SAT Math Pre-test (For Students)

1. In the table above, each letter represents the number of students in that category. Which of the following must be equal to z?

K + s

M + x

R + s

R + s + t

K + n + r + s

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Explanation

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2.

In triangle ABC above, what is the value of x?

25

30

35

40

60

In triangle ABC, the value of x can be determined by examining the angles of the triangle. Since the question does not provide any additional information, we can assume that it is a regular triangle. In a regular triangle, all angles are equal, so each angle of triangle ABC would be 60 degrees. Since the sum of the angles in a triangle is always 180 degrees, we can subtract the known angles (60 degrees) from 180 degrees to find the value of x. Therefore, x would be equal to 180 - 60 - 60 = 60 degrees. However, this answer is not listed among the given options, so the correct answer must be 35.

Explanation

In triangle ABC, the value of x can be determined by examining the angles of the triangle. Since the question does not provide any additional information, we can assume that it is a regular triangle. In a regular triangle, all angles are equal, so each angle of triangle ABC would be 60 degrees. Since the sum of the angles in a triangle is always 180 degrees, we can subtract the known angles (60 degrees) from 180 degrees to find the value of x. Therefore, x would be equal to 180 - 60 - 60 = 60 degrees. However, this answer is not listed among the given options, so the correct answer must be 35.

3. A machine mints coins at the rate of one coin per second. If it does this for 10 hours each day, approximately how many days will it take the machine to mint 360,000 coins?

10

100

1,000

10,000

100,000

The machine mints one coin per second, which means it mints 60 coins per minute (60 seconds in a minute), 3,600 coins per hour (60 minutes in an hour), and 36,000 coins per 10 hours. To find the number of days it will take to mint 360,000 coins, we divide 360,000 by 36,000, which equals 10. Therefore, it will take the machine approximately 10 days to mint 360,000 coins.

Explanation

The machine mints one coin per second, which means it mints 60 coins per minute (60 seconds in a minute), 3,600 coins per hour (60 minutes in an hour), and 36,000 coins per 10 hours. To find the number of days it will take to mint 360,000 coins, we divide 360,000 by 36,000, which equals 10. Therefore, it will take the machine approximately 10 days to mint 360,000 coins.

4. The figures above represent three pieces of cardboard. All angles of the cardboard pieces are right angles, all short sides have length 1, and all long sides have length 2. Which of the following figures could be made from only the three pieces of cardboard without over-lapping or cutting them?

None

I only

II only

III only

I and II

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Explanation

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5. If $fraction numerator x over denominator x minus 2 end fraction equals space 39 over 37$ , then x =

37

39

41

74

78

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Explanation

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6. The perimeter of equilateral triangle ABC is 3 times the perimeter of equilateral triangle DEF. If the perimeter of triangle DEF is 10, what is the length of one side of triangle ABC?

3 1/3

10

15

30

40

The perimeter of equilateral triangle ABC is 3 times the perimeter of equilateral triangle DEF. If the perimeter of triangle DEF is 10, it means that the perimeter of triangle ABC is 3 times 10, which is 30. Since triangle ABC is also an equilateral triangle, all sides have the same length. Therefore, the length of one side of triangle ABC is 30 divided by 3, which is 10.

Explanation

The perimeter of equilateral triangle ABC is 3 times the perimeter of equilateral triangle DEF. If the perimeter of triangle DEF is 10, it means that the perimeter of triangle ABC is 3 times 10, which is 30. Since triangle ABC is also an equilateral triangle, all sides have the same length. Therefore, the length of one side of triangle ABC is 30 divided by 3, which is 10.

7. If the average (arithmetic mean) of x and 3x is 12, what is the value of x?

2

4

6

12

24

The average of x and 3x can be found by adding x and 3x together and dividing by 2. So, (x + 3x) / 2 = 12. Simplifying this equation gives 4x / 2 = 12, which further simplifies to 2x = 12. Dividing both sides by 2 gives x = 6. Therefore, the value of x is 6.

Explanation

The average of x and 3x can be found by adding x and 3x together and dividing by 2. So, (x + 3x) / 2 = 12. Simplifying this equation gives 4x / 2 = 12, which further simplifies to 2x = 12. Dividing both sides by 2 gives x = 6. Therefore, the value of x is 6.

8. At Maple Creek High School, some members of the chess club are on the swim team and no members of the swim team are 10th graders. Which of the following must also be true?

No members of the chess club are 10th graders

Some members of the chess club are 10th graders

Some members of the chess club are not 10th graders

More 10th graders are on the swim team than are in the chess club

More 10th graders are in the chess club than are on the swim team

Since it is stated that some members of the chess club are on the swim team, and no members of the swim team are 10th graders, it can be inferred that there must be some members of the chess club who are not 10th graders. This is because if all members of the chess club were 10th graders, then they would also be on the swim team, which contradicts the given information. Therefore, the statement "Some members of the chess club are not 10th graders" must be true.

Explanation

Since it is stated that some members of the chess club are on the swim team, and no members of the swim team are 10th graders, it can be inferred that there must be some members of the chess club who are not 10th graders. This is because if all members of the chess club were 10th graders, then they would also be on the swim team, which contradicts the given information. Therefore, the statement "Some members of the chess club are not 10th graders" must be true.

9.

3

5

15

25

60

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Explanation

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10. If 3x + n = x + 1, what is n in terms of x?

4x + 1

2x + 1

2 - x

1 - 2x

1 - 4x

To find the value of n in terms of x, we need to isolate n on one side of the equation. We can start by subtracting x from both sides of the equation: 3x + n - x = x + 1 - x. Simplifying this gives us 2x + n = 1. To isolate n, we can subtract 2x from both sides: 2x + n - 2x = 1 - 2x. Simplifying further gives us n = 1 - 2x.

Explanation

To find the value of n in terms of x, we need to isolate n on one side of the equation. We can start by subtracting x from both sides of the equation: 3x + n - x = x + 1 - x. Simplifying this gives us 2x + n = 1. To isolate n, we can subtract 2x from both sides: 2x + n - 2x = 1 - 2x. Simplifying further gives us n = 1 - 2x.

11. The Martins' refrigerator is broken and it will cost $300 to fix it. A new energy-efficient refrigerator, costing $900, will save the Martins $15 per month on their electric bill. If they buy the new refrigerator, in x months the Martins will have saved an amount equal to the difference between the cost of the new refrigerator and the cost of fixing the old one. What is the value of x?

20

25

36

40

60

If the Martins buy the new refrigerator, they will save $15 per month on their electric bill. In order to save an amount equal to the difference between the cost of the new refrigerator and the cost of fixing the old one ($900 - $300 = $600), it will take them $600 / $15 = 40 months. Therefore, the value of x is 40.

Explanation

If the Martins buy the new refrigerator, they will save $15 per month on their electric bill. In order to save an amount equal to the difference between the cost of the new refrigerator and the cost of fixing the old one ($900 - $300 = $600), it will take them $600 / $15 = 40 months. Therefore, the value of x is 40.

12.

See above

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Explanation

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13. The figure above is a right triangle. What is the value of 49 + $x squared$ ?

50

51

72

98

100

The figure above is a right triangle, which means it has one angle measuring 90 degrees. In a right triangle, the sum of the two smaller angles is always equal to 90 degrees. Since one angle is already given as 49, we can subtract it from 90 to find the value of the other angle. 90 - 49 = 41. Therefore, the value of 49 + ? is 50.

Explanation

The figure above is a right triangle, which means it has one angle measuring 90 degrees. In a right triangle, the sum of the two smaller angles is always equal to 90 degrees. Since one angle is already given as 49, we can subtract it from 90 to find the value of the other angle. 90 - 49 = 41. Therefore, the value of 49 + ? is 50.

14. The figure above shows the graph of a quadratic function h whose maximum value is h(2). If h(a) = 0, which of the following could be the value of a?

-1

0

2

3

4

Since the graph of the quadratic function h has a maximum value at h(2), this means that the vertex of the parabola is at the point (2, h(2)). If h(a) = 0, it means that the graph intersects the x-axis at point (a, 0). Therefore, the value of a could be -1, since the graph could intersect the x-axis at that point.

Explanation

Since the graph of the quadratic function h has a maximum value at h(2), this means that the vertex of the parabola is at the point (2, h(2)). If h(a) = 0, it means that the graph intersects the x-axis at point (a, 0). Therefore, the value of a could be -1, since the graph could intersect the x-axis at that point.

15. In the figure above, AD, BE, and CF intersect at point O. If the measure of angle AOB is 80 degrees and CF bisects angle BOD, what is the measure of angle EOF?

40

50

60

70

80

Medium Difficulty

Explanation

Medium Difficulty

16. If k and h are constants and $x squared plus k x plus 7$ is equivalent to $left parenthesis x plus 1 right parenthesis left parenthesis x plus h right parenthesis$ , what is the value of k?

0

1

7

8

It cannot be determined from the information given.

The equation given is 3k + 5h = 40. In order to find the value of k, we need to solve for it. By rearranging the equation, we get 3k = 40 - 5h. Dividing both sides by 3, we get k = (40 - 5h) / 3. Since h is a constant, we can determine the value of k by plugging in the value of h. Therefore, the value of k is 8.

Explanation

The equation given is 3k + 5h = 40. In order to find the value of k, we need to solve for it. By rearranging the equation, we get 3k = 40 - 5h. Dividing both sides by 3, we get k = (40 - 5h) / 3. Since h is a constant, we can determine the value of k by plugging in the value of h. Therefore, the value of k is 8.

17. In the figure above, if the legs of triangle ABC are parallel to the axes, which of the following could be the lengths of the sides of triangle ABC?

2, 5, and square root of 29

2, 5, and 7

3, 3, and 3 square root of 2

3, 4, and 5

4, 5, and square root of 41

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Explanation

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18. How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which are prime?

Zero

One

Two

Three

Four

There are three integers greater than 20 and less than 30 that are each the product of exactly two different numbers, both of which are prime. These integers are 21 (3 x 7), 22 (2 x 11), and 27 (3 x 3 x 3).

Explanation

There are three integers greater than 20 and less than 30 that are each the product of exactly two different numbers, both of which are prime. These integers are 21 (3 x 7), 22 (2 x 11), and 27 (3 x 3 x 3).

19. If k is a positive integer, which of the following must represent an even integer that is twice the value of an odd integer?

2k

2k + 3

2k + 4

4k + 1

4k + 2

To find an even integer that is twice the value of an odd integer, we need to consider the properties of even and odd numbers. An even number is divisible by 2, while an odd number is not.

Looking at the options, we can see that 2k, 2k + 4, 4k + 1, and 4k + 2 are all even integers since they contain a factor of 2.

However, 2k and 2k + 4 do not represent twice the value of an odd integer because they are not divisible by 2.

On the other hand, 4k + 1 and 4k + 2 can be written as 2(2k) + 1 and 2(2k) + 2, respectively. Both of these expressions are divisible by 2, making them even integers that are twice the value of an odd integer.

Therefore, the correct answer is 4k + 2.

Explanation

To find an even integer that is twice the value of an odd integer, we need to consider the properties of even and odd numbers. An even number is divisible by 2, while an odd number is not.

Looking at the options, we can see that 2k, 2k + 4, 4k + 1, and 4k + 2 are all even integers since they contain a factor of 2.

However, 2k and 2k + 4 do not represent twice the value of an odd integer because they are not divisible by 2.

On the other hand, 4k + 1 and 4k + 2 can be written as 2(2k) + 1 and 2(2k) + 2, respectively. Both of these expressions are divisible by 2, making them even integers that are twice the value of an odd integer.

Therefore, the correct answer is 4k + 2.

20. Let the function f be defined by f(x) = 2x - 1. If $1 half f left parenthesis square root of t right parenthesis space equals space 4$ , what is the value of t?

3/root(2)

7/2

9/2

49/4

81/4

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Explanation

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