# SAT MATH(Calc Not Allowed) Practice Tests

*65mins*

**You have 25 minutes to finish the task.Your response will be judged on the quality of your writing and on how well your response presentsthe key points presented in the lectures**

00:25:00 |

1. The use of a calculator is not 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) of x is a real number.

**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 Triangles

Reference 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.

Additional Reference Information

The 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.

**End skippable figure descriptions.**

For student produced response questions, students will also see the following directions:

For questions 31 through 38, solve the problem and enter your answer in the grid, as described below, on the answer sheet.

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

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

3. No question has a negative answer.

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

5. Mixed numbers such as three and one half must be recorded as three point five or seven slash two. (If three and one half is entered into the grid as , three, one, slash, two, 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 grid can accommodate, it may be either rounded or truncated, but it must fill the entire grid.

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

Beging skippable figure description.

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

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

End skippable figure description.

Example 3

Beging skippable figure description.

Example 3: Acceptable ways to record two thirds are: two slash three, point six six six, and point six six seven.

End skippable figure description.

Example 4

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

Beging skippable figure description.

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 two in the first space, zero in the second space, and one in the third space. Alternatively, you may record two in the second space, zero in the third space, and one in the fourth space. Spaces not needed should be left blank.

End skippable figure description.

**
Question 1.
If line ℓ is translated up 5 units and right 7 units, then what is the slope of the new line?**
A. negative two fifths

B. negative three halves

C. negative eight ninths

D. negative eleven fourteenths

**Question 2.**

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

A. The estimated mean number of students per classroom in 2004.

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

B. The estimated mean number of students per classroom in 2014.

C. The estimated yearly decrease in the mean number of students per classroom.

D. The estimated yearly increase in the mean number of students per classroom.

**Question 3.**

If a, squared plus 14 a, equals 51 and a, is greater than zero, what is the value of a, plus 7?

If a, squared plus 14 a, equals 51 and a, is greater than zero, what is the value of a, plus 7?

**Question 4.**

If the fraction whose numerator is 2, and whose denominator is a, minus 1, equals, the fraction whose numerator is 4 and whose denominator is y, where y does not equal zero and a does not equal 1, what is y in terms of a?

A.

If the fraction whose numerator is 2, and whose denominator is a, minus 1, equals, the fraction whose numerator is 4 and whose denominator is y, where y does not equal zero and a does not equal 1, what is y in terms of a?

B.

C.

D.

**Question 5.**

If y equals x cubed, plus 2 x, plus 5 and z equals x squared, plus 7 x, plus 1, what is 2 y plus z in terms of x?

A.

If y equals x cubed, plus 2 x, plus 5 and z equals x squared, plus 7 x, plus 1, what is 2 y plus z in terms of x?

B.

C.

D.

**Question 6.**

If a, to the power of negative one half, equals x, where a is greater than zero and x is greater than zero, which of the following equations gives a in terms of x?

A.

If a, to the power of negative one half, equals x, where a is greater than zero and x is greater than zero, which of the following equations gives a in terms of x?

B.

C.

D.

**Question 7.**

The graph of y equals, parenthesis 2 x minus 4 close parenthesis, parenthesis x minus 4 close parenthesis is a parabola in the x y plane. In which of the following equivalent equations do the x- and y coordinates of the vertex of the parabola appear as constants or coefficients?

A.

The graph of y equals, parenthesis 2 x minus 4 close parenthesis, parenthesis x minus 4 close parenthesis is a parabola in the x y plane. In which of the following equivalent equations do the x- and y coordinates of the vertex of the parabola appear as constants or coefficients?

B.

C.

D.

**Question 8.**

Which of the following is equal to parenthesis, 14 minus 2 i, close parenthesis, parenthesis, 7 plus 12 i, close parenthesis? (Note: i equals the square root of negative 1.)

A. 74

Which of the following is equal to parenthesis, 14 minus 2 i, close parenthesis, parenthesis, 7 plus 12 i, close parenthesis? (Note: i equals the square root of negative 1.)

B. 122

C. 78+154i

D. 122+154i

**Question 9.**

the fraction whose numerator is 5, parenthesis, k plus 2, close parenthesis, minus 7, and whose denominator is 6, equals the fraction whose numerator is 13 minus, parenthesis, 4 minus k, close parenthesis, and whose denominator is 9. In the equation above, what is the value of k?

A. 9/17

the fraction whose numerator is 5, parenthesis, k plus 2, close parenthesis, minus 7, and whose denominator is 6, equals the fraction whose numerator is 13 minus, parenthesis, 4 minus k, close parenthesis, and whose denominator is 9. In the equation above, what is the value of k?

B. 9/13

C. 33/17

D. 33/13

**Question 10.**

Based on the system of equations above, what is the value of the product x y?

A. 3/2

Based on the system of equations above, what is the value of the product x y?

B. 1/4

C. 1/2

D. 11/9

Question 11.

If one half x, plus one third y, equals 4, what is the value of 3 x plus 2 y?

Question 11.

If one half x, plus one third y, equals 4, what is the value of 3 x plus 2 y?

**A.**

Question 12.

Which of the following is equal to

Question 12.

Which of the following is equal to

B.

C.

D.

**A. 1/2.**

Question 13.

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

Question 13.

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

B. 2.

C. 6

D. 12

**A. The time, in hours, that it takes the slower printer to complete the printing job alone**

Question 14.

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 the fraction one over x represents in this equation?

Question 14.

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 the fraction one over x represents in this equation?

B. The portion of the job that the slower printer would complete in one hour

C. The portion of the job that the faster printer would complete in two hours

D. The time, in hours, that it takes the slower printer to complete one fifth of the printing job

Begin skippable figure description.

The figure presents a semicircle with a horizontal diameter labeled A B and a horizontal line segment labeled C D intersecting the semicircle at points C and D.

End skippable figure description.

B.

C.

D.

B.

C.

D.

**Question 15 is based on the following figure.**Begin skippable figure description.

The figure presents a semicircle with a horizontal diameter labeled A B and a horizontal line segment labeled C D intersecting the semicircle at points C and D.

End skippable figure description.

**Question 15.**

The semicircle above has a radius of r inches, and chord line segment C D is parallel to the diameter line segment A B. If the length of line segment C D is two thirds of the length of line segment A B, what is the distance between the chord and the diameter in terms of r?

A.The semicircle above has a radius of r inches, and chord line segment C D is parallel to the diameter line segment A B. If the length of line segment C D is two thirds of the length of line segment A B, what is the distance between the chord and the diameter in terms of r?

B.

C.

D.

**Question 16.**

It is given that sin x = a, where x is the radian measure of an angle and the fraction pi over 2, is less than x, and x is less than pi. If sin w = - a, which of the following could be the value of w?

A.It is given that sin x = a, where x is the radian measure of an angle and the fraction pi over 2, is less than x, and x is less than pi. If sin w = - a, which of the following could be the value of w?

B.

C.

D.

Question 17.

The equation of a circle in the x y plane is shown above. What is the diameter of the circle?Question 17.

The equation of a circle in the x y plane is shown above. What is the diameter of the circle?

Question 18.

What is one possible solution to the equation

Question 18.

What is one possible solution to the equation