Math Flashcards
median
middle # of a series if odd, take average of two middle digits if even
mode
that appears the most
factors/GCF
71 = 2^3 x 3^3 - GCF between two #s is the repeated factors in each number
multiples/LCM
9, 18, 27, 36, etc. LCM = take factors of each number, multiple the greatest number of each factor
absolute value
can NEVER equal a negative number, |x-7| = both -5 and 5, if inequality, change sign AND -/+
Proportion
A C
- = -
B D
Special linear equations
X + 1 = consecutive integers
X + 2 = even/odd integers
Product property of exponents
X^m • x^n = x^m+n
Ex) (3m^5)(-4m^3) = -12m^8
Factoring polynomials
If c is negative, then signs will be different. If c is positive, then signs will be the same.
Factoring with prime numbers
Carry over, multiply, factor, divide, carry over
Arithmetic sequence formula
A(n) = a(1) + (n-1)d Where... A(n) is nth term A(1) is first term N is number of terms D is common difference
Arithmetic series formula
S(n) = n/2(a(1) + a(n)) Where... S(n) is sum of sequence N is number of terms A(1) is first term A(n) is nth term
Geometric sequence formula
A(n) = a(1) • r^(n-1)
Where…
R is common ratio
Geometric series formula
S(n) = [a(1)(1-r^n)]/1-r
Combinations
-order doesn't matter nCr = [n!]/[r!(n-r)!] Where... R is number you're selecting N is total number of choice Ex) 15 children in class, 5 needed for chores, possible combos -Calculator: 15, MATH, PRB, 3: nCr, 5
Permutations
-order does matter
nPr = [n!]/[(n-r)!]
-Ex) 10 horses running, possible combos for 1st, 2nd, and 3rd
Calculator: 2 instead of 3
Matrices
Multiply/divide/add/subtract with corresponding number
Quotient rule of exponents
X^m/x^n = x^(m-n)
Power rule of exponents
(x^m)^n = x^mn
Logarithmic functions
If b^x = y, then log(b)Y = x
Product property of logs
Log(b)MN = log(b) M + log(b) N
Quotient property of logs
Log(b) M/N = log(b) M - log(b) N
Power property of logs
Log(b) M^x = x • log(b) M
Change of base formula
Log(b) M = log(c) M / log(c) b
Discriminant
B^2 - 4ac
If 0, 1 real solution
If negative, non-real.
If positive, 2 real.
Parabola formula
Y=a(x-h)^2+k
Where…
(H,k) = vertex
A determines orientation and width
Circle equation
(X-h)^2 + (y-k)^2=r^2
(H,k) is center point
R is radius
Ellipse equation
[(x-h)^2]/a^2 + (y-k)^2/b^2 = 1
(H,k) center point equidistant from extremes on x and y
A is distance from center on x
B is distance from center on y
Hyperbola equation
Same for ellipse except minus sign
360 equals what in radians?
180?
90?
2pi
Pi
Pi/2
Complementary angles
Add up to 90
Supplementary angles
Add up to 180
Congruent triangles/similar triangles
Same/proportional
Area
1/2bh
How are triangles proportional?
Shortest side = shortest angle
Same length = sam angle
Longest side = longest angle
Triangular congruence
SAS
SSS
ASA
CPCTC - corresponding parts of triangles are congruent
45:45:90
1:1:square root of 2
Square root of 2 times side length
Isosceles: equal sides and…
Corresponding equal angles
30:60:90
1:square root of 3:2
Twice as long as shortest side
Equilateral triangle height
Square root of 3 • 1/2s
Sum of angles for triangles
For quadrilaterals
180/360
Parallelogram
Opposite angles are equal
Rhombus
All 4 sides are same length
Square
4 right angles and 4 congruent sides (rectangle, rhombus, and parallelogram)
Rectangle
4 right angles, parallelogram
Diagonal of square
S•square root of 2
Rhombus/parallelogram area
S times h
Area of trapezoid
1/2(b1 + b2)h
Diagonal for rectangle
Square root of l^2 + w^2
Chord
Line that connects two points on circumference
Sector
2 radii and arc
Area = pi • r^2 • angle/360
Arch length
Arc around sector
Pi • r • angle/180
Central angle
Angle between 2 radii
Arc measure same as central angle
Arc measure/2 = inscribed angle
Line tangent to circle = what angle
90
Volume of cylinder, cone, sphere, and pyramids
Cy: pi•r^2h
Co: 1/3•pi•r^2h
Sphere: 4/3•pi•r^3
Pyramids: 1/3bh
Linear equation
Y=mx+b
B is y intercept
M is slope
Perpendicular/parallel
-reciprocal/same
Graphing inequalities
= dashed line
Anything else solid
Midpoint formula
(X+x/2,y+y/2)
Slope
-\ +/
Y=2 (-)
X=2 (|)
Formula: y-y/x-x
Point slope and standard form
Y-y(1) = m(x-x(1))
Finding y intercept
Ax+By = C
Distance
Square root of (x(1)-x(2))^2 + [y(1)-y(2)]^2
VLT/HLT
If a vertical line intersects the graph twice, then it is not a function. If a horizontal line intersects the graph twice, then the inverse is not a function.
Rational and radical expression
Can be written as a fraction
Contains radicals/roots
Can only multiply radicals with same degree
Quadratic equations and parabolas
If parabola is completely above the line, no solutions
If parabola is on the x axis, one solution
If parabola crosses x axis with both arms, 2 solutions
Cosecant, secant, and cots gent
- Reciprocal of sin (h/o)
- Reciprocal of cos (h/a)
- Reciprocal of tan (a/o)
Table of Common Values
Radian 0 pi/6 pi/4 pi/3 pi/2 Angle 0 30 45 60 90 Sin 0 1/2 (2)/2 (3)/2 1 Cos 0 (3)/2 (2)/2 1/2 0 Tan 0 (3)/3 1 (3) undefined
Trig identities
Sin^2(x) + cos^2(x) = 1
Divide by cos^2(x): tan^2(x) + 1 = sec^2(x)
Divide by sin^2(x): cot^2(x) + 1 = csc^2(x)
Double angle identity
Sin(2x) = 2sin(x)cos(x)
Law of Sines
A/sin(a) = B/sin(b) = C/sin(c)
Period
- The distance along the x axis that it takes for the function to repeat itself (2pi)
- 2pi/b
Graphing trig functions
Sin = cos(x-pi/2)
Cos, sin
Complex numbers
i^2 = -1 i^3 = -i i^4 = 1 I^5 = i
Axis of symmetry and how to find vertex
x = -b/2a
Use axis to find x, then plug x into equation
SA
- area of the sides of the box
- cylindrical surface area: 2•pi•r(h+r)
- rectangular SA: 2(lw + lh + wh)
- LSA: SA without the bases
- spherical SA: 4•pi•r^2
Polygons
Straight lines, enclosed area, regular is all sides the same
Diagonals of polygon
N(n-3)/2
Interior angles
180(n-2)/n
Exterior angles
360/n or 180 - interior angle
