# Self-Check Practice

> TSI Math Test Study Guide · Hightower High School P-TECH (2023)
>
> Source: [complete Markdown guide](../TSI-Math-Test-Study-Guide.md) · [original PDF](../1062198634-Hightower-TSI-Test-Study-Guide-v2-MATH.pdf)


#### 1. You received 10% off the original price (P) of air jordans. Write an expression for the sale price of the jordans.

**A.** $P - 10$

**B.** $P - 10P$

**C.** \$0.9P$

**D.** $0.1P - 1P$


#### 2. The formula below represents how long a ball dropped from s feet takes to hit the ground in t seconds. How much longer would it take the ball to hit the ground from 32 feet than from 8 feet? t = $\frac{\sqrt{s}}{4}$

**A.** $\sqrt{2}$ sec

**B.** $\sqrt{0.5}$ sec

**C.** 0.707 sec

**D.** 1.414 sec


#### 3. Alice earns x dollars per hour for the first 40 hours she works and 1.5 times as much for each hour over 40. If Alice works for 48 hours, how much money will she earn?

**A.** \$52x$

**B.** \$48x$

**C.** $40 + 12x$

**D.** $40x + 12$


#### 4. Last week Maria bought k pounds of cherries at \$2.75 per pound. This week cherries are on sale for 20% off, and Maria bought twice as many pounds as she did last week. What is the total, in dollars, she paid for last and this week’s cherries?

**A.** \$3k$

**B.** \$4.95k$

**C.** \$7.15k$

**D.** \$8.25k$


#### 5. If $xy = k$, where $k$ is a constant, and $y = 4$ when $x = 6$, what is $y$ when $x = 8$?

**A.** 2

**B.** 4

**C.** 3

**D.** 18


#### 6. If $xy = k$, where $k$ is a constant, and $y = 5$ when $x = 8$, what is $y$ when $x = 4$?

**A.** 4

**B.** 10

**C.** 20

**D.** 5


#### 7. If $xy = k$, where $k$ is a constant, and $y = 3$ when $x = 4$, what is $y$ when $x = 24?$

**A.** 2

**B.** $\frac{1}{2}$

**C.** $\frac{3}{2}$

**D.** 6


#### 8. If y varies directly as x, and y = 8 when x = 2, what is x when y = 2?

**A.** $\frac{1}{2}$

**B.** 4

**C.** $\frac{1}{4}$

**D.** 16


#### 9. If y varies directly as x, and y = 24 when x = 6, what is y when x = 4?

**A.** 16

**B.** 8

**C.** 12

**D.** 32


#### 10. Which is equivalent to $7x^2 + 21$?

**A.** $3(7x^2 - 7)$

**B.** $7(x^2 - 3)$

**C.** $7(x^2 + 3)$

**D.** $3(x^2 + 7)$


#### 11. If the length of a rectangle is 4 more than its width and the perimeter is 52, find the width.

**A.** $w = 11$

**B.** $w = 8$

**C.** $w = 52$

**D.** $w = 12$


#### 12. If a circle has a radius, r, and area, A, find r in terms of A.

**A.** $r = A\pi^2$

**B.** $r = \frac{A}{\pi}$

**C.** $r = \sqrt{\frac{A}{\pi}}$

**D.** $r = \frac{\sqrt{A}}{\pi}$


#### 13. Which two are NOT factors of $2x^2 - x - 6$?

**A.** $(2x-3)$

**B.** $(2x + 3)$

**C.** $(x + 2)$

**D.** $(x-2)$

**E.** B and D are the two non-factors


#### 14. Sarah bought 7 pens from a bookstore. Some of the pens cost \$3 each, and the rest cost \$4 each. If she paid a total of \$23 for the pens, how many of the \$3 pens did she buy?

**A.** 2

**B.** 3

**C.** 4

**D.** 5


#### 15. It costs Jenny 31.95d + 0.10m dollars to rent a car for d days and drive it m miles. How much does it cost Jenny to rent a car for 5 days if the car is driven a total of 600 miles?

**A.** \$159.75

**B.** \$165.75

**C.** \$219.75

**D.** \$759.75


#### 16. If $\frac{5}{2}x + 4 = 8$, then x =

**A.** $\frac{8}{5}$

**B.** 4

**C.** $\frac{24}{5}$

**D.** 10


#### 17. If x − 10 = 5x − 10 what is the value of x?

**A.** $- 5$

**B.** $-3 \frac{2}{3}$

**C.** 0

**D.** 5


#### 18. If $6(t - 2) - 4 = 2t$, then t =

**A.** $-2$

**B.** 0

**C.** 2

**D.** 4


#### 19. The formula for converting temperature from Fahrenheit (F) to Celsius (C) is C = ($\frac{5}{9}$)(F − 32). If the temperature is 77 Fahrenheit degrees, what is it in Celsius?

**A.** 25 degrees Celsius

**B.** 41⅔ degrees Celsius

**C.** 45 degrees Celsius

**D.** 60⁵⁄₉ degrees Celsius


#### 20. At a restaurant, the cost for a breakfast taco and a small glass of milk is \$2.10. The cost for 2 tacos and 3 small glasses of milk is \$5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk?

> Added practice choices; these options were not printed in the original PDF.

**A.** $t + m = 5.15; 2t + 3m = 2.10$


**B.** $t - m = 2.10; 2t - 3m = 5.15$


**C.** $t + m = 2.10; 2t + 3m = 5.15$


**D.** $t + m = 2.10; 2t - 3m = 5.15$


#### 21. The Frosty Ice-Cream Shop sells sundaes for \$2 and banana splits for \$3. On a hot summer day, the shop sold 8 more sundaes than banana splits and made \$156.

> Added practice choices; these options were not printed in the original PDF.

**A.** 28 sundaes and 36 banana splits


**B.** 36 sundaes and 28 banana splits


**C.** 32 sundaes and 24 banana splits


**D.** 40 sundaes and 32 banana splits


#### 22. Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of bubble gum for a total of \$5.70. Sara bought 2 pieces of fudge and 10 pieces of bubble gum for a total of \$3.60. Which system of equations could be used to determine the cost of 1 piece of fudge, f, and 1 piece of bubble gum, g?

> Added practice choices; these options were not printed in the original PDF.

**A.** $5f + 3g = 5.70; 2f + 10g = 3.60$


**B.** $5f + 3g = 3.60; 2f + 10g = 5.70$


**C.** $5f - 3g = 5.70; 2f - 10g = 3.60$


**D.** $3f + 5g = 5.70; 10f + 2g = 3.60$


#### 23. At a college bookstore, Carla purchased a math textbook and a novel that cost a total of \$54, not including tax. If the price of the math textbook, m, is \$8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

> Added practice choices; these options were not printed in the original PDF.

**A.** $m + n = 54; m = 3n + 8$


**B.** $m + n = 54; n = 3m + 8$


**C.** $m - n = 54; m = 3n - 8$


**D.** $m + n = 46; m = 3n + 8$


#### 24. Marcos had 15 coins in nickels and quarters. He had 3 more quarters than nickels. He wrote a system of equations to represent this situation, letting x represent the number of nickels and y represent the number of quarters. Then he solved the system by graphing. What is the solution?

> Added practice choices; these options were not printed in the original PDF.

**A.** $(x, y) = (9, 6)$


**B.** $(x, y) = (5, 10)$


**C.** $(x, y) = (6, 9)$


**D.** $(x, y) = (7, 8)$