Tip #31 to Get a Top ACT Math Score

Example Problems

Easy

1. What is the sum of 2x² and 2x³ ?
   1. 4x⁵
   2. 2x⁶
   3. 2x² + 2x³
   4. 2x⁴ + 2x⁴
   5. (2x²)(2x³)

Medium

2. The product of 3m^–2 and 2m^–5 is

Hard

3. For positive real numbers a, b, and c, which of the following expressions is equivalent to a^2/3b^1/6c^1/2 ?



4. If , then x = ?
   6. 2
   7. 1
   8. 0
   10. –1
   11. –2

Answers

1. C 2x² and 2x³ are not like terms and do not combine. To combine, the variable (x) and the exponents would have to match.
2. F To multiply 3m^–2 by 2m^–5, we add the exponents, so (3m^–2)(2m^–5) = 6m^–7 =
3. E Get the common denominator for the fraction exponents, which is 6, and then the top of each converted fraction is the exponent in the answer. If that gave you a headache, just "Make It Real." Convert fractions to decimals (a^2/3b^1/6c^1/2 = a^0.666b^0.1666c^0.5), and then choose numbers for a, b, and c, such as a = 3, b = 4, and c = 5. Get an answer, and see which answer choice gives the same answer. (3)^0.666(4)^0.1666(5)^0.5 = 5.855. Choice E is correct, since "Make It Real" makes "hard" questions easy!
4. K There is the long "math class" way to do this "hard" question, and there is the flawless crazy-easy "Use the Answers" way! First, translate fractions to decimals. Then just try each choice in the question and see which one makes the equation work. Choice K is correct, since

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