PSAT Math Grid-Ins Practice Test 15

The use of a calculator is not permitted.

1. In a certain right triangle, the sine of angle A is and the cosine of angle A is .

What is the ratio of the smallest side of the triangle to the median side of the triangle?


In the isosceles trapezoid above, what is the measure of the smallest interior angle?

3. Given that (x, y) is a solution to the following system of equations, what is the sum of x and y?
2x – y = 3
4y = 6x

4. On a particular college campus, there are two men for every three women. If the total number of men and women on campus is equal to 4,000, how many more women are there on campus than men?

5. Given that x ≠ 0, find the value of

6. Solve for x in the equation below:

7. If f(x) = 7x + 3 and g(x) = 2x2, what is the value of f(g(1))?

8. Consider the following system of equations with variables A and B and constant integers X and Y:

a + 2b = 4
XA + YB = 4x

By what number must the sum of X and Y be divisible in order for the two equations to have infinitely many solutions?

9. If a circle has the equation (x - 4)2 + (y - 3)2 = 36, what is the shortest straight-line distance from the center of the circle to the origin?

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