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ACT American College Testing: Math Section Sample Questions:

1. For what positive real value of k , if any, is the determinant of the matrix

equal to k ? (Note: The determinant of matrix

equalsad - bc .)

A) 3
B) There is no such value of k.
C) 4
D)

E) 12

2. John took out a cash advance of x dollars from a financing company. The company deducts a fee of 1/4 of the original advanced amount along with a transfer fee of $25.
Which of the following represents the final advanced amount that John receives after all applied fees in dollars?

A) 3/4x - 25
B) 1/4 × (x - 25)
C) 1/4x - 25
D) 3/4 × (x - 25)

3. Marcus's favorite casserole recipe requires 3 eggs and makes 6 servings. Marcus will modify the recipe by using 5 eggs and increasing all other ingredients in the recipe proportionally.
What is the total number of servings the modified recipe will make?

A) 15
B) 6
C) 10
D) 8
E) 12

4. In the standard (x, y) coordinate plane, what is the midpoint of the line segment that has endpoints (3, 8) and (1, -4)?

A) (4, -12)
B) (11/2, -3/2)
C) (-2, -12)
D) (-1, -6)
E) (2, 2)

5. Given the following figure with one tangent and one secant drawn to the circle, what is the measure of

?

A) 60
B) 50
C) 85
D) 110
E) 25

Solutions: