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# Tip #31 to Get a Top ACT Math Score (page 2)

By McGraw-Hill Professional
Updated on Sep 7, 2011

I fear that I will always be

A lonely number like root three.

A three is all that's good and right,

Why must my three keep out of sight?

Beneath a vicious square root sign,

I wish instead I were a nine …

Kumar Patel, Harold & Kumar Escape from Guantanamo Bay (Warner Bros., 2008)

2n2 + n2 = 3n2               When adding with matching bases and matching exponents, add coefficients.

2n + n2                           Does not combine. When adding, they combine only if they have matching bases and matching coefficients.

n–2 =                     A negative exponent means "take the reciprocal."

N4/3 =                   For a fractional exponent, the top number is the power and the bottom number is the root.

Let's take a look at this question:

Solution: Great review of Skill 3. "What is m in terms of p" means "solve for m—use algebra to get m alone."

8m2p3 = m5p                     Divide both sides by p.

8m2p2 = m5                     Divide both sides by m2.

8p2 = m3                     Put both sides to the one-third exponent, since (m3)1/3 = m

(8p2)1/3 = m                     Distribute the exponent.

2p2/3 = m

### Easy

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

### Medium

1. The product of 3m–2 and 2m–5 is

### Hard

1. For positive real numbers a, b, and c, which of the following expressions is equivalent to a2/3b1/6c1/2 ?
2. If , then x = ?
1. 2
2. 1
3. 0
1. –1
2. –2

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 (a2/3b1/6c1/2 = a0.666b0.1666c0.5), 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

Go to: Tip #32