ACT MATH FORMULA REVIEW · 2019. 10. 15. · ACT MATH FORMULA REVIEW Ellipses: # of diagonals =...
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ACT MATH FORMULA REVIEW Ellipses: # of diagonals = ½*N(N-3) Sum of angles in a regular polygon with n sides: 180 (n-2) Pythagorean Theory: 2 + 2 = 2 3, 4, 5 5, 12, 13 6, 8, 10 7, 24, 25 8, 15, 17 Averages Roots, Powers and Exponents Prime numbers First ten primes: 2,3,5,7,11,13,17,19,23,29 Perfect squares Commonly used on the ACT: 11 2 =121; 12 2 =144; 13 2 =169; 14 2 =196; 15 2 =225; 16 2 =256; 25 2 =625 Irrational numbers Cannot be written as a ratio of two integers: Examples π, √2, √3, etc. Imaginary Numbers When squared, gives a negative result ∗ = −1 = √−1 √(−) = √ 1 = ; 2 = −1; 3 = − ; 4 =1; 5 = 1 Mean: Average ǁ Median: Middle number Mode: Most frequent number Weighted average: Add the values for each occurrence; divide by total occurrences. CYLINDER: Area: πr 2 + πr 2 + h*2πr Volume: 2 ∗ℎ A 0 = 1 A 1 = A √ = √ √ √ = √ √ A m A n = A m+n ( ) = = − − = 1 = √ log a a x =x (log 2 8 = log 2 2 3 = 3) log a (xy) = log a x + log a y log a ( x y ) = log a x − log a y Quadratic Formula 2 + + = 0 = −±√ 2 −4 2 Distance Time Formula Speed (v) = () () v = CIRCLE Area = 2 Perimeter = 2 Formula: x 2 + y 2 = r 2 (x-a) 2 + (y-b) 2 = r 2 Midpoint = (a,b); radius = r For interactive formulas visit www.myclass101.com Equilateral triangle: Volume: Cube: V = s 3 Cone: V = 1/3 πr 2 h Pyramid: V = 1/3 lwh Sphere: V= 4/3 π r 3 TRIGONOMETRY: SOH-CAH-TOA Sin ʘ = Csc ʘ = = 1 Cos ʘ = Sec ʘ = = 1 Tan ʘ = Cot ʘ = = 1 Triangles ʘ = ʘ ʘ Isosceles triangle ≅ Congruent (shape and size) ~ Similar (shape) Area of a trapezoid: Half-point line: (A+B)/2 * h Area of a parallelogram: L*H Linear Equations = + y intercept is b (x=0) X intercept is + = 0 (y=0) = − The slope is = = 2 − 1 2 − 1 A line with a perpendicular slope has an opposite reciprocal of m: − 1 Distance Formula = √( 2 − 1 ) 2 + ( 2 − 1 ) 2 Midpoint Formula ( 1 + 2 2 , 1 + 2 2 )
Transcript of ACT MATH FORMULA REVIEW · 2019. 10. 15. · ACT MATH FORMULA REVIEW Ellipses: # of diagonals =...
ACT MATH FORMULA REVIEW
Ellipses:
# of diagonals
= ½*N(N-3)
Sum of angles in a regular
polygon with n sides:
180 (n-2)
Pythagorean
Theory:
𝑎2 + 𝑏2 = 𝑐2
3, 4, 5
5, 12, 13
6, 8, 10
7, 24, 25
8, 15, 17
Averages
Roots, Powers and Exponents
Prime numbers First ten primes: 2,3,5,7,11,13,17,19,23,29
Perfect squares
Commonly used on the ACT:
112=121; 122=144; 132=169;
142=196; 152=225; 162=256; 252=625
Irrational numbers
Cannot be written as a ratio of
two integers: Examples π, √2, √3, etc.
Imaginary Numbers
When squared, gives a negative result
𝑖 ∗ 𝑖 = −1 𝑖 = √−1 √(−𝑥) = 𝑖√𝑥
𝑖1 = 𝑖; 𝑖2 = −1; 𝑖3 = −𝑖 ; 𝑖4 = 1; 𝑖5 = 𝑖1
Mean: Average ǁ Median: Middle number
Mode: Most frequent number
Weighted average: Add
the values for each
occurrence; divide
by total occurrences.
CYLINDER:
Area: πr2 + πr2 + h*2πr
Volume: 𝜋𝑟2 ∗ ℎ
A0 = 1
A1 = A
√𝑎
𝑏=
√𝑎
√𝑏
√𝑎𝑏 = √𝑎√𝑏
AmAn = Am+n
(𝐴𝑚)𝑛 = 𝐴𝑚𝑛
𝐴𝑚
𝐴𝑛= 𝐴𝑚−𝑛
𝐴−𝑚 = 1
𝐴𝑚
𝐴𝑚𝑛 = √𝐴𝑚𝑛
logaax = x (log28 = log223 = 3)
loga(xy) = logax + logay
loga (x
y) = logax − logay
Quadratic Formula
𝐴𝑥2 + 𝑏𝑥 + 𝑐 = 0
𝑥 = −𝑏±√𝑏2−4𝑎𝑐
2𝑎
Distance Time Formula
Speed (v) = 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑑)
𝑇𝑖𝑚𝑒 (𝑡) v =
𝑑
𝑡
CIRCLE Area = 𝜋𝑟2 Perimeter = 2𝜋𝑟
Formula: x2 + y2 = r2
(x-a)2 + (y-b)2 = r2
Midpoint = (a,b); radius = r
For interactive formulas visit www.myclass101.com
Equilateral
triangle:
Volume: Cube: V = s3 Cone: V = 1/3 πr2 h
Pyramid: V = 1/3 lwh Sphere: V= 4/3 π r3
TRIGONOMETRY: SOH-CAH-TOA
Sin ʘ = 𝑂𝑝𝑝
𝐻𝑦𝑝 Csc ʘ =
𝐻𝑦𝑝
𝑂𝑝𝑝=
1
𝑆𝑖𝑛
Cos ʘ = 𝐴𝑑𝑗
𝐻𝑦𝑝 Sec ʘ =
𝐻𝑦𝑝
𝐴𝑑𝑗=
1
𝐶𝑜𝑠
Tan ʘ = 𝑂𝑝𝑝
𝐴𝑑𝑗 Cot ʘ =
𝐴𝑑𝑗
𝑂𝑝𝑝=
1
𝑇𝑎𝑛
Triangles
𝑡𝑎𝑛ʘ =𝑠𝑖𝑛ʘ
𝑐𝑜𝑠ʘ
Isosceles triangle
≅ Congruent (shape and size)
~ Similar (shape)
Area of a trapezoid: Half-point line: (A+B)/2 * h
Area of a parallelogram: L*H
Linear Equations 𝑦 = 𝑚𝑥 + 𝑏
y intercept is b (x=0)
X intercept is 𝑚𝑥 + 𝑏 = 0 (y=0) = −𝑏
𝑚
The slope is 𝑚 =𝑟𝑖𝑠𝑒
𝑟𝑢𝑛=
𝑦2−𝑦1
𝑥2−𝑥1
A line with a perpendicular slope has an
opposite reciprocal of m: −1
𝑚
Distance Formula 𝑑 = √(𝑥2 − 𝑥1)2 + (𝑦2 − 𝑦1)2
Midpoint Formula (𝑥1+𝑥2
2,
𝑦1+𝑦2
2)
ACT MATH FORMULA REVIEW
Ellipses
# of diagonals
= _______
Averages
Roots, Powers and Exponents
Prime numbers First ten primes: _______________
Perfect squares
Commonly used on the ACT:
112=____; 122=____; 132=____;
142= ___; 152=____; 162=____; 252=___
Irrational numbers
Definition: _____________________
Examples: _____________________
Imaginary Number,
Definition: ___________ _________
𝑖1 =___; 𝑖2 = ___; 𝑖3 = ___; 𝑖4 =___
Mean: __________
Median: __________
Mode: __________
Weighted average: _____________
Triangles
A0 = ___
A1 = ___
√𝑎
𝑏= ___
√𝑎𝑏 = ___
AmAn = ___
(𝐴𝑚)𝑛 = ___ 𝐴𝑚
𝐴𝑛 = ___
𝐴−𝑚 = ___
𝐴𝑚
𝑛 = ___
logaax = ___ loga(xy) = ___
loga (x
y) = ___
Quadratic Formula 𝐴𝑥2 + 𝑏𝑥 + 𝑐 = 0
𝑥 =
Distance-Time Formula
D = ___*___ T= ?
?
t
Linear Equations
𝒚 = 𝒎𝒙 + 𝒃
y intercept is ______
X intercept is ______
The slope 𝑚 =?
? ______
The line with a perpendicular slope
has a slope of ______
Distance Formula 𝑑 = _______________
Midpoint Formula ___________
CIRCLE:
Area
= _______
Perimeter
= ______
Formula:
(___) (___) = __
Midpoint = __ , __
CYLINDER:
Area: ________
Volume: ________
Isosceles triangle
For interactive formulas visit www.myclass101.com
Equilateral triangle
TRIGONOMETRY:
Sin ʘ = _c_ /_b_
Sec ʘ= __ /__
Cos ʘ= __ /__
Cot ʘ= __ /__
Csc ʘ= __ /__
Tan ʘ = __ /__
Area of a trapezoid:
______________
Sum of angles in a
regular polygon with n sides:
_____
Volume: Cube: V = Cone: V =
Pyramid: V = Sphere: V=
° °
𝑡𝑎𝑛ʘ =____ʘ
____ʘ
≅ ________
~ ________
Area of a parallelogram:
_____
L*H
Pythagorean Theory:
Formula: __________
Examples:
3, ___ , ___
5, ___ , ___
6, ___ , ___
7, ___ , ___
8, ___ , ___
