SAT Math Problem Solving

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Problem 1 :

The frequency table above gives the distribution of heights, in inches, for a random sample of 56 male basketball players and 56 female basketball players. What is the positive difference between the median height (in inches) for male players and the median height (in inches) for female players?

Solution :

Problem 2 :

In the xy-plane, a parabola has vertex (–5, –12) and has no x-intercepts. If the equation of the parabola is written in the form y = ax² + bx + c, where a, b and c are constants, which of the following could be the value of a + b + c ?

A) –19

B) –12

C) –10

D) –5

Solution :

Problem 3 :

The scatterplot shows the relationship between two variables, x and y, for data set P. A line of best fit is shown. Data set Q is created by multiplying the y-coordinate of each data point from data set P by 4.3. The equation for the line of best fit for data set Q can be written in the form Q(x) = a + bx. What is the value of a – b?

Solution :

Problem 4 :

(3x – a)² = (2x + j)(jx – k)

The given equation has infinitely many solutions, where a, j and k are constants. What is the value of a?

Solution :

Problem 5 :

f(x) = –a^x + b

The function f is defined by the equation above, where a and b are constants. The graph of g(x) is formed by taking the graph of f(x) and translating it both 6 units in the negative x direction and 2 units in the negative y direction. The x-coordinate of the x-intercept for the graph of g(x) is –3 and g(-6) = 61/64 , what is the value of a?

Solution :

Problem 6 :

The function g is defined by g(x) = |x|/a – 14, where a < 0. What is the product of g(15a) and g(7a)?

Solution :

Problem 7 :

Point F lies on a unit circle in the xy-plane and has coordinates (1, 0). Point G is the center of the circle and has coordinates (0, 0). Point H also lies on the circle and has coordinates (-1, y), where y is a constant. Which of the following could be the positive measure of angle FGH, in radians?

A) 27π/2

B) 29π/2

C) 24π

D) 25π

Solution :

Problem 8 :

An equilateral triangle is inscribed in a circle with a radius of 8 inches. What is the area of the region that lies within the circle but outside the triangle, in square inches? Round your answer to the nearest tenth.

Solution :

Problem 9 :

In the given system of equations, a and b are positive constants. The system has no solution. If b is p% less than a, what is the value of p?

Solution :

Problem 10 :

The function f is defined by f(x) = ax² + bx + c, where a, b and c are constants. The graph of y = f(x) is a parabola where f(-11) = f(-1). If b is an integer less than -3, what is the greatest possible value of a + b?

Solution :

Problem 11 :

The function f is defined by f(x) = 78(0.39)^x. For any positive integer n, the value of f(n) is p% less than the value of f(n – 1). What is the value of p?

A) 78

B) 61

C) 39

D) 22

Solution :

Problem 12 :

For which value of a, does the quadratic equation (7x – 8)² + 9 = a have only one solution?

Solution :

Problem 13 :

What is the perimeter of an equilateral triangle with an area of 289√3?

Solution :

Problem 14 :

92x - 1,789 = kx - 1,790

In the given equation, k is a positive integer constant greater than 91. The equation has exactly one solution. What is the least possible value of k?

Solution :

Problem 15 :

f(x) = a^x - b

The exponential function given above passes through points (c, 12) and (2c, 768). What is a possible value of b?

Solution :

Problem 16 :

If r = ∛k, for the equation r¹²^a^{- 9} = k, what is the value of a for which r and k are equal?

Solution :

Problem 17 :

4x³ + bx² - 528x = 0

In the given equation, b is a positive integer constant. Which value could be a solution to the equation?

A) -13

B) -12

C) -6

D) 12

Solution :

Problem 18 :

Circle A has the equation (x - 18)² + y² = 27. Circle B has the equation (x - 18)² + (y - m)² = 50. If Circle B passes through the center of circle A, what is a possible value of m?