Tip #31 to Get a Top ACT Math Score

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."

N^4/3 =                   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.

2p^2/3 = m

Correct answer: B

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