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ACT Math Test Prep
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Gravity
Key Concepts:
Terms in this set (43)
Area of Trapezoid
Volume of a Prism
V=(l)(h)(w)
Area of a Rectangle/Parallelogram
Area = bh
Equation of a Circle
Area and Circumference of a circle
A=πr^2
C=2πr
Length Of Arc
(n°/360°)x2πr
Area Of Sector
(n°/360°)xπr^2
Radians
π/180°
SOH (Sin)
Opposite/Hypotenuse
CAH (Cos)
Adjacent/Hypotenuse
TOA (Tan)
Opposite/Adjacent
...
sin2 θ + cos2 θ = 1.
Equilateral:
These triangles have three equal sides, and all three angles are 60◦.
Isosceles:
An isosceles triangle has two equal sides. The base angles
are equal
Similar:
Two or more triangles are similar if they have the same shape. The corresponding angles are equal, and the corresponding sides
are in proportion.
Area of a Triangle
A=(1/2)bh
Pythagorean Theorem
a^2 + b^2 = c^2
Special Right Triangles
30°-60°-90°
Special Right Triangles
45°-45°-90°
Slope of the line:
Mid-point of the segment
Distance Formula
Perpendicular lines
have negative reciprocal slopes: m1 · m2 = −1.
Parallel lines
Parallel lines have equal slopes.
Slope Intercept Form
Point Slope Form
complex number
i^0 = 1
i^1 = i
i^2 = −1
i^3 = −i
FOIL
(x+a)(x+b)=x^2 +(b+a)x+ab
Difference Of Squares
a^2 − b^2 = (a + b)(a − b)
SOAP
same
opposite
always positive
used to factor sum and difference of cubes:
a^2 +2ab+b^2 = (a+b)(a+b)
a^2 −2ab+b^2 = (a−b)(a−b)
Powers of Exponents
x^a · x^b = x^a+b
x^a/x^b = x^a−b
1/x^b = x^−b
(xy)^a =x^a·y^a
(x^a)^b =x^a·b
x^0 = 1
√xy = √x · √y
Probability Equation
number of desired outcomes / number of total outcomes
median
median = middle value in the list
Mode
mode = value in the list that appears most often
Average(Mean)
average = sum of terms/ number of terms
Average Speed
average speed = total distance/ total time
Factors
the factors of a number divide into that number
without a remainder
Multiples
the multiples of a number are divisible by that number without a remainder
Percent
Percent/100 x Part/Whole
Rationals
fractions, that is, anything expressable as a ratio of integers
Reals
integers plus rationals plus special numbers such as √2, √3 and π
Integers
..., -3, -2, -1, 0, 1, 2, 3, ...
Pythagorean Triples
3-4-5
5-12-13
7-24-35
(Including Multiples)
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