10 Hard SAT Math Questions (Part - 16)

Question 1 :

If the square of a is equal to the cube of b, where a ≥ 0 and b ≥ 0, for what value of x is √a^x equal to b?

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Question 2 :

The scatterplot shows the relationship between the number of sandwiches sold on a given day, y, at a restaurant and the number of days after February 1, x. The average rate of change, in sandwiches per day, of the number of sandwiches the retaurant sold on February 4 to the number of sandwiches the retaurant sold on February 8 is equal to a. The average rate of change, in sandwiches per day, of the number of sandwiches the restaurant sold on February 7 to the number of sandwiches the restaurant sold on February 11 is equal to b. The number b is p% greater than the number a. What is the value of p, rounded to the nearest hundredth?

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Question 3 :

The function f is defined by f(x) = ax² + bx + c, where a, b, and c are constants and 2 < b < 5. The graph of y = f(x) in the xy-plane is a parabola where f(–12) = f(7). If b is an integer, what could be the value of b – a?

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Question 4 :

The value of a video game console increased by 285% from the end of 2015 to the end of 2016. The value of the console then decreased by 21% from the end of 2016 to the end of 2017. Finally, the value of the console increased by 63% from the end of 2017 to the end of 2018. What was the net percentage increase in the value of the video game console from the end of 2015 to the end of 2018?(Round to the nearest hundredth of a percent)

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Question 5 :

The functions f and g are defined by the given equations, where 2 ≤ x ≤ 8. Which of the following equations displays, as a constant or coefficient, the minimum value of the function it defines, where 2 ≤ x ≤ 8?

I. f(x) = 0.0625(0.5)(2)^x^{+ 2}

II. g(x) = 1500(0.2)^x^{- 3}

A) I only

B) II only

C) I and II

D) Neither I nor II

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Question 6 :

On data set of 26 integers is summarized in the histogram shown. For the histogram, the first interval represents the frequency of integers greater than or equal to 70, but less than 75. The second interval represents the frequency of integers greater than or equal to 75, but less than 80, and so on. What is the largest possible value of the median?

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Question 7 :

–2x² + 8x – b/a = 0

In the equation above, a, b, and c are positive constants. The product of the solutions to the given equation is 5/7. The number b is 64% less than the number c. The number a is p% less than the number c. What is the value of p?

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Question 8 :

A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object is launched off an elevated surface. The model indicates the object hits the ground 16 seconds after being launched; the object reaches its maximum height of 1,296 feet above the ground 7 seconds after being launched. Based on the model, at what time after the object is launched, in seconds, does the object first reach a height of 972 feet?

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Question 9 :

A 30-60-90 triangle has a perimeter of 18 + 6√3 inches. What is the triangle’s area, in square inches? Round your answer to the nearest hundredth of a square inch.

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Question 10 :

A circle in the xy-plane has the equation (x + 3)² + (y – 8)² = 25. Line k is tangent to the circle (1, 5). The equation for line k is represented by the linear function, k(x). For what value of x, does k(x) = 2?