Home->ACT Math

In the figure below, ABCD is a square. Points are connected on each pair of adjacent sides of ABCD to form 4 congruent right triangles, as shown below. Each of these triangles has one leg that is twice as long as the other leg. If the area of the shaded region is 25 square feet, what is the area of square ABCD in square feet?

(A)225

(B) 112.5

(C) 56.25

(D) 45

(E) 27

Which of the following values for a in the equation 3x + 3a - 5 = 5x - a causes the solution for x to be 6?

（A）-8.5 （B） -4.25 （C） 4.25 （D） 8.5 （E） 13.25

Correct Answer: C

What is the solution set for the inequality 6 - 4(x - 2) > 4x + 5?

（A）x < - （B） x < - （C） x < （D） x > - （E） x >

Correct Answer: C

The graphs of the equations y = –(x) + 1 and y = -(x + 1)² + 4 are shown in the standard (x,y) coordinate plane below. What real values of x, if any, satisfy the following inequality: –(x + 1)² + 4 > –(x) + 1?

（A）x < -3 and x > 1 （B） x < -2 and x > 1 （C） -3 < x < 1 （D） -2 < x < 1 （E） No real values

Correct Answer: D