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FUNCTIONS

PEMDAS

Parentheses first, then Exponents, then Multiplication and Division (leftto right), and lastly Addition and Subtraction (left to right).

Median and Mode

The median is thevalue that falls in the middle of the set.

The mode is thevalue that appears most often.

Counting the Possibilities

If there aremways one event can happen andnways a second eventcan happen, then there arem nways for the 2 events to happen.

ESSENTIAL FORMULAS

Average Rate Formula Average Formula

Average A per B = Average =

Average Speed = Probability Formula

Probability =

Percent Formula

Part = Percent Whole

Multiplying and Dividing Powers

To multiply powers with the same base, add the exponents and keep thesame base.

To divide powers with the same base, subtract the exponents and keepthe same base.

Raising Powers to Powers

To raise a power to a power, multiply the exponents.

Negative Exponent and Rational Exponent

xn = x = nx

Direct and Inverse Variation

In direct variation,y=kx, wherek is a nonzero constant. Ininverse variation,xy=k, wherek is a constant.

Domain and Range of a Function

The domain of a function is the set of values for which thefunction is defined.

Determining Absolute Value

The absolute value of a number is the distance of the number from zeroon the number line.

Multiplying BinomialsFOIL

To multiply binomials, use FOIL. First multiply the First terms. Next theOuter terms. Then the Inner terms. And finally the Last terms. Then addand combine like terms.

Factoring the Difference of Squares

a2 b2 = (a b)(a +b)

Factoring the Square of a Binomial

a2 + 2ab +b2 = (a +b)2 a2 2ab +b2 = (a b)2

Quadratic Equation

ax2 +bx+ c= 0

Solving an Inequality

When you multiply or divide both sides by a negative number, youmust reverse the sign.

Finding the Distance Between Two Points

d= (x1

x2)2 +

(y1

y2)2

Using Two Points to Find the Slope

Slope = =

Using an Equation to Find the Slope (slope-intercept)

y = mx + b

Finding the Midpoint

If the endpoints are (x1,y1) and (x2,y2), the midpoint is.

,

Intersecting LinesWhen two lines intersect, adjacent angles are supplementary andvertical angles are equal.

(y1 +y2)

2

(x1 +x2)

2

1

xn

Sum of the terms

Number of terms

Change iny

Change inxRise

Run

Favorable Outcomes

Total Possible Outcomes

TotalA

Total B

1

n

Total distance

Total time

GEOMETRY

Interior and Exterior Angles ofa Triangle

The 3 angles of any triangle addup to 180 degrees.The 3 exterior angles of a triangleadd up to 360 degrees.

Area of a Triangle

Area of Triangle = (base)(height)

Pythagorean Theorem

For all right triangles: (leg1)2 +

(leg2)2 = (hypotenuse)2

Special Right Triangles

The 3-4-5 TriangleThe 30-60-90 TriangleThe 5-12-13 TriangleThe 45-45-90 Triangle

Area of a Rectangle

Area of Rectangle = length width

Area of a Parallelogram

Area of Parallelogram =base height

Area of a Square

Area of Square = (Side)2

Interior Angles of a Polygon

The sum of the measures of the

interior angles of a polygon =(n 2) 180, wheren is thenumber of sides.

Circumference of a Circle

Circumference = 2r

Length of an Arc

Ifn is the degree measure ofthe arcs central angle, then theformula is:

Length of an Arc = 1 (2r)

Area of a Circle

Area of a Circle = r2

Area of a Sector

Ifn is the degree measure of thesectors central angle, then theformula is:

Area of a Sector = 1 (r)2

Surface Area of a Rectangular

SolidSurface Area = 2lw+ 2wh + 2lh

Volume of a Rectangular Solid

Volume of a Rectangular Solid =lwhVolume of a Cube = 3

Volume of a Cylinder

Volume of a Cylinder = r2h

n

360

n

360

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ACT Math SkillsBASIC OPERATIONS | ESSENTIAL FORMULAS | FUNCTIONS | GEOMETRY

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Kaplans 3-Step Method for ACT EnglishStep 1: Does It Belong Here?

Step 2: Does It Make Sense?

Step 3: Does It Sound Like English?

Kaplans 3-Step Method for ACT MathStep 1: Understand

Step 2: Analyze

Step 3: Select

Kaplans Special Math StrategiesBacksolve

Pick Numbers

Guesstimate

Eyeball

Kaplans 5-Step Method for ACT ReadingStep 1: Preread the Passage

Step 2: Consider the Question StemStep 3: Refer to the Passage

Step 4: Answer the Question in Your OwnWords

Step 5: Match Your Answer With One of theChoices

Kaplans Special Reading Strategies forProse Fiction

Who Are the Characters?

What Is Their State of Mind?

Whats Happening on the Surface? Whats

Happening Under the Surface?

Kaplans 5-Step Method for ACT ScienceStep 1: Preread the Passage

Step 2: Consider the Question Stem

Step 3: Refer to the Passage

Step 4: Answer the Question in Your OwnWords

Step 5: Match Your Answer With One of theChoices

Kaplans Special Strategies for Reading

Tables and GraphsDetermine Whats Being Represented

Determine What the Axes (or Columns andRows) Represent

Take Note of Units of Measurement

Look for Trends in the Data

Kaplans 3-Step Method for ExperimentQuestions

Step 1: Find Whats Being Varied

Step 2: Identify the Control Group

Step 3: Analyze the Results

ACT SkillsKAPLANS PROVEN METHODS | MOST-TESTED GRAMMAR ERRORS

19 Most-Tested Grammar Errors

1. Singular nouns must match with singular verbs and pronouns, and pluralnouns must go with plural verbs and pronouns.

2. Know the rules for compound subjectsie, when to use I versus when touse me.

3. Parenthetical phrases must begin and end with the same punctuation mark.

4. Dont combine two sentences into one with a comma; instead, use a semi-colon or a conjunction.

5. Avoid sentence fragments.

6. Know your punctuation marks as well as their basic usage and meaning.

7. Nouns and pronouns must be modified by adjectives while verbs andadjectives themselves must be modified by adverbs.

8. Dont confuse the wordsgoodand well. Goodis an adjective; wellis anadverb.

9. Understand how to use the wordslayandlie, as well as their past tenses(which includelaid,lay, andlain).

10. Whenever you see a preposition, make sure it makes sense and that itmatches the other words in the sentence.

11. Know when to use the word who and when to use whom.

12. Never use apostrophes to make a pronoun possessive. Also, know when touseits andits.

13. Be aware of the differences between the words there, their, and theyre.

14. Know how and when to properly use irregular forms of common verbs.Some, likesing andbring, have unusual forms that are commonly testedon the ACT.

15. Know the proper verb forms, especially for the verb to be.

16. Dont useing endings when they arent needed; rather, use them primari-ly to indicate repeated or continuous action.

17. Whenever you see the endingserorest, or the wordsmore ormost,make sure theyre used logically. Words witheror withmore should beused to compare only two things. If more than two things are involved, use

estormost.

18. Use the wordbetween only when there are two things involved. Whenthere are more than two things, or an unknown number of things, useamong.

19. Use the wordless only for uncountable things. When things can be count-ed, they are fewer. People are always countable, so use fewerwhen writingabout them.

Kaplans Special Strategies forConflicting Viewpoints Passages

Determine Each Scientists BasicTheory

Identify the Evidence Each ScientistGives

Kaplans 4-Step Method for ACTWriting

Step 1: Pause to Know the Prompt

Step 2: Plan

Step 3: Produce

Step 4: Proofread