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ACT Math
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Match
Gravity
Terms in this set (35)
Test Info
60 Minutes, Questions are ordered easy to difficult, TIP focus on first 50 q
Topics
Properties and real numbers, algebra, statistics, plane and coordinate geometry, trig, pre calc
General Strategies
1) Break it down- find goal and relevant info
2) Categorize the question to recall a strategy
3) Pick an approach (Backwards, forwards, or possibly switch gears)
Forwards Approach
Underline given, circle goal, categorize the question, pick a strategy, write out steps to solve, double check goal
Backwards Approach v1
Use the answers to solve the question, plug in answer choice if given equation or expression or numerical answer (start with middle value)
Backwards Approach v2
Plug in own value for a variable in the question and answers, focus on relationships between values such as fractions, ratios and percents
Always plug easy numbers except 0,1,2
Estimation Tip
Estimate the answer by comparing what is given to values in answer choices,
Switching Gears
Do not keep working if stuck, change approach at any time if you are not getting closer to answer
Formulas for area
Triangle: A= (1/2)b*h
Rectangle: A= l*w
Square: A= l^2
Circle: (pi)r^2
Trapezoid: 1/2h (b1+b2)
Steps for Geo Forward Approach
After finds/givens start marking the figure:
1) identify vertical, alternate interior or linear angles
2) check to apply rule for isosceles triangle (opposite sides and angles = congruent)
3) use sum of angles or angle relationships (congruent or supplementary) to determine missing measurement
Alternate Interior Angles
Congruent
Corresponding Angles
Congruent
Consecutive Interior Angles
Supplementary (= 180)
Linear Angles
Supplementary
Vertical Angles
Congruent
Isosceles
A triangle with two sides that are equal (opposite angles are congruent)
Equilateral
all sides and angles are congruent
Sum of Angles
180 (n-2)
n=Number of sides
Logarithm
the power, y, to which a base was raised in order to produce a certain value, x
Slope Formula
Slope is Rise OVER Run
Rise = distance between y values
run
Midpoint Formula
Average of points divided by number of points
Trig Identities
Dividing Fractions
Same as multiplying by the inverse
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Asymptote
a line that a graph approaches but never crosses
Unit Circle
Sin= Y = 90
Cos= X = 0/360
Circumference
the perimeter of a circle
the sum of the arcs
Probability of Independent Events
Probability of events that can happen at any given time, in any order
P(A and B) = P(A) x P(B)
Probability of Dependent Events
Probability of events that can happen in SUCCESSIVE order only.
If A and B are dependent events, then the probability that both A and B occur is: P(A and B) = P(A)* P(B|A).
Probability of Mutually Exclusive Events
Probability of events that can happen, but never at the same time
P(A or B) = P(A) + P(B)
Probability of Inclusive Events
Probability of events that MAY, but do not necessarily have to, happen at the same time.
P(A or B) = P(A) + P(B) - P(A and B)
percent
A ratio that compares a number to 100, may be written as a decimal or fraction (ie. 5% means 5 of 100 => 5/100 = .05)
Permutations and Combinations
An arrangement, or listing, of objects in which order is important.
a grouping of items in which order does not matter
Equation of a Cirlce
(h,k) represents the center point
Equation of an Ellipse
(h,k) represents the center point
a = major axis
b = minor axis
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