y2
C) 2x2y+2xy2
D) 2x2y+8xy2?6y2
6.h= 3a+28.6
A pediatrician uses the model above to estimate the height h of a boy, in inches,
in terms of the boy’s age a, in years, between the ages of 2 and 5. Based on the model, what is the estimated increase, in inches, of a boy’s height each year?
A) 3
B) 5.7
C) 9.5
D) 14.3
7.
The formula above gives the monthly payment m needed to pay off a loan of P dollars at r percent annual interest over N months. Which of the following gives P in terms of m, r, and N ?
8.If a
b
=2, what is the value of 4b
a
?
A) 0
B) 1
C) 2
D) 4
9. 3x+4y=-23
2y-x=-19
What is the solution (x, y) to the system of equations above?
A) (?5, ?2)
B) (3,?8)
C) (4,?6)
D) (9,?6)
10.g(x) = ax2 + 24
For the function g defined above, a is a constant
and g(4) = 8. What is the value of g(?4) ?
A) 8
B) 0
C) ?1
D) ?8
11. b=2.35+0.2x
c=1.75+0.4x
In the equations above, b and c represent the price per pound, in dollars, of beef and chicken, respectively, x weeks after July 1 during last summer. What was the price per pound of beef when it was equal to the price per pound of chicken?
A) $2.60
B) $2.85
C) $2.95
D) $3.35
12.A line in the xy-plane passes through the origin and has a slope of 1
7. Which
of the following points lies on the line?
A) (0, 7)
B) (1, 7)
C) (7, 7)
D) (14,2)
13.
14. If 3x?y=12, what is the value of 8x
?
2y
A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.
15.If (ax+2)(bx+7)=15x2+cx+14 for all values of x, and a+b=8,what are the two possible values for c ?
A) 3and5
B) 6 and 35
C)10and21
D) 31 and 41
16.If t>0 and t2?4=0,whatisthevalueof t ?
17.
A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD, and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and ∠AE
B and
∠CDB have the same measure. What is the value of x ?
18. x+ y = ?9
x+ 2y = ?25
According to the system of equations above, what is the value of x ?
, what is
19.In a right triangle, one angle measures x°, where sin x°=4
5
cos(90°-x°)
20. If a =52 and 2a=2x, what is the value of x ? Mathematics Test –
Calculator
55 MINUTES, 38 QUESTIONS
Turn to Section 4 of your answer sheet to answer the questions in this section.
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 31-37, 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.
Notes
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.
Reference
1.John runs at different speeds as part of his training program. The graph shows his target heart rate at different times during his workout. On which interval is the target heart rate strictly increasing then strictly decreasing?
A) Between 0 and 30 minutes
B) Between 40 and 60 minutes
C) Between 50 and 65 minutes
D) Between 70 and 90 minutes
2.If y=kx, where k is a constant, and y=24when x=6, what is the value of y when x=5?
A) 6
B) 15
C) 20
D) 23
3.In the figure above, lines and m are parallel and lines s and t are parallel. If the measure of ∠1 is 35°, what is the measure of ∠2 ?
A) 35°
B) 55°
C) 70°
D) 145°
4.If 16+4x is 10 more than 14,what is the value of 8x ?
A) 2
B) 6
C) 16
D) 80
5.Which of the following graphs best shows a strong negative association between d and t ?
6.
1 decagram = 10 grams
1,000 milligrams = 1 gram
A hospital stores one type of medicine in 2-decagram containers. Based on the information given in the box above, how many 1-milligram doses are there in
one 2-decagram container?
A) 0.002
B) 200
C) 2,000
D) 20,000
7.
The number of rooftops with solar panel installations in 5 cities is shown in the graph above. If the total number of installations is 27,500, what is an appropriate label for the vertical axis of the graph?
A) Number of installations (in tens)
B) Number of installations (in hundreds)
C) Number of installations (in thousands)
D) Number of installations (in tens of thousands)
8.For what value of n is n-1+1equal to 0 ?
A) 0
B) 1
C) 2
D) There is no such value of n.
Questions 9 and 10 refer to the following information.
a= 1,052 + 1.08t
The speed of a sound wave in air depends on the air temperature. The formula above shows the relationship between a, the speed of a sound wave, in feet per second, and t, the air temperature, in degrees Fahrenheit (°F).
9.Which of the following expresses the air temperature in terms of the speed of
a sound wave?
A) t=a-1052
1.08
B) t=a+1052
1.08
C) t=1052-a
1.08
D)t= 1.08
a+1052
10.At which of the following air temperatures will the speed of a sound wave be closest to 1,000 feet per second?
A) ?46°F
B) ?48°F
C) ?49°F
D) ?50°F
11.
Which of the following numbers is NOT a solution of the inequality
3x?5≥4x?3 ?
A) ?1
B) ?2
C) ?3
D) ?5
12.
Based on the histogram above, of the following, which is closest to the average (arithmetic mean) number of seeds per apple?
A) 4
B) 5
C) 6
D) 7
13.
A group of tenth-grade students responded to a survey that asked which math course they were currently enrolled in. The survey data were broken down as shown in the table above. Which of the following categories accounts for approximately 19 percent of all the survey respondents?
A) Females taking Geometry
B) Females taking Algebra II
C) Males taking Geometry
D) Males taking Algebra I
14.
The table above lists the lengths, to the nearest inch, of a random sample of 21 brown bullhead fish. The outlier measurement of 24 inches is an error. Of the mean, median, and range of the values listed, which will change the most if the 24-inch measurement is removed from the data?
A) Mean
B) Median
C) Range
D) They will all change by the same amount.
Questions 15 and 16 refer to the following information.
15.What does the C-intercept represent in the graph?
A) The initial cost of renting the boat
B) The total number of boats rented
C) The total number of hours the boat is rented
D) The increase in cost to rent the boat for each additional hour
16. Which of the following represents the relationship between h and C ?
A) C=5h
B) C=3
h+5
4
C) C=3h+5
D) h=3C
17.
The complete graph of the function f is shown in the xy-plane above. For what value of x is the value of f (x) at its minimum?
A) ?5
B) ?3
C) ?2
D) 3
18.
In the xy-plane, if (0, 0) is a solution to the system of inequalities above, which of the following relationships between a and b must be true?
A) a>b
B) b>a
C)a?b
D) a=?b
19. A food truck sells salads for $6.50 each and drinks for $2.00 each. The food truck’s revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day?
A) 77
B) 93
C) 99
D) 105
20.Alma bought a laptop computer at a store that gave a 20 percent discount off its original price. The total amount she paid to the cashier was p dollars, including an 8 percent sales tax on the discounted price. Which of the following represents the original price of the computer in terms of p ?
A) 0.88p
B) p
0.88
C) (0.88)(1.08)p
D)
p (0.88)(1.08)
21.
The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. If a person is chosen at random from those who recalled
at least 1 dream, what is the probability that the person belonged to Group Y ?
A)68
100
B)79
100
C)79
164
D)164
200
Questions 22 and 23 refer to the following information.
22. Which of the following best approximates the average rate of change in the annual budget for agriculture/natural resources in Kansas from 2008 to 2010 ?
A) $50,000,000 per year
B) $65,000,000 per year
C) $75,000,000 per year
D) $130,000,000 per year
23.Of the following, which program’s ratio of its2007 budget to its 2010 budget is closest to the human resources program’s ratio of its 2007 budget to its 2010 budget?
A) Agriculture/natural resources
B) Education
C) Highways and transportation
D) Public safety
24.Which of the following is an equation of a circle in the xy-plane with center (0, 4) and a radius with endpoint(3
,5)?
4
A)x2+(y-4)2=25
9
B)x2+(y+4)2=25
9
C)x2+(y-4)2=5
3
D)x2+(y+4)2=5
3
25.h=-4.9t2+25t
The equation above expresses the approximate height h, in meters, of a ball t seconds after it is launched vertically upward from the ground with an initial velocity of 25 meters per second. After approximately how many seconds will the ball hit the ground?
A) 3.5
B) 4.0
C) 4.5
D) 5.0
26.Katarina is a botanist studying the production of pears by two types of pear trees. She noticed that Type A trees produced 20 percent more pears than Type B trees did. Based on Katarina’s observation, if the Type A trees produced 144 pears, how many pears did the Type B trees produce?
A) 115
B) 120
C) 124
D) 173
27.A square field measures 10 meters by 10 meters. Ten students each mark off
a randomly selected region of the field; each region is square and has side lengths of 1 meter, and no two regions overlap. The students count the earthworms contained in the soil to a depth of 5 centimeters beneath the ground’s surface in each region. The results are shown in the table below.
Which of the following is a reasonable approximation of the number of earthworms to a depth of 5 centimeters bene ath the ground’s surface in the entire field?
A) 150
B) 1,500
C) 15,000