ACT Math Practice Test 35

For all a ≠ 0 and b ≠ 0, $\frac{a + b}{b(a + b) − 2a(a + b)}$ = ?

If tan x = ³⁄₄ and 0◦ ≤ x◦ ≤ 90◦, then cos x = ?

Which of the following represents the values of x that are solutions for the inequality (x − 1)(4 − x) < 0?

Let x = 3y − 4z + 7. What happens to the value of x if the value of y decreases by 2 and the value of z is increased by 1?

What is the smallest possible value for a where y = sin 2a reaches its maximum?

What are the solutions for the equation 3x²−5x+2 = 0?

Anne made apple jelly and applesauce out of a bushel of apples. If the number of jars of jelly, j, is 3 less than twice the number of jars of applesauce, a, which expression shows the relationship of jars of jelly, j, to the jars of applesauce, a?

If two lines in the standard (x,y) coordinate plane are perpendicular and the slope of one of the lines is −⁵⁄₇, what is the slope of the other line?

Three vertices of a rectangle in the standard (x,y) coordinate plane have the coordinates (−2,3), (4,3) and (4,2).
What are the coordinates of the fourth vertex?

A total of f men went on a fishing trip. Each of the r boats that were used to carry the fishermen could accommodate a maximum number of m passengers. If one boat had 5 open spots and the remaining boats were filled to capacity, which of the following expresses the relationship among f , r, and m?

If cos x = ⁵⁄₇ and tan x = ⁴⁄₅, what is sin x?

Which of the following intervals contains the solution to the equation x − 2 = $\frac{2x + 5}{3}$ ?

What values of x make the inequality −5x − 7 > 3x + 1 true?

José is building a scale model of a sailboat, complete with a main sail. The actual sailboat’s main sail measures 56 feet high with a base of 32 feet. If the model sailboat’s main sail has a base of 8 inches, how tall will the model’s main sail be, in inches?

A line in the standard (x,y) coordinate plane has a slope of ²⁄₃ and passes through points (3,4) and (t,−2). What is the value of t?