## Saturday, March 20, 2010

### IMPROVING ACT MATH, PART ONE

Let's face facts. Math is not the favorite subject for every student. The good news is that the ACT Math section is geared toward an average high school curriculum. If you've completed an Algebra II course, you have been exposed to all the knowledge necessary to achieve a 30 on the test. A Trigonometry course adds the possibility of even more points.

Concentrate on achieving a perfect score on the first 30 questions. You need to review a few elementary concepts, some lower level Algebra, and maybe a couple of concepts that are unexpected because they receive such little attention in school.

ELEMENTARY ISSUES
- fractions - What do yo need to add or subtract fractions? (a common denominator, then add or subtract the numerators) How do you multiply fractions? (multiply straight across the numerator and straight across the denominator) How do you divide by a fraction? (invert and multiply)
- percents - convert to decimals and, usually, multiply
- percent change - divide the amount of change by the original amount
- word problems - write an algebra sentence. "Of" means multiply. "Is" means equals. "And" means add. "Per" creates a fraction or ratio. I try to avoid mistakes with "less THAN" and "greater or more THAN" by putting them at the end of the expression from the start. (X is 3 less than Y) translates to
"X = Y - 3."
- ratios - Try naming the numerator and denominator so they don't get mixed up. If you're writing a proportion, be sure the numerators have the same label. Cross multiply only in proportions, otherwise multiply like fractions.
- average - (also called arithmetic mean or simply mean) add the items up and divide by the number of items.
- area - know the formulas for parallelogram, trapezoid, circle, and triangle. They will come up more than once. And while you're at it, know perimeter and circumference too.
- Pythagorean Theorem - "A squared plus B squared equals C squared" (aˆ2 + bˆ2 = cˆ2)

ALGEBRA BASICS
- distributive property -
a common mistake in distributing is losing a sign, especially from the negative terms.
- FOIL - (sometimes taught as "double distributive" because two distinct terms are distributed to those of the second binomial) First, Outer, Inner, Last. The most common error is from squaring a binomial -- (x + 3)ˆ2 -- does NOT equal (xˆ2 + 3ˆ2). (x+3)ˆ2 = (x+3)(x+3). FOIL.
- factoring - be prepared to factor out commons to make a problem easier; factor 4 terms by grouping; factor quadratics and cubics. Recognizing special situations like the difference of 2 perfect squares can save time in problem completion.
- distance formula - d = √[(X -x)ˆ2 + (Y -y)ˆ2]. Did you know that this is actually the Pythagorean Theorem?
- midpoint formula - call upon your outstanding knowledge of "average." The midpoint is (the average X, the average Y), so add 'um up and divide by 2.
- slope - Rise over Run -- ∆Y/∆X -- (Y - y)/(X -x) -- Up and Over (On Saturday morning, you've got to GET UP before you can GO OVER to a friend's house.) Common problems include mixing up the numerator and denominator and missing the importance of the slope's direction. Use your knowledge of positive and negative slope to eliminate misleading alternative answers.

THE UNEXPECTED
- probability - the number of successes divided by the possible outcomes (Success/Possibles). This number is never more than one.
- variation - I start by setting up an equation for either direct or inverse variation and then plugging in values, making this a substitution problem. Direct variation (Y varies directly with X) --
Y = kX. Inverse variation (Y varies inversely with X) -- Y =k/X.

A flawless first half of the Math section will provide a firm foundation for achieving a score well above average and you're ready to focus on the last 30 problems. More (higher level) Math concepts will be in the next post. For now, celebrate your Math Genius who just earned an A+.