2024 SAT Test Math Practice 13

6.

Sat math 23 4

Based on the chart above, which of the following could express the relationship between x and y ?

A. y = x – 4
B. y = 2x – 1
C. y = 2x + 2
D. y = 3x – 3

Correct Answer: B

Answer Explanation:

Plug in the values from the chart! Use the pair (-3, -7) from the top of the chart and eliminate answers that are not true: (A) becomes -7 = -3 – 4, which is true. Keep it. Keep (B): -7 = 2(-3) – 1 is true. Get rid of (C), which becomes -7 = 2(-3) + 2: -7 does not equal -4. Get rid of (D): -7 = 3(-3) – 3. -7 does not equal -12. Now use another pair just to test (A) and (B). Using (-1, -3), (A) gives -3 = -1 – 4, which is not true, so eliminate it, leaving only (B). The values (-1, -3) work: -3 = 2(-1) – 1.

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7. Line l contains points (3, 2) and (4, 5). If line m is perpendicular to line l, then which of the following could be the equation of line m ?

A. x + 5y = 15
B. x + 3y = 15
C. 3x + y = 5
D. -5x + y = ​\( \frac{1}{3} \)

Correct Answer: B

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8. If f(x) = 2x² + 4 for all real numbers x, which of the following is equal to f(3) + f(5) ?

A. f(4)
B. f(6)
C. f(10)
D. f(15)

Correct Answer: B

Answer Explanation:

To find the value of f(3) + f(5), find the values of f(3) and f(5) separately: f(3) = 2(3)2 + 4 = 22 and f(5) = 2(5)2 + 4 = 54. So f(3) + f(5) = 76. You can tell that f(4) will be between 22 and 54, so you can cross out (A). If you ballpark (C) and (D), putting 10 or 15 in the function will give you a number bigger than 100, and you’re looking for 76, so (C) and (D) are too big. That means the answer is (B) by POE.

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9.

Sat math 23 5

The graph of y = g(x) is shown in the figure above. If g(x) = ax² + bx + c for constants a, b, and c, and if abc ≠ 0, then which of the following must be true?

A. ac > 1
B. c > 1
C. ac > 0
D. a > 0

Correct Answer: C

Answer Explanation:

Sat math 23 6

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10. Carlos and Katherine are estimating acceleration by rolling a ball from rest down a ramp. At 1 second, the ball is moving at 5 meters per second (m/s); at 2 seconds, the ball is moving at 10 m/s; at 3 seconds, the ball is moving at 15 m/s; and at 4 seconds, it is moving at 20 m/s. When graphed on an xy-plane, which equation best describes the ball’s estimated acceleration where y expresses speed and x expresses time?

A. y = 5x + 5
B. y = 25x
C. y = 5x
D. y = (4x + 1)² + 5

Correct Answer: C

Answer Explanation:

Figure out the points that will be on the graph from the data given: (0, 0), (1, 5), (2, 10), (3, 15), (4, 20). Draw a line through or close to these points to get an idea of what the graph will look like. Then use POE. The line is linear, not quadratic, so you can eliminate (D). It is also clear that the line begins at the origin, so the y-intercept will be 0. This will eliminate (A). A slope of 25 is far too big-ballpark-so you can eliminate (B), leaving (C).

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