Post on 04-Feb-2018
7/21/2019 ACT Study Sheet
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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
7/21/2019 ACT Study Sheet
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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