SAT 7/16/21 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. Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a one-time service fee for processing the purchase of the tickets. The equation T n = 15 + 12 represents the total amount T, in dollars, Salim will pay for n tickets. What does 12 represent in the equation?

2. A gardener buys two kinds of fertilizer. Fertilizer A contains 60% filler materials by weight and Fertilizer B contains 40% filler materials by weight. Together, the fertilizers bought by the gardener contain a total of 240 pounds of filler materials. Which equation models this relationship, where x is the number of pounds of Fertilizer A and y is the number of pounds of Fertilizer B?

3. What is the sum of the complex numbers 2 + 3i and 4 + 8i, where i = √−1 ?

4. 4x² – 9 = (px + t)(px – t)

In the equation above, p and t are constants.
Which of the following could be the value of p ?

5. Which of the following is the graph of the equation y = 2x −5 in the xy-plane?

6. If x = ⅔y and y = 18, what is the value of 2x – 3?

7. A bricklayer uses the formula n = 7Lh to estimate the number of bricks, n, needed to build a wall that is L feet long and h feet high. Which of the following correctly expresses L in terms of n and h ?

8.

9. If √x + √9 = √64, what is the value of x ?

10. Jaime is preparing for a bicycle race. His goal is to bicycle an average of at least 280 miles per week for 4 weeks. He bicycled 240 miles the first week, 310 miles the second week, and 320 miles the third week. Which inequality can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal?

11.

12. Which of the following is equivalent to (4x² + 6x) / (4x + 2) ?

13. 2x² – 4x = t
In the equation above, t is a constant. If the
equation has no real solutions, which of the following
could be the value of t ?

14. A laundry service is buying detergent and fabric softener from its supplier. The supplier will deliver no more than 300 pounds in a shipment. Each container of detergent weighs 7.35 pounds, and each container of fabric softener weighs 6.2 pounds. The service wants to buy at least twice as many containers of detergent as containers of fabric softener. Let d represent the number of containers of detergent, and let s represent the number of containers of fabric softener, where d and s are nonnegative integers. Which of the following systems of inequalities best represents this situation?

15. Which of the following is equivalent to (a + (b/2))² ?

16. If a^(b/4) = 16 for positive integers a and b, what is one possible value of b ?

17. (2 / 3)t = (5 / 2)

What value of t is the solution of the equation above?

18.

19. How many liters of a 25% saline solution must be added to 3 liters of a 10% saline solution to obtain a 15% saline solution?

20. Points A and B lie on a circle with radius 1, and arc AB has length (π / 3) . What fraction of the circumference of the circle is the length of arc AB  ?