SAT Math Challenge Problems

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Problem 1 :

The scatterplot shows the relationship between two variables, x and y, for data set E. A line of best fit is shown. Data set F is created by multiplying the y-coordinate of each data point from data set E by 3.9. Which of the following could be an equation of a line of best fit for data set F?

A) y = 46.8 + 5.9x

B) y = 46.8 + 1.5x

C) y = 12 + 5.9x

D) y = 12 + 1.5x

Solution :

Problem 2 :

48x - 64y = 48y + 24

ry = ⅛ - 12x

In the given system of equations, r is a constant. If the system has no solution, what is the value of r ?

Solution :

Problem 3 :

The function f is defined by f(x) = |x - 4x|. What value of a satisfies f(5) - f(a) = -15?

A) -20

B) 5

C) 10

D) 45

Solution :

Problem 4 :

The given equations relates the variables n, t and w, where n > 0, t > 0 and w > t. Which expression is equivalent to n?

Solution :

Problem 5 :

(x - 40)(x + 32) = p

In the equatio0n above, p is a positive constant such that the quadratic equation has two irrational solutions of the form n + √s and n - √s. Determine the value of n.

Solution :

Problem 6 :

The table shows three values of x and their corresponding values of y, where s is a constant. There is a linear relationship between x and y. Which of the following equations represents this relationship?

A) sx + 3y = 18s

B) 3x + sy = 18s

C) 3x + sy = 18

D) sx + 3y = 18

Solution :

Problem 7 :

2x² - 8x - 7 = 0

One solution to the given equation can be written as

where k is a constant. What is the value of k?

Solution :

Problem 8 :

A line intersects two parallel lines, forming four acute angles and four obtuse angles. The measure of one of the acute angles is (9x - 560)°. The sum of the measures of one of the acute angles and three of the obtuse angles is (-18x + w)°. What is the value of w?

Solution :

Problem 9 :

In triangle XYZ, angle Y is a right angle, point P lies on XZ, and point Q lies on YZ such that PQ is parallel to XY. If the measure of angle XZY is 63°, what is the measure, in degrees, of angle XPQ?

Solution :

Problem 10 :

h(t) = -16t² + b

The function h estimates an object’s height, in feet, above the ground t seconds after the object is dropped, where b is a constant. The function estimates that the object is 3,364 feet above the ground when it is dropped at t = 0. Approximately how many seconds after being dropped does the function estimate the object will hit the ground?

A) 7.25

B) 14.50

C) 105.13

D) 210.25

Solution :

Question 11 :

A 180 gram metal alloy is 50% aluminum. It contains a metal alloy that is 30% aluminum and a second metal alloy made up of 60% aluminum. What is the mass of the second metal alloy?

Answer :

Question 12 :

In the given figure, the hypotenuse is 64. What is the cos x?

A) √3/2

B) 1/2

C) 2√3/3

D) 2

Answer :

Question 13 :

The table shows the distribution of 88 basketball players and their positions on a basketball club. Each player is categorized in one position.

If one of the 88 players is selected at random, the probability of selecting a player who is categorized as a power forward, given the player is not categorized as a shooting guard, is 3/12. How many of these players are categorized as a center?

Answer :

Question 14 :

A rectangular pyramid has a square base with an area of 324 square meters. What is the surface area, in square meters, of one of the triangular faces if the rectangular pyramid has a volume of 4,320 cubic meters?

Answer :

Question 15 :

n^5/3 = k^2/5 and n^{4a + 1} = k, what is the value of a?

Answer :

Question 16 :

A quadratic function models the height, in feet, of an object above the ground in terms of time, in seconds, after the object is launched off an elevated surface. The model indicates that at a time of 9 seconds, the object is 294 feet above the ground. At a time of 13 seconds, the object is 310 feet above the ground. If the object was at a height of 24 feet when it was launched, what is the height, in feet, of the object above ground 18 seconds after being launched?

A) 96

B) 192

C) 222

D) 240

Answer :

Question 17 :

3x² + bx – 112 = (ax + m)(x – ℓ). Given that a, m and ℓ are integers, which of the following must be true?

A) m is a factor of b

B) a is a factor of 112

C) a is a factor of b

D) ℓ is a factor of 112

Answer :

Question 18 :

The perimeter of a right isosceles triangle is 76 + 76√2. What is the length of the hypotenuse?

Answer :

Question 19 :

The results of two random samples of votes for a proposition are given in the table. The samples were selected from the same population, and the margins of error were calculated using the same method. Which of the following is the most appropriate reason that the margin of error for sample A is greater than the margin of error for sample B?

A) Sample A had a larger sample size.

B) Sample A had a smaller sample size.

C) Sample A had a smaller number of votes that could not be recorded.

D) Sample A had a lower percent of favorable responses.

Answer :