PSAT Math Practice Test

Solve for \( x \): \( 3x + 7 = 22 \).

If \( 2x + 3 = 11 \), what is \( x \)?

Solve for \( x \): \( x^2 - 6x + 8 = 0 \).

Find \( x \) when \( 4x + 5 = 25 \).

Find the value of \( y \) when \( 2y + 10 = 30 \).

If \( 3x - 7 = 11 \), what is \( x \)?

Given that \( y = 3x + 2 \), find \( x \) when \( y = 11 \).

Solve for \( x \): \( x - 4 = 3 \).

Given that \( y = 2x - 1 \), what is \( x \) when \( y = 9 \)?

Solve for \( x \): \( x - 7 = -4 \).

What is the solution for \( x \): \( 5x - 2 = 18 \)?

If \( y = 4x + 1 \), what is \( x \) when \( y = 17 \)?

Find \( x \) when \( x - 5 = 3 \).

Given \( 2x + 8 = 24 \), what is \( x \)?

If \( 3x - 4 = 17 \), what is \( x \)?

Given \(f(x) = 3x^2 - 2x + 7\), what is the derivative of \(f(x)\) with respect to \(x\)?

If the sum of two numbers is 10 and their product is 21, what is the value of the smaller number?

What is the area of a circle with a circumference of 12??

The function \(g(x) = 2\log(x) + 3\). What is the value of \(g(100)\)?

A rectangle has a length of \(2x + 3\) and a width of \(x - 1\). If its perimeter is 34, what is \(x\)?

If \(x^2 - y^2 = 21\), what is the value of \(x - y\)?

If \(f(x) = x^3 - 3x^2 + 2x\), what is the value of \(f'(x)\) at \(x = 3\)?

A sphere has a volume of \(36\pi\). What is the radius of the sphere?

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

If \(a + b = 3\) and \(a^2 - b^2 = 7\), what is the product \(a \times b\)?

If \(f(x) = x^3 + 2x^2 - x\), what is the second derivative \(f''(x)\)?

If \(x^3 - x = k\), what is the value of \(x\) when \(k = 6\)?

A quadratic equation is given as \(ax^2 + bx + c = 0\). If \(a = 2\), \(b = -8\), and \(c = 6\), what is the larger solution \(x\)?

If the geometric series has the first term \(a_1 = 2\) and a common ratio \(r = 3\), what is the fourth term in the series?

If a graph has a linear trend with a slope of -3 and a y-intercept of 12, what is the x-coordinate when the y-coordinate is 0?

A test score has a mean of 80 with a standard deviation of 5. What is the score at the 95th percentile?

A bag contains 8 red, 6 blue, and 10 green marbles. If 2 marbles are drawn at random, what is the probability that both are red?

An investor buys a stock at USD 50 per share. It appreciates by 25 percent and then depreciates by 20 percent. What is the final price per share?

A graph shows a linear trend with a y-intercept of 7 and a slope of -5. At what x-coordinate does the graph cross the x-axis?

If the median of a dataset is 40 and the range is 30, what is the maximum value in the dataset if the minimum value is 25?

If the correlation coefficient between two variables is -0.75, what is the coefficient of determination?

In a linear relationship, if the x-intercept is -4 and the slope is 2, what is the y-intercept?

If the median of a dataset is 40 and the range is 30, what is the maximum value in the dataset if the minimum value is 25?

If the circumference of a circle is 31.4 units, what is the approximate diameter?

A triangle has sides measuring 7 units, 24 units, and 25 units. What type of triangle is this?

In a right triangle, one angle is 45 degrees. If the hypotenuse is 10 units, what is the length of each of the other two sides?

A regular hexagon has a side length of 6 units. What is the perimeter of the hexagon?

What is the area of a circle with a radius of 7 units?

An equilateral triangle has a side length of 12 units. What is the area of the triangle?