ACT Math: Five Problems from Your Weekend (2/13/15)

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 will be posted on Monday.

11.  Michael has $120 in his savings account and is planning to add $10 per week.  Sarah has $210 in her account and she is planning to withdraw $5 per week. If the amount in their two accounts is changed at these constant rates, in how many weeks will they have the same amount of money in their accounts?

A.  4
B.  5
C.  6
D.  8
E.  10

28.  You survey seven adults asking them how many countries they have visited.  The results appear in the table below. If the median number of countries is 8, then the number of countries Brendan has visited (represented by x in the table) can be any of the following EXCEPT what?

Five Problems 2-13-2

F.  6
G.  9
H.  11
J.  17
K.  25

39.  A circle has its center at Point P. One of its diameters has endpoints with coordinates (3, 6) and (11, 6) in the standard (xy) coordinate plane.  Which of the following must be true of the circle?

I.  Point P, the center of the circle, is at (7, 6)
II.  The radius of the circle is 4
III.  The circle intersects the x-axis in two places.

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

48.  A circle has its center at (7, 9) in the standard (xy) coordinate plane. One of the points on the circle is (13, 17). What is the area of the circle?

F.  10π
G.  14π
H.  25π
J.  100π
K.  200π

57.  An angle in the standard (xy) coordinate plane shown below has its vertex at the origin.  One side of this angle with a measure of θ passes through the point (12, -5), and the other side includes the positive x-axis.  What is the sine of θ?

Five Problems 2-13-5

A.  -12/13
B.  -5/13
C.  -5/12
D.  5/13
E.  12/13

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.  C
28.  F
39.  C
48.  J
57.  B

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