COPY – SAT 10/30/21 Math Test – No Calculator

Math Test – No Calculator
25 MINUTES, 20 QUESTIONS

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.

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) is a real number.

1. x + y = 75

The equation above relates the number of minutes, x, Maria spends running each day and the number of minutes, y, she spends biking each day.
In the equation, what does the number 75 represent?

2. Which of the following is equivalent to 3(x + 5) − 6 ?

3. x = y − 3
     x / 2 + 2y = 6

Which ordered pair (x, y) satisfies the system of equations shown above?

4. Which of the following complex numbers is equal to (5 + 12i) − (9i² − 6i), for i = √-1 ?

5. 

6. A company that makes wildlife videos purchases camera equipment for $32,400. The equipment depreciates in value at a constant rate for 12 years, after which it is considered to have no monetary value. How much is the camera equipment worth 4 years after it is purchased?

7. x² + 6x + 4

Which of the following is equivalent to the expression above?

8. Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

9. Marisa needs to hire at least 10 staff members for an upcoming project. The staff members will be made up of junior directors, who will be paid $640 per week, and senior directors, who will be paid $880 per week. Her budget for paying the staff members is no more than $9,700 per week. She must hire at least 3 junior directors and at least 1 senior director. Which of the following systems of inequalities represents the conditions described if x is the number of junior directors and y is the number of senior directors?

10. ax³ + bx² + cx + d = 0

In the equation above, a, b, c, and d are constants. If the equation has roots −1, −3, and 5, which of the following is a factor of ax³ + bx² + cx + d ?

11. 

12. The function f is defined by f(x) = (x + 3)(x + 1). . The graph of f in the xy-plane is a parabola. Which of the following intervals contains the x-coordinate of the vertex of the graph of f ?

13. 

14. A shipping service restricts the dimensions of the boxes it will ship for a certain type of service. The restriction states that for boxes shaped like rectangular prisms, the sum of the perimeter of the base of the box and the height of the box cannot exceed 130 inches. The perimeter of the base is determined using the width and length of the box. If a box has a height of 60 inches and its length is 2.5 times the width, which inequality shows the allowable width x, in inches, of the box?

15. The expression ⅓x² – 2 can be rewritten as ⅓(x – k)(x + k)  , where k is a positive constant. What is the value of k ?

Directions: For questions 16-20, solve the problem and enter your answer in the black space under the question.

16. If 2x + 8 = 16, what is the value of x + 4 ?

17. 

18. The number of radians in a 720-degree angle can be written as aπ, where a is a constant. What is the value of a ?

19. The graph of a line in the xy-plane passes through the point ( 1, 4 ) and crosses the x-axis at the point ( 2, 0 ). The line crosses the y-axis at the point ( 0, b ). What is the value of b ?

20. ( 7532 + 100y² ) + 10( 10y² – 110 ) 

The expression above can be written in the form ay² + b, where a and b are constants. What is the value of a + b ?