2024 SAT Standardized Test Math Practice Paper 26

6. Sai is ordering new shelving units for his store. Each unit is 7 feet in length and extends from floor to ceiling. Sai’s store has 119 feet of wall space that includes 21 feet of windows along the walls. If the shelving units cannot be placed in front of the windows, which of the following inequalities includes all possible values of r, the number of shelving units that Sai could use?

Sat math 26 4

Correct Answer: A

Answer Explanation:

To figure out the total number of shelving units Sai could use, find the total available wall space and divide by the length of the units. The total amount of wall space can be calculated as 119 – 21. Because the length of each unit is 7 feet, the maximum number of units Sai could put up can be calculated as ​ \frac{119-21}{7} ​. Because this is the maximum number of units Sai could put up, r has to be less than or equal to this number. Therefore, the correct answer is (A).

7.

Sat math 26 5

The scatterplot above shows the weight, in ounces, of the fruits on a certain truffula tree from days 55 to 85 after flowering. According to the line of best fit in the scatterplot above, which of the following is the closest approximation of the number of days after flowering of a truffula fruit that weighs 5.75 ounces?

A. 63
B. 65
C. 77
D. 81

Correct Answer: C

Answer Explanation:

Weight is shown on the vertical axis of the graph, given in ounces. Make your own mark indicating 5.75 on this axis; then draw a horizontal line from that mark to the line of best fit. Once you hit it, draw a vertical line straight down to the horizontal axis. It should hit between 75 and 80 days, slightly closer to the mark for 75. This makes (C) the credited response. Draw your lines carefully, using your answer sheet as a straightedge if necessary.

8. Hannah placed an online order for shirts that cost $24.50 per shirt. A tax of 7% is added to the cost of the shirts, before a flat, untaxed shipping rate of $6 is charged. Which of the following represents Hannah’s total cost for s shirts, in dollars?

A. 0.07(24.50s + 6)
B. 1.07(24.50 + 6)s
C. 1.07(24.50s) + 6
D. 1.07(24.50 + s) + 6

Correct Answer: C

Answer Explanation:

Whenever the question includes variables, plug in. If s = 2, the shirts cost 2($24.50) = $49. The tax on the shirts is 0.07($49) = $3.43. So, the shirts with tax and the $6 shipping fee cost $49 + $3.43 + $6 = $58.43. Plug in 2 for s in the answers to see which answer equals the target number of $58.43. In (A), 0.07[24.50(2) + 6] = 3.85. This is not the target number, so eliminate (A). In (B), 1.07(24.50 + 6)(2) = 65.25. Again, this is not the target number, so eliminate (B). In (C), 1.07[24.50(2)] + 6 = 58.43. This is the target number, so keep it, but be sure to check the remaining answer choice. In (D), 1.07(24.50 + 2) + 6 = 34.355, which is not the target number. Therefore, the correct answer is (C).

9. Once a certain  plant begins to grow, its height increases at a linear rate. After six weeks, the plant is 54 centimeters tall. Which of the following functions best models the relationship between h(w), the height, in centimeters, of the plant, and w, the number of weeks that the plant has been growing?

A. h(w) = 6w
B. h(w) = 9w
C. h(w) = 54w
D. h(w) = 54 + w

Correct Answer: B

Answer Explanation:

The question states that after 6 weeks the plant is 54 centimeters tall. Therefore, when w = 6, h(w) = 54. Plug in 6 for w in the answers to see in which answer h(w) equals the target number of 54. In (A) h(w) = 6(6) = 36. Eliminate (A). In (B), h(w) = 9(6) = 54. The correct answer is (B).

10. Which of the following is equivalent to (12x² + 4x + 5y) + (3x² – 2x + 3y) ?

A. 2x² – 2x + 8y
B. 2x² + 15x + 8y
C. 15x² – 2x + 8y
D. 15x² + 2x + 8y

Correct Answer: D

Answer Explanation:

Because the operation between the parentheses is addition, the parentheses can be removed, and the resulting expression becomes 12x² + 4x + 5y + 3x² – 2x + 3y. Reorder the terms so that like terms are next to each other: 12x² + 3x² + 4x – 2x + 5y + 3y. Combine like terms to get 15x² + 2x + 8y. The correct answer is (D).


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