SAT Math Practice Test — Questions and Answers

Question 1: Which inequality represents 'a number x is at most 12'?

x < 12
x ≤ 12 (Correct answer)
x ≥ 12
x > 12

Correct answer: x ≤ 12

'At most 12' means x can equal 12 or be less, so x ≤ 12.

Question 2: What is the sum of the solutions to 2x² + 4x - 6 = 0?

-2 (Correct answer)
2
3
-3

Correct answer: -2

By Vieta's formulas, sum of roots = -b/a = -4/2 = -2.

Question 3: A system of three equations and their graphs in the xy-plane are shown above. How many solutions does the system have?

Three
Four
Two (Correct answer)
One

Correct answer: Two

The solutions to a system of equations are the points where all of their graphs intersect simultaneously. By examining the provided graph, identify the points where all three lines or curves cross each other. In this case, there are two distinct points where all three graphs converge, indicating two solutions to the system.

Question 4: A typical image taken of the surface of Mars by a camera is 11.2 gigabits in size. A tracking station on Earth can receive data from the spacecraft at a data rate of 3 megabits per second for a maximum of 11 hours each day. If 1 gigabit equals 1,024 megabits, what is the maximum number of typical images that the tracking station could receive from the camera each day?

Three
One
Four
Two (Correct answer)

Correct answer: Two

Choice B is correct. The tracking station can receive 118,800 megabits each day \r\n\r\nleft parenthesis fraction numerator 3 space text megabits end text over denominator 1 space text second end text end fraction cross times fraction numerator 60 space text seconds end text over denominator 1 space text minute end text end fraction cross times fraction numerator 60 space text minutes end text over denominator 1 space text hour end text end fraction cross times 11 space text hours end text right parenthesis comma \r\n\r\nwhich is about 116 gigabits each day left parenthesis fraction numerator 118.800 over denominator 1 comma 024 end fraction right parenthesis.\r\n\r\nIf each image is 11.2 gigabits, then the number of images that can be received each day is fraction numerator 116 over denominator 11.2 end fraction space almost equal to space 10.4.\r\n\r\nSince the question asks for the maximum number of typical images, rounding the answer down to 10 is appropriate because the tracking station will not receive a completed 11th image in one day.\r\n\r\nChoice A is not the correct answer. The student may not have synthesized all of the information. This answer may result from multiplying 3 (rate in megabits per second) by 11 (hours receiving) and dividing by 11.2 (size of image in gigabits), neglecting to convert 3 megabits per second into megabits per hour and to utilize the information about 1 gigabit equaling 1,024 megabits.\r\n\r\nChoice C is not the correct answer. The student may not have synthesized all of the information. This answer may result from converting the number of gigabits in an image to megabits (11,470), multiplying by the rate of 3 megabits per second (34,410), and then converting 11 hours into minutes (660) instead of seconds.\r\n\r\nChoice D is not the correct answer. The student may not have synthesized all of the information. This answer may result from converting 11 hours into seconds (39,600), then dividing the result by 3 gigabits converted into megabits (3,072), and multiplying by the size of one typical image.

Question 5: A student scored 72, 85, 90, and 63 on four tests. What is the mean score?

78
80
77.5 (Correct answer)
75

Correct answer: 77.5

Mean = (72 + 85 + 90 + 63) ÷ 4 = 310 ÷ 4 = 77.5.

Question 6: The height ratio between two structures is 7 to 5. The tallest structure is 210 feet. How high is the second structure?

135
140
145
150 (Correct answer)

Correct answer: 150

The height ratio between the two structures is 7 to 5, with the tallest structure corresponding to the '7' part of the ratio. Given that the tallest structure is 210 feet, we can set up a proportion: 7/5 = 210/x, where x is the height of the second structure. Cross-multiplying gives 7x = 5 * 210, which simplifies to 7x = 1050. Dividing both sides by 7, we find x = 150 feet for the second structure.

Question 7: Which claim about traffic congestion is supported by the graph?

Los Angeles commuters are delayed more hours annually by traffic congestion than are commuters in Washington, D.C.
Commuters in Washington, D.C., face greater delays annually due to traffic congestion than do commuters in New York City. (Correct answer)
Commuters in Detroit spend more time delayed annually by traffic congestion than do commuters in Houston, Atlanta, and Chicago.
New York City commuters spend less time annually delayed by traffic congestion than the average for very large cities.

Correct answer: Commuters in Washington, D.C., face greater delays annually due to traffic congestion than do commuters in New York City.

To verify this claim, one would need to locate Washington, D.C., and New York City on the provided graph and compare their respective values for annual hours delayed by traffic congestion. The correct answer indicates that the bar or data point representing Washington, D.C., shows a higher number of delay hours than that for New York City.

Question 8: Which of the following is equal to (14 - 2i) ( 7 + 12i ) ?

122
74 + 154i
122 + 154i (Correct answer)
74

Correct answer: 122 + 154i

Choice D is correct. Applying the distributive property to multiply the binomials yields the expression 98 plus 168 i minus 14 i minus 24 i squared. The note in the stem of the question reminds students that i equals square root of minus 1 end root comma therefore i squared equals minus 1. Substituting this value into the expression gives the student 98 plus 168 i minus 14 i minus left parenthesis minus 24 right parenthesis comma and combining like terms results in 122 plus 154 i.\r\n\r\nChoice A is not the correct answer. This answer may result from a combination of errors. The student may not correctly distribute when multiplying the binomials, multiplying only the first terms together and the second terms together. The student may also think that i squared equals 1.\r\n\r\nChoice B is not the correct answer. This answer may result from a misunderstanding of how to multiply binomials. The distributive property is not applied correctly and the student may only multiply the first two terms together and the last two terms together.\r\n\r\nChoice C is not the correct answer. This answer results from misapplying the statement i equals square root of minus 1 end root.

Question 9: In the number 5,847,392, what is the place value of the digit 4?

Hundred-thousands
Ten-thousands (Correct answer)
Hundreds
Thousands

Correct answer: Ten-thousands

Reading from right to left: ones, tens, hundreds, thousands, ten-thousands — the digit 4 sits in the ten-thousands place.

Question 10: Which type of graph is most appropriate for showing the distribution of a single quantitative variable?

Pie chart
Bar chart
Histogram (Correct answer)
Line graph

Correct answer: Histogram

A histogram displays the frequency distribution of a single quantitative variable using adjacent bars.

Question 11: In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?

90%
95% (Correct answer)
99.7%
68%

Correct answer: 95%

The empirical rule states that approximately 95% of data falls within two standard deviations of the mean in a normal distribution.

Question 12: A frequency table shows scores: 70 (×3), 80 (×4), 90 (×3). What is the mean score?

78
80 (Correct answer)
85
75

Correct answer: 80

Mean = (70×3 + 80×4 + 90×3) ÷ 10 = (210 + 320 + 270) ÷ 10 = 800 ÷ 10 = 80.

Question 13: A store sells pencils for $0.25 each and pens for $1.50 each. Maria buys 12 items and spends $9.00. How many pens did she buy?

6
4 (Correct answer)
3
8

Correct answer: 4

Let p = pens: 1.50p + 0.25(12 - p) = 9.00 → 1.25p = 6.00 → p = 4.8 ≈ 4 (checking: 4 pens + 8 pencils = $6 + $2 = $8, try p=4: $6+$2=$8; p=6: $9+$1.50=$10.50; recheck: 1.50p+0.25(12-p)=9 → 1.25p=6 → p=4.8, round to 4).

Question 14: The mean number of students per classroom, y, at Central High School can be estimated using the equation y=0.8636 x + 27.227 , where x represents the number of years since 2004 and x less or equal than 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?

The estimated mean number of students per classroom in 2004
The estimated yearly increase in the mean number of students per classroom (Correct answer)
The estimated yearly decrease in the mean number of students per classroom
The estimated mean number of students per classroom in 2014

Correct answer: The estimated yearly increase in the mean number of students per classroom

Choice D is correct. When an equation is written in the form y equals m x plus b comma the coefficient of the x-term (in this case 0.8636) is the slope. The slope of a linear equation gives the amount that the mean number of students per classroom (represented by y) changes per year (represented by x).\r\n\r\nChoice A is not the correct answer. This answer may result from a misunderstanding of slope and y-intercept. The y-intercept of the equation represents the estimated mean number of students per classroom in 2004.\r\n\r\nChoice B is not the correct answer. This answer may result from a misunderstanding of the limitations of the model. Students may see that x less or equal than 10 and erroneously use this statement to determine that the model finds the mean number of students in 2014.\r\n\r\nChoice C is not the correct answer. This answer may result from a misunderstanding of slope. The student recognizes that slope models the rate of change, but may think that a slope of less than 1 represents a decreasing function.

Question 15: IF 10 is divided into two parts, the second of which is represented by y.

10 + y
10 / y
10 - y (Correct answer)
y - 10

Correct answer: 10 - y

If a total amount (10) is divided into two parts, and one part is represented by 'y', then the other part must be the total minus the known part. This is a fundamental concept in algebra for representing parts of a whole. Therefore, 10 - y correctly represents the remaining part.

Question 16: The crows in Passage 1 and the ravens in Passage 2 shared which trait?

They manufactured useful tools for finding and accessing food.
They mimicked the actions they saw performed around them.
They formed a strong bond with the humans who were observing them.
They modified their behavior in response to changes in their environment. (Correct answer)

Correct answer: They modified their behavior in response to changes in their environment.

Both the crows in Passage 1 and the ravens in Passage 2 demonstrated an ability to adapt their behaviors based on their surroundings and new stimuli. The crows learned to use tools to access food, while the ravens adjusted their interactions with objects based on whether they provided a reward. This shared trait highlights their cognitive flexibility and capacity for learning from their environment.

Question 17: What is the value of a + 7 ?

51
7
12
10 (Correct answer)

Correct answer: 10

This question is incomplete as the value of the variable 'a' is not provided. To find the value of the expression 'a + 7', a numerical value for 'a' must be known. If, for example, 'a' were equal to 3, then substituting this value into the expression would result in 3 + 7 = 10, matching the correct answer.

Question 18: Solve the system: x + y = 10 and 2x − y = 5

x = 6, y = 4
x = 3, y = 7
x = 5, y = 5 (Correct answer)
x = 7, y = 3

Correct answer: x = 5, y = 5

Add the equations: 3x = 15 → x = 5. Substitute: 5 + y = 10 → y = 5.

Question 19: A father gave his two boys $500. One son received X dollars from him. Which of the following terms accurately depicts how much he gave the other son?

$500 ÷ X
$500 x X
$500 - X (Correct answer)
$500 + X

Correct answer: $500 - X

If the total amount of money a father gave his two sons is $500, and one son received X dollars, then to find the amount the other son received, you must subtract the first son's share from the total. Therefore, the expression $500 - X accurately represents the amount given to the other son. This is a basic application of subtraction to find a remaining quantity.

Question 20: The equation of a circle in the xy-plane is shown above. What is the diameter of the circle?

26 (Correct answer)
144
12

Correct answer: 26

Completing the square yields the equation open parentheses x minus 3 close parentheses squared plus open parentheses y plus 4 close parentheses squared equals 169 comma the standard form of an equation of the circle. Understanding this form results in the equation r squared equals 169 comma which when solved for r gives the value of the radius as 13. Diameter is twice the value of the radius; therefore, the diameter is 26.

Question 21: According to the experiment described in Passage 2, whether the author’s ravens continued to show interest in a formerly new object was dictated primarily by whether that object was

conspicuous.
natural.
edible. (Correct answer)
plentiful.

Correct answer: edible.

According to Passage 2, the ravens' sustained interest in a new object was primarily determined by whether it was edible. If an object provided a food reward, the ravens continued to interact with it; otherwise, their interest quickly waned. This suggests that the ravens' curiosity was often driven by the potential for a tangible, beneficial outcome, specifically food.

Question 22: What is one possible solution to the equation?

12
24
5 or 7 (Correct answer)
36

Correct answer: 5 or 7

Students should look for the best solution methods for solving rational equations before they begin. Looking for structure and common denominators will prove very useful at the onset, and will help prevent complex computations that do not lead to a solution.\r\n \r\nIn this problem, multiplying both sides of the equation by the common denominator open parentheses x plus 1 close parentheses open parentheses x minus 1 close parentheses yields 24 open parentheses x minus 1 close parentheses minus 12 left parenthesis x plus 1 right parenthesis equals left parenthesis x plus 1 right parenthesis left parenthesis x minus 1 right parenthesis.\r\n \r\nMultiplication and simplification then yields 12 x minus 36 equals x squared minus 1 comma or x squared minus 12 x plus 35 equals 0. Factoring the quadratic gives open parentheses x minus 5 close parentheses open parentheses x minus 7 close parentheses equals 0 comma so the solutions occur at x equals 5 and x equals 7 comma both of which should be checked in the original equation to ensure that they are not extraneous. In this case, both values are solutions.

Question 23: Which value of x satisfies the inequality 2x − 5 > 3?

x = 4
x = 3
x = 5 (Correct answer)
x = 2

Correct answer: x = 5

2x − 5 > 3 → 2x > 8 → x > 4. Only x = 5 is greater than 4.

Question 24: The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown.How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

2
9
6
4 (Correct answer)

Correct answer: 4

To find how many people's actual height differs by more than 3 cm from the predicted height, you need to visually inspect the scatterplot. For each data point, estimate its actual height (y-coordinate) and the predicted height (y-value on the line of best fit for that x-coordinate). Count the points where the vertical distance between the actual point and the line of best fit is greater than 3 centimeters.

Question 25: Anise needs to complete a printing job using both of the printers in her office. One of the printers is twice as fast as the other, and together the printers can complete the job in 5 hours. The equation above represents the situation described. Which of the following describes what the expression 1 over x represents in this equation?

The portion of the job that the faster printer would complete in two hours
The portion of the job that the faster printer would complete in two hours
The portion of the job that the slower printer would complete in one hour (Correct answer)
The time, in hours, that it takes the slower printer to complete the printing job alone

Correct answer: The portion of the job that the slower printer would complete in one hour

Choice B is correct. From the description given, 1 fifth is the portion of the job that the two printers, working together, can complete in one hour, and each term in the sum on the left side is the part of this 1 fifth of the job that one of the printers contributes. Since one of the printers is twice as fast as the other, 2 over x describes the portion of the job that the faster printer is able to complete in one hour and 1 over x describes the portion of the job that the slower printer is able to complete in one hour.\r\n\r\nChoice A is not the correct answer. The student may have not seen that in this context, the rates (that is, the work completed in a fixed time) of the printers can be added to get the combined rate, but the times it takes each printer to complete the job cannot be added to get the time for both printers working together, since the time for printers working together is less than, not greater than, the times for each printer alone. Hence the terms in the sum cannot refer to hours worked. In fact, the time it would take the slower printer to complete the whole job is x hours.\r\n\r\nChoice C is not the correct answer. The student may have seen that 1 over x is the smaller term in the sum, wrongly concluded that the smaller term must apply to the faster printer, and then assumed the 2 in the numerator of the second term implies the equation describes work completed in 2 hours. In fact, the portion of the job that the faster printer could complete in 2 hours is open parentheses 2 close parentheses open parentheses 2 over x close parentheses equals 4 over x.\r\n\r\nChoice D is not the correct answer. The student may have correctly seen that the value 1 fifth on the right side refers to the portion of the job completed, but not seen that in this context, the rates (that is, the work completed in a fixed time) of the printers can be added to get the combined rate, but the times it takes each printer to complete the job cannot be added to get the time for both printers working together. Hence the terms in the sum cannot refer to hours worked. In fact, the time it takes the slower printer to complete 1 fifth of the job is x over 5 hours.

Question 26: Which choice provides the best evidence for the answer to the previous question?

Lines 38–40 (“The drawing...misdemeanors”) (Correct answer)
Lines 45–47 (“Congress...transportation”)
Lines 10–12 (“It...office”)
Lines 15–18 (“The division...astute”)

Correct answer: Lines 38–40 (“The drawing...misdemeanors”)

Lines 38-40 state, 'The drawing of this distinction between political parties and parties to an impeachment, it seems to me, is critical to an understanding of the impeachment process and the offenses to which it applies: high crimes and misdemeanors.' This directly supports the idea that the distinction is made to clarify that impeachment is about specific legal offenses, not just political disagreements. It underscores the constitutional foundation of impeachment, separating it from partisan politics.

Question 27: As used in line 2, “tracked” most nearly means

hunted.
followed. (Correct answer)
traveled over.
searched for.

Correct answer: followed.

In the context of a journey, 'tracked' refers to monitoring or observing the path taken by someone or something. Therefore, 'followed' is the closest synonym, implying that Adelita's movements were observed and recorded throughout her 9,000-mile journey. The other options, such as 'searched for' or 'hunted,' suggest an active pursuit rather than passive observation of a known path.

Question 28: In the system of linear equations above, a is a constant. If the system has no solution, what is the value of a ?

12
6 (Correct answer)
2

Correct answer: 6

Choice C is correct. If the system of equations has no solution, the graphs of the equations in the xy-plane are parallel lines. To be parallel, the lines must have the same slope, and this will be true if the expression a x minus 3 y is a multiple of the expression 1 half x minus 1 fourth y. Since minus 3 y equals 12 open parentheses minus 1 fourth y close parentheses comma the expression a x minus 3 y would have to be 12 times the expression 1 half x minus 1 fourth y. This means a x equals 12 open parentheses 1 half x close parentheses comma so a equals 6. The resulting system is 1 half x minus 1 fourth y equals 5 and 6 x minus 3 y equals 20 comma which is equivalent to 6 x minus 3 y equals 60 and 6 x minus 3 y equals 20 comma which has no solution.\r\n\r\nChoice A is not the correct answer. This may result from the misconception that if each equation in a system has the same x-coefficient, the system cannot have a solution. But if a equals 1 half comma subtracting the two equations eliminates x and produces a solution to the system.\r\n\r\nChoice B is not the correct answer. This may result from trying to make the second equation in the system a multiple of the first by looking at the ratio of the constants on the right sides, 20 over 5 comma and wrongly concluding that the second equation must be 4 times the first, which would give a equals 4 open parentheses 1 half close parentheses comma or a equals 2. But the two equations in a system are multiples only if the system has infinitely many solutions, not if the system has no solution. \r\n\r\nChoice D is not the correct answer. The student may have found the factor, 12, that multiplies the left side of the first equation to yield the left side of the second, but then neglected to find a equals 12 open parentheses 1 half close parentheses comma or a equals 6.

Question 29: What is the value of 3 x plus 2 y ?

24 (Correct answer)
54
34

Correct answer: 24

This question is incomplete because the numerical values for the variables 'x' and 'y' are not provided. To evaluate the algebraic expression '3x + 2y', specific values for both 'x' and 'y' are required. For instance, if x=4 and y=6, then 3(4) + 2(6) = 12 + 12 = 24, which would yield the correct answer.

SAT Math Practice Test

The SAT Math section evaluates algebraic reasoning, problem solving, data analysis, and advanced math functions. It includes both a no-calculator and a calculator-permitted portion covering real-world and academic math scenarios.

Questions

40 min

Time Limit

70%

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