EA Math Flashcards
When to flip the sign (> or <)
When multiplying or dividing by negative number
How to solve systems of (2) equations? When do I use the various methods?
Methods are substitution and elimination. Use elimination to eliminate a variable through addition.
What is the quadratic equation (standard form)? What are the two methods for solving?
How do you factor the quadratic equation?
What is the Quadratic Formula? When do I use it?
Use this as an alternative to factoring.
Solving quadratic inequalities
Similar to solving quadratics. However, you must use the two values for “x” to determine which of the three resulting intervals hold true. In the example “x” is equal to 5 and -2.
Division of polynomials? (Need to look up)
(Need to look up)
What is the greatest common factor?
3x
Use difference of squares identity
Example
Factoring trinomial that does not follow the straightforward format (see example)
(1) Find two numbers that multiply to “a” times “c” and add to “b.” Then (2) rewrite the middle term using these numbers.
Rearrange
Consider other direction
Rearrange
Consider other direction
Rearrange
Consider other direction
Rearrange
Consider other direction
Rearrange
Consider other direction
Equivalent?
Rearrange
Consider other direction
For exponents, “combine like terms using the product and quotient rules to simplify complex expressions.”
Rearrange
Consider other direction
Rearrange
Simplify
Triangles - sum of interior angles?
180 degrees
Area of a triangle?
1/2 base x height
Circles - circumference and arc length?
For arc length, multiply by the proportion (angle / 360)
Circle - area and sector area?
For sector area, multiply by the proportion (angle / 360)
Area of parallelogram
Same as a rectangle
Area of trapezoid
Triangles - Pythagorean Theorem and common triples (top 3)?
3,4,5
5,12,13
7,24,25
Also consider scaled versions (e.g. 9,12,15)
Triangles - Ratios for 45-45-90 and 30-60-90?
For 45-45-90: 1, sqr 2
For 30-60-90: 1, sqr 3, 2
Cylinder - volume and surface area?
Prism - volume and surface area?
Volume: length x width x height
Sphere - volume and surface area?
Cube - volume and surface area?
Distance between two points?
Midpoint of a line segment?
Slope of a line?
Sum of angles in a polygon?
Notation for basic probability?
Probability of independent events?
Multiply
Probability of mutually exclusive events?
Add
Probability of an event NOT occurring?
What are the different types of combinations and permutations?
- Combination without repetition
- Combination with repetition (wrong below! - in both it is N+r-1)
- Permutation of all items
- Permutation of subset without repetition
- Permutation of subset with repetition
- Permutation of subset with limited repetition
What is the basic equation for combinations WITHOUT repetition? For example, how many ways can you choose 2 fruits from a basket of 5 different fruits?
Here order does NOT matter.
What is the basic equation for combinations WITH repetition? For example, how many ways can you choose 3 scoops of ice cream from 5 flavors if repetitions are allowed?
Below is wrong. Numberator and demoninator based on n + K -1
How many ways can you choose 3 scoops of ice cream from 5 flavors if repetitions are allowed?
How many ways can you choose 2 fruits from a basket of 5 different fruits?
How many ways can you choose 2 fruits from 5 different fruits and 1 vegetable from 3 different vegetables?
Note this is multiplication
A deck of cards has 52 cards. What is the probability of drawing an Ace or a King?
How many ways can a committee of 3 members be chosen from a group of 7 people?
What is the equation for permutations (subset, WITHOUT repetition)?
Here order DOES matter
What is the equation for permutations (WITH repetition)? For example, how many 4-digit PIN codes can be created if each digit can be any number from 0 to 9?
n^r (where “n” is number in full set and “r” is number in subset)
How many 4-digit PIN codes can be created if each digit can be any number from 0 to 9?
What is the equation for a permutation of ALL items?
n!
How many ways can you arrange 3 out of 5 different books on a shelf?
N!. This is a permutation of all Items
Equation for permutations with limited repetition (i.,e. repetition of some elements)? For example, how many ways can you arrange the letters in the word “BALLOON”?
How many ways can you arrange the letters in the word “BALLOON”?
How many ways can 4 people be seated in a row?
In a race with 8 runners, how many ways can gold, silver, and bronze medals be awarded?
How many distinct ways can the letters in “STATISTICS” be arranged?
Formula for simple interest?
Formula for future value of an annuity?
Formula for present value of an annuity?
Formula for present value?
Present value is used to determine the current value of a future amount of money
Formula for net present value?
Net Present Value is used to evaluate the profitability of an investment
Formula for internal rate of return (IRR)?
The IRR is the discount rate that makes the NPV of an investment zero
Formula for break even point (in number of units sold)?
Debt to equity ratio?
This ratio indicates the relative proportion of shareholders’ equity and debt used to finance a company’s assets
Formula for return on investment (ROI)?
ROI measures the gain or loss generated relative to the amount invested:
Price to earnings ratio?
This ratio is used to value a company by measuring its current share price relative to its per-share earnings
A company is considering investing $100,000 in a project that is expected to generate $30,000 per year for 5 years. If the discount rate is 8%, what is the NPV of the project?
The NPV of the project is approximately $19,806.20. Since the NPV is positive, the project is financially viable.
Solve
The NPV of the project is approximately $70,281.10. Since the NPV is positive, the project is financially viable.
Does simplification of square root result in two solutions (+/-)?
Yes.
What does it mean to rationalize the denominator?
Relevant when square in denominator. Multiply top and bottom by the same.
Remember the order/operation here
The sum of the lengths of two pieces of rope is 65 feet. How long is the shorter piece if the lengths of the pieces of rope are in the ratio 8:5?
Given that the lengths of the pieces of rope are in the ratio 8:5, it follows that 8x+5x=65, for some value of x. Hence, 13x=65 and x=5. The length of the shorter piece is 5(5)=25
Simplify 14.25 / 91.25
(a) Find a simple fraction that is closest, e.g. in this case 1/6. Know that 1/6 is 0.1666. Adjust for actual numbers slightly if possible.
(b) Simplify (in this case divide by 25). Then do the above. The smaller numbers will make adjusting easier
For systems of equations, don’t hesitate to modify and add.
