PSAT Math Multiple-Choice Practice Test 53: Passport to Advanced Math Drill

The use of a calculator is not permitted.

1. A square piece of paper is folded in half n times. If L is the length of an edge, what is the area of the piece of paper after it is folded in half n times?

2. equals

3. Which of the following is equivalent to for x not equal to -2?

4. What relationship must exist between the constants a, b, and c for the equation ax 2 + bx + c = 0 to have only real solutions?

5. (3x3 - 2x2 + 5x + 7) - (x4 + x(x + 2)) = ?

6. How many solutions does the following equation have?

7. Out of all possible solutions (x, y) to the pair of equations below, what is the greatest possible product xy that can be obtained?

x(y + 2) - 3x - 4(y + 2) = -12
and
3x - 6 = 3y

8. Based on the graph of f(x) below, f(x) is divisible by which of the following expressions?

I. x - 4

II. x + 1

III. x + 3

9. What happens to the vertex (h, k) of y = x2 + 3 if the 3 is replaced by a 6 and if x is changed to (x - 5)?

10. If f (x) = g(x) + 4 and if , what is the value of f(10)?

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