Math Flashcards
What do you read first on long word problems?
Beginning and end
What are natural numbers?
Positive counting numbers
What are integers
Natural numbers with their negative counterparts
What are rational numbers
Numbers that can be written as a fraction
What are irrational numbers
Numbers that can’t be written as a fraction
What are conplex numbers.
Imaginery numbers
Difference of two squares
(A^2+B^2)(A^2-B^2)
Square of a sum
A^2+2AB+B^2
Square of a difference
A^2-2AB+B^2
Difference of two cubes
(A-B)(A^2+AB+B^2)
Sum of two cubes
(A+B)(A^2+AB+B^2)
Cube of a sum
A^3+3A^2B+3AB^2+B^3
Cube of a difference
A^3-3A^2B+3AB^2-B^3
What is the inverse of a log?
An exponential function
(Log3x=5)=(3^5=x)
What is a reciprocal?
Inverse fraction
What is prime factorization?
Factoring a number down until its no longer divisible by natural numbers.
What is cosecant or csc of Theta?
Reciprocal of sin or 1/sin
What is secant or sec of theta?
1/cos
What is cot of theta?
1/tan
What is the standard equation of a circle?
(X-H)^2 + (Y-K)^2=R^2
H,K= Circle’s center
How do you factor by grouping?
Section parts of the polynomial, factor common factors, then rewrite the equation.
What are A and B in A[sin(Btheta)]
A=amplitude
B=period
What are special trig identities?
Sin^2theta + cos^2theta = 1
Sin of theta/ cos of theta = tan of theta
Whatis the formula for averages?
TAN
Total=Average×Number of items
Ex: 522 total test points divided by 6 test means the average score is 87
How can you rewrite multiplying logarithms?
Add them
Log(xy) = Log(x)+log(y)
What do you do when dividing logarithms?
You subtract them
Log (x/y) = log(x)-log(y)
What’s the formula for simple interest?
I=PRT
Interest=principle×annual rate×total time
What’s the determinant of a 2by2 matrix?
[Ab over cd] = ad-bc
Whats the equation for finding the hypotenuse of an isoceles right triangle?
The hypotenuse equals the product of one of the sides and the root of 2
What is the expected value formula?
Multiplying the number of items in a row by their own probability then adding those outcomes together.
How do you find the area of a circle?
πr^2
How do you find the circumference of a circle?
2πr
How do you solve combination problems?
- Figure out the number of slots you need to fill.
- Fill in those slots with how many times its value can change according to the rule.
- Multiply each slot together.
Ex: In the word HAWKS, how many ways can you rearrange the letters so none repeat and W goes last?
4×3×2×1×1=24
How do you write a quadratic function in vertex form?
f(x) = a(x^2-h)+k
(h,k) = vetices
h = -b/2a
k = -determinant/4a
Determinant = b^2-4ac
How do you convert radians to degrees?
Degrees(π)/180
How do you convert radians to degrees?
Multiply degrees by 180 then divide by π
20^2
400
30^2
900
25^2
625
Multiplying matrices
Multiply each row of the first matrix by each column of the second matrix.
What’s a substitute for the distance formula?
Picture the distance like the hypotenuse of a right triangle
Commom right triangles
3-4-5
6-8-10
5-12-13
7-24-25
Standard equation of an eclipse
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
Here, (h, k) represents the center of the ellipse, “a” is the semi-major axis (the distance from the center to the farthest point on the ellipse in the x-direction), and “b” is the semi-minor axis (the distance from the center to the farthest point on the ellipse in the y-direction).
Note that if “a” and “b” are equal, then the ellipse is a circle. Additionally, if “a” is greater than “b,” the major axis is along the x-axis, and if “b” is greater than “a,” the major axis is along the y-axis.
I hope this helps! Let me know if you have any further questions.
Exponential growth formula
y = a * (1 + r)^t
Here,
- “y” represents the final value or the value at time “t” in the exponential growth.
- “a” is the initial value or starting point.
- “r” is the growth rate expressed as a decimal (not a percentage).
- “t” is the time period or the number of intervals elapsed.
In this formula, the exponential term (1 + r)^t represents the factor by which the initial value “a” grows over time. By multiplying the initial value “a” with this exponential factor, we can calculate the final value or the value at any specific time “t”.
What is the hypotenuse of a 30-60-90 triangle
Smallest side time 2
How do you find the second longest side of a 30-60-90 triangle?
Smallest side times the root of 3
What is GCF
The biggest factor that goes into all numbers being factored.
What’s the area of a triangle?
Base times heighth divided by 2
What’s the pythagoream theorm?
A^2×B^2=C^2
How do you divide fractions?
Invert the second fraction and multiply horizontally
Area of a pyramid
Area of the base, times the heighth, divided by 2.
What is the least commom multiple?
The smallest multiple two numbers can go into.
What is a prime number?
A number only divisible by 1 and itself?
What is a multiple?
A number divisible by other numbers.
How do you add matrices?
Add their corresponding parts.
What are supplementary angles?
Numbers that add to 180°
What is an opposite reciprical?
Opposite sign and inverse fraction.
What’s the standard form of a quadratic function?
f(x) = ax^2+bx+c
How do you square root an imperfect square?
Factor the imperfect square and attach its remainder
What is a factorial
The product of all of a numbers factors.
Tough problem guessing tricks
Plug and chug
Plug in C
What’s the area of a trapazoid?
((a+b)/2)h
Average of the top and bottom times the height
What do you do with an inequality when yoh divide by a negative?
Flip the inequality
