ACT Math Practice Test 4

Front

If 15% of n is 300, what is 22% of n?

Back

To find n, set up the equation: 0.15n = 300. Solving for n gives n = 2000. Then, 22% of n is 0.22 * 2000 = 440.

Front

The ratio of adults to girls to boys on a class field trip is 1:4:5. If there are 6 more boys than girls, how many adults are there?

Back

Let the number of girls be 4x and boys be 5x. Then, 5x = 4x + 6, solving gives x = 6. Therefore, adults = 1x = 6.

Front

Jane ran around the perimeter of a rectangular park with an area of 67,500 square feet. If the length is three times the width, how long did she run?

Back

Let width = w, then length = 3w. Area = lw = 3w^2 = 67500, so w^2 = 22500, w = 150. Perimeter = 2(l + w) = 2(450 + 150) = 1200 feet. Time = distance/speed = 1200/10 = 120 seconds.

Front

What is the equation of a line that is perpendicular to y = 1/3 x + 9 and includes the point (3, 4)?

Back

The slope of the given line is 1/3, so the perpendicular slope is -3. Using point-slope form: y - 4 = -3(x - 3) gives y = -3x + 13.

Front

If pq = 3, what is p^3q^4 + p^4q^5?

Back

Factor out q: p^3q^4 + p^4q^5 = pq^4(p^2 + pq) = 3q^4(3) = 108q.

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the Pythagorean theorem?

Back

In a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse.

Front

What is the formula for the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Front

What is the quadratic formula?

Back

For ax^2 + bx + c = 0, the solutions are x = (-b ± √(b^2 - 4ac)) / (2a).