ACT Math: Five Problems for Your Weekend (3/6/15)

Your ACT Math score can only get better with practice. Getting the score you want takes time and effort on your part, but hard work is usually rewarded on test day. Here are five problems similar to what you’ll encounter on the ACT. I hope you have a few minutes this weekend to find a quiet place and give them a try.

The numbering of the problems is meant to give you an idea of where in a section a problem might appear.

Answers appear at the end of the post. Full solutions can be found here.

11. The product of two numbers x and y is added to 8 and the result is 44.  Which of the following could NOT be values for x and y.

A.  x = 1 and y = 36
B.  x = 4 and y = 8
C.  x = 6 and y = 6
D.  x = 9 and y = 4
E.  x = 18 and y = 2

26. If | x – 4 | = 5, then x = ?

F.  1 only
G.  9 only
H.  {1, 9}
J.  {- 1, 9}
K.  {-4, 5}

35. In an arithmetic sequence, each term after the first term is found by adding the same number to the preceding term. In an arithmetic sequence, the third term is 18 and the sixth term is 39. What is the first term?

A.  4
B.  7
C.  11
D.  14
E.  25

44.  In the figure below, segment CB is tangent to the circle at point B and has a length of 10 units.  The circle has its center at point A. If the perimeter of rectangle ABCD is 28, what is the area, in square units, of the shaded region?

Five Problems 3-6-4

F.  2π
G.  4π
H.  8π
J.  10π
K.  16π

53. The x-axis and y-axis together divide the standard xy-coordinate plane into four quadrants as shown in the diagram below. If the circle represented by the equation (x + 4)² + (y  + 2)² = 9 is graphed in the standard xy-coordinate plane, in what quadrant(s) will the circle lie?

Problem 5-3

A.  I only
B.  II only
C.  III only
D.  I and IV
E.  II and III

If you have questions about these problems or anything else to do with the ACT, leave a comment below or send me an email at info@cardinalec.com.

Solutions:

11. B
26. J
35. A
44. G
53. E

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