Pre-Algebra Flashcards
Formula: Perimeter of Square
P=4x (Perim. = 4*length of one = side)
Formula: Area of a Square
A=x² (area=length of an =side squared)
Formula: perimeter of rectangle
P=2L+2w (perim.=2 times length plus 2 times width)
Formula: Area of a rectangle
A=Lw (Area=length times width)
Formula:Perimeter of a parallelogram
P=2x + 2y (Perim.=2 times one parellel side plus 2 times other parellel side) x and y are not parallel
Formula:Area of a parallelogram
A=Bh (Area = base length times height)
Formula:Diameter of a circle
D=2r (Diameter= radiusx2
Formula:Circumference of a circle
C=2πr (Circ. = 2 times pi times radius)
Formula:Area of a circle
A= π r² (Area=pi times the square of the radius)
Formula:Perimeter of a triangle
P=s₁+s₂+s₃ (Perimeter=the sum of the sides)
Formula:Area of a triangle
A=1/2Bh (Area=1/2 times Base length times height) (for a right triangle one of the lines on the right angle is the height. Otherwise height is from the center of the base to the opposing angle)
Formula:Formula for volume of all straight solids
V=Bh (Volume =AREA of the base * height), so if you can calculate the area of the base shape, you just multiply that times the height.
Formula:Volume of a box (rectangular or square solid)
V=LWh (volume = Length*Width (area) * height)
Formula:Volume of a cylinder
V=π r²h (Volume =pi times the square of the radius times height) **if none of the dimensions is a multiple of 3 you will have a remainder
Formula:Volume of a cone
V=1/3 π r²h (Volume +1/3 times pi times the square of the radius times height)
Formula:Volume of a pyramid
V=1/3Lwh (Volume=1/3 times length times width times height) **if none of the dimensions is a multiple of 3 you will have a remainder
0 / 0
undefined
anything / 0
undefined
0 / anything except 0
0, if it is 0/0 it is undefined
12(10⁶)
12,000,000 (Power of 10 ALWAYS just tack on the # of zeros represented in the exponent)
22,000,000/10⁶
22 (Just remove the # of zeros in the exponent)
645⁰ (645 to the powerof zero)
1 (Any number to the power of zero equals 1)
56(exp 1)
56 (Any number to the power of 1 = that number or base)
First 10 prime numbers
1, 3, 5, 7, 11, 13, 17, 19, 23, 29
Second 10 prime numbers
31, 37, 41, 43, 47, 53, 59, 61, 67, 71
Third 10 prime numbers
73, 79, 83, 89, 97, 101, 103, 107, 109, 113
A number that is NOT a prime number
A composite number (has at least one other factor that is not 1 or itself)
What is the prime factorization of 48?
(3)(2⁴) (32222) (Breaks the number down into its prime numbers)
What are the three cases to find the least common multiple of two numbers and what is the respective method to solve each?
- Largest # is multiple of smaller: it is the LCM
- Both #’s are primes: their product is the LCM
- Neither 1 or 2 is true: Multiply largest by 2, 3, 4 etc until the smaller number goes into the product evenly.
Define proper fraction
numerator less than denominator
Define improper fraction
numerator greater than denominator
Defined mixed number/mixed fraction
a number containing a whole number and a proper fraction
What are the four steps to multiply two or more fractions
- Factor; 2. Cancel; 3. Multiply denominators;. 4. Multiply numerators
What are the three steps to divide two fractions
- Keep first fraction the same;
- Flip the second fraction
- Multiply the two fractions following the multiplication steps
What are complex fractions and how do you simplify them?
Fractions with fractions in both numerator and denominator. Solve by dividing the upper one by the lower one.
How do you add or subtract fractions without a common denominator? (3 steps)
- Find the LCM for the two denominators
- Multiply both numerator and denominator by the missing fractions so that the LCM is the denominator for both fractions.
- Add or subtract the numerators.
What are three cases of LCM for the denominator of the two fractions
Case 1: If the larger denominator is a multiple of the smaller, the larger is the LCM.
Case 2: If both denominators are primes, the LCM is the product of those two primes.
Case 3. The default, start with larger denominator and multiply it by 2, 3, 4 et until you get a number that divides evenly by the smaller denominator.
What are the factors of 111
1, 3, 37, 111 (Remember 111 is NOT a prime)
What are the factors of 57
1, 3, 19, 57 (Remember 57 is NOT a prime)
What are the factors of 91
1, 7, 13, 91 (Remember 91 is NOT a prime)
What are the factors of 117
1, 3, 9, 13, 39, 117 (Remember 117 is NOT a prime)
What are the factors of 119
1, 7, 17, 119 (Remember 119 is NOT a prime)
First 10 powers of 2 & (not including to the 0 power) Pattern
2^0 1 2^1 2 2^2 4 2^3 8 2^4 16 2^5 32 2^6 64 2^7 128 2^8 256 2^9 512 2^10 1024 *Note pattern 2, 4, 8, 6 that goes on forever
First 6 powers of 3 (not including to the 0 power) & Pattern
3^0 1 3^1 3 3^2 9 3^3 27 3^4 81 3^5 243 3^6 729
*Pattern 1, 3, 9, 7
3^7 2,187
3^8 6,561
3^9 19,683
3^10 59,049
First 5 powers of 4 (not including to the 0 power) and pattern
4^0 1 4^1 4 4^2 16 4^3 64 4^4 256 4^5 1024
*pattern 4, 6, 4, 6
4^6 4096 4^7 16,384 4^8 65,536 4^9 262,144 4^10 1,048,576
First 3 powers of 9 (not including to the 0 power) and pattern
9^0 1 9^1 9 9^2 81 9^3 729 -pattern 9,1,9,1 9^4 6,561 9^5 59,049 9^6 531,441 9^7 4,782,969 9^8 43,046,721 9^9 387,420,489 9^10 3,486,784,401
Explain the order of operation
- First do Parentheses
- Exponents, roots (L to R)
- Multiplication, Divison (L to R)
- Addition, Subtraction (L to R)
How do you solve a linear equation?
Isolate x by opposite operations
What is a literal equation?
An equation that is all or mostly variables.
To solve the sum of consecutive integers…
- Determine how many integers
- Determine if they are odd or even
- add x+(x+1)+(x+2) etc =number if consecutive
- Use x+2, x+4 etc form if odd or even
How many ounces are in a cup?
Eight (8)
How many feet are in a mile?
5280 feet in a mile.
How many cups are in a pint?
Two cups
What is an irrational number?
Any real number that cannot be expressed as a ratio of integers. Repeating or terminating decimals ARE Rational but un repeating endless decimals are irrational. All square roots of rational numbers, other than perfect squares are irrational.
What is a rational number?
Any number that can be expressed as a quotient or a fraction of two integers if denominator is not 0.
What is an integer?
Any number that can be written without a fractional component. (no fractions or decimals) including negatives.
What is a natural/whole number?
Counting/ ordering numbers starting from zero. No fractions, decimals or negatives. (some books do not count zero)
What is a real number?
A number that represents a quantity along a continuous line. The numbers in the complete totally ordered field. Includes Integers, rational and irrational numbers. Does not include imaginary numbers.
What is an imaginary number?
A complex number written as a real number multiplied by the imaginary unit i.
What is the formula to solve the volume of *a sphere
V=4/3πr³
What are the factors of 51?
3*17 51 is not a prime
What are the factors of 87
7 * 17 87 is not a prime
How are the four quadrants of the coordinate plane labelled?
The top R plane (NE) (x and y positive) is quadrant I. Then go counterclockwise: II (NW) (y positive, X negative), III (SW) (x and y negative) and IV (SE) (x positive, y negative)
What is the order of coordinates?
x, y
What is the formula of a line (linear equation)?
ax+by=C (x, y are variables, a,b coefficents, c is a number called the constant.
How do you graph a linear equation? (3 steps)
- Solve equation for y
- Plug in a few values for x and record resulting y values
- Plot the points on the plane and connect them to form a graph
What is the Pythagorean theorem
a²+b²=c² (The square of the hypotenuse of a right triangle is equal to the sum of the squares of the opposing sides)
What is the formula for the circumference of a sphere?
C=2πr (like a circle, because it is a circle)
What is the formula for the surface area of a sphere?
A=4π r²
