# 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 (X-1)/3= k and k = 3, what is the value of x ?
**

**A.**2

**B.**4

**C.**9

**D.**10

**Question 2.**

(x

(x

^{2}y − 3 y^{2}+ 5xy^{2}) − (− x^{2}y + 3 xy^{2}− 3y^{2}) Which of the following is equivalent to the expression above?**A.**4x

^{2}y

^{2}

**B.**8xy

^{2}− 6y

^{2}

**C.**2x

^{2}y + 2xy

^{2}

**D.**2x

^{2}y + 8xy

^{2}− 6y

^{2}

**Question 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

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?

B. 20mp

C. 5m + 4p

D. 4m + 5p

**Question 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.

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?

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.

**Question 5.**

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 ?

A.

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 ?

B.

C.

D.

**Question 6.**

For i= ,what is the sum (7 + 3 i ) + (−8 + 9 i )

A. -1 + 12i

For i= ,what is the sum (7 + 3 i ) + (−8 + 9 i )

B. -1 - 6i

C. 15 + 12i

D. 15 - 6i

**Question 7.**

h = 3 a + 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

h = 3 a + 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?

B. 5.7

C. 9.5

D. 14.3

**Question 8.**

if a/b=2, what is the value of 4b/a?

A. 0

if a/b=2, what is the value of 4b/a?

B. 1

C. 2

D. 4

**Question 9.**

3 x + 4 y = −23

2 y − x = −19

What is the solution (x , y) to the system of equations above?

A. (-5,-2)

3 x + 4 y = −23

2 y − x = −19

What is the solution (x , y) to the system of equations above?

B. (3,-8)

C. (4,-6)

D. (9,-6)

**Question 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

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) ?

B. 0

C. -1

D. -8

**A. $2.60**

Question 11.

b = 2.35 + 0.25x

c = 1.75 + 0.40x

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?

Question 11.

b = 2.35 + 0.25x

c = 1.75 + 0.40x

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?

B. $2.85

C. $2.95

D. $3.35

**A. (0,7)**

Question 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?

Question 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?

B. (1,7)

C. (7,7)

D. (14,2)

**A.**

Question 13.

If x > 3, which of the following is equivalent to ?

Question 13.

If x > 3, which of the following is equivalent to ?

B.

C.

D.

**A. 2**

Question 14.

if 3x - y = 12, what is the value of 8

Question 14.

if 3x - y = 12, what is the value of 8

^{x}/2y?^{12}

B. 4

^{4}

C. 8

^{2}

D. the value cannot be determined by the given information

**Question 15**

If (ax + 2)(bx + 7) = 15 x

If (ax + 2)(bx + 7) = 15 x

^{2}+ cx + 14 for all values of x, and a + b = 8, what are the two possible values for c ?A. 3 and 5

B. 6 and 35

C. 10 and 21

D. 31 and 41

**Question 16.**

If t > 0 and t

If t > 0 and t

^{2}− 4 = 0 , what is the value of t ?**Question 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 ∠AEB and ∠CDB have the same measure. What is the value of x ?

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 ∠AEB and ∠CDB have the same measure. What is the value of x ?

Question 18.

x + y = −9 x + 2 y = −25 According to the system of equations above, what is the value of x ?

Question 18.

x + y = −9 x + 2 y = −25 According to the system of equations above, what is the value of x ?