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Students : Grade 11 and 12 
Math Review for
ACT
College Entrance Exam
Part I  The Review
by
Elaine
Ernst Schneider
February
4, 2001
AMAZON PRODUCTS

1. If x + 6 = 9, then 3x + 1 = ? Answer choices: (A) 3 (B) 9 (C) 10 (D) 34 (E) 46 Let’s think it
through.
Choice A is to tempt you into a quick (wrong) decision. When you solve
for x in the first equation (x + 6 = 9) you get 3, which is choice A.
Substitute 3
for the x
in the 2nd equation. 3x + 1 = ?. Therefore, 2. If x > 1, which of the following decreases as x decreases? I. x + x²
II.
2x² – x
III.
__1__ Answer choices: (F) I only (G) II only (H) III only (J) I & II only (K) II & III The easiest way to solve this problem is to work from the answers, eliminating the wrong answers. Substitute a simple number you can work with quickly.
I. x + x² (substitute 2 for x)
x + x² (substitute 3 for x) We know that I does what the question asks. We can see that x decreases as the equation decreases. However, the choices give us the possibility of I & II, so we must check out II as well.
II. 2 x² – x (substitute 2 for x)
2 x² – x (substitute 3 for x) Again, this does what the questions asks. We can see that x decreases when x is decreased.
The correct answer is J: I & II only 3. Barney can mow the lawn in 5 hours, and Fred can mow the lawn in 4 hours. How long will it take them to mow the lawn together? (A) 1 hour (B) 2 2/9 hour (C) 4 hours (D) 4 ½ hours (E) 5 hours We must set up a formula that determines both Barney and Fred’s work for one hour. From this, we can then determine their work potential together. The formula for this problem would be set up as follows: 1/5 (Barney working 1 hour) + ¼ (Fred working 1 hour) = 1/x (Both working 1 hour)
Find a common
denominator: 9/20 = 1/x 9x = 20 x = 2 2/9 Even if you
weren’t able
to figure out the appropriate formula, common sense would help you
eliminate
some of the answers. For example, if Fred can mow the lawn in 4 hours
by
himself, he would need less than 4 hours if someone helped him. That
makes
choices C, D, and E ridiculous. If Barney worked as quickly as Fred (4
hours) then together, it would take half as long, or 2 hours. But we
know 4. If a mixture is 3/7 alcohol by volume and 4/7 water by volume, what is the ratio of the volume of alcohol to the volume of water? Answer choices: (F) 3/7 (G) 4/7 (H) ¾ (J) 4/3 (K) 7/4 A ratio is read aloud as “is to” something “as” something “is to” something else. When you see “as” or “is to,” it tells you to draw the line for the fraction. For example, 3 “is to” 7 means 3/7. So, let’s set up our equation, substituting math symbols for the words “as” and “is to.” 3 is to 7 = 3/7
To solve this problem, divide 3/7 by 4/7. To divide
fractions, you
must “flip” the second fraction and multiply. 5. What is the maximum number of pieces of birthday cake size 4” X 4” that can be cut from a cake 20” X 20”? Answer choices: (A) 5 (B) 10 (C) 16 (D) 20 (E) 25 Sketch this diagram in the margin of your test booklet. (Write in your test booklet, but NOT on your answer sheet.) Five pieces of cake (each one 4”) will fit down each side. Therefore 5 X 5 = 25. The answer is 25, E.
6. In the triangle given, AD is an angle bisector. <DAC is 30 degrees and angle ABC is a right angle. Find the measure of angle x. Answer choices:
The definition
of a bisector
is that it divides an angle evenly in half. Therefore, if <DAC is 30
degrees, then <BAD must be 30 degrees. <ABC is a right triangle.
Right triangles measure 90 degrees. There are 180 degrees in a
triangle. 7. Estimate the value for:
Estimate your answer to the nearest tenth. Answer choices: (A) .5 (B) 4.63 (C) 4.9 (D) 7.7 (E) 49.1 You don’t want to take the time to work this out. Besides, the problems clearly indicates that the desired answer is an estimation. Round up and
approximate:
8. Find the counting number that is less than 15 and when divided by 3, has a remainder of 1, and when divided by 4, has a remainder of 2. Answer choices: (F) 5 (G) 8 (H) 10 (J) 12 (K) 13 Once again, the most expeditious way to work this problem is from the answers. Plug the different numbers in and see what works and what doesn’t. Answer F is 5.
Let’s try
it. When you divide 5 by 3, you get 1 with the remainder of 2, not 1;
so
F isn’t the answer. Answer G is 8. When you divide 8 by 3, you get 2
with
a remainder of 2; so G isn’t the answer either. Answer H is 10. 10
divided
by three is 3 with 1 as the remainder. This is the answer.
Part 2 is available for sale through the Shop@LT : See Math Review for SAT/ACT College Entrance Exams; Sample Test and Answers 

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