Algebra Flashcards

Question

Even & Odd Functions

Answer 1

*** Even Function:** Even if the input is negative, the output will be the same. The exponents are either even numbers or 0 f(x) = x², when x =1, output is 1 and when x =-1, output is also 1 *** Odd Function:** If the input is negative, the output will be the same value but now the opposite sign. The exponents are odd numbers or 0 f(x) = x³, when x =1, output is 1 and when x =-1, output is -1

Answer 2

* "+ : more, in excess of * "- : under, remaining * x : increase by a factor, into * ÷ : third of, decrease by a factor, ratio * = : corresponds to, equivalent * exponent : raised to, times itself n times * decimal movement: x 10ⁿ = move decimal n places to the right, ÷10ⁿ = move decimal n places to the left

Answer 3

Same amount of interest money each year t = p + pn(r/100) t: Total amount including interest p: principal/money deposited n: number of yrs r: interest rate

Answer 4

The interest you receive each year gets bigger and bigger t = p(1+r/100)ⁿ t: Total amount including interest p: principal/money deposited n: number of yrs r: interest rate If the interest compounds several times per year: 1. Calculate interest rate of each compound time: annual interest rate÷compound times per yr 2. Calculate total compounding times in the asking period by multiplying the number of years x compound times per yr. 3. Calculate using formula ## Footnote 1. Interest Rate each compound: 8% ÷ 4 = 2% 2. Total compound times in 3 years: 3 x 4 = 12 times in 3 yrs 3. 100 (1 + 2%) ¹² →100 (1.02) ¹²

Answer 5

A problem where you mix two or more solutions to create a combined mixture. You then have to calculate the percentage of some element in the combined mixture. asking element ÷ total combined mixture The Mixture Trick 1. Put the lower percentage on the left, the combined percentage in the middle, and the higher percentage on the right. 1. Calculate the "distance" between each number and the middle number. 1. The two "distance" we found in step 2 represent the initial mixing ratio. 2. A/B = "distance" of B/"distance" of A Solution A contains 12% alcohol and Solution B contains 25%. If the combined solution contains 17%, what is the ratio of A to B? 1. 12%......17%.....25% 1. "distance" between 17% - 12% = 5%, 25% - 17% = 8 1. The initial mixing ratio = 8:5 2. Since 17% is closer to 12%, the ratio is A/B = 8/5

Answer 6

Distance = Rate x Time

Answer 7

* 1km = 1000m * 1L = 1000ml * 1 hr = 60 mins = 3600 secs * 1 mile = 5,280 feet = 1,760 yards

Answer 8

Refers to one's speed RELATIVE (in comparison) to some other speed. * Toward each other: Add the speeds * Opposite Directions: Add the speeds * Catching up: Subtract the speeds

Answer 9

Work = Rate x Time * If working together: add the rates * If working against each other: subtract the rate * Identical machines: w = number of identital machines x rate x time

Answer 10

For identical Machines, the more machines you have, the more work you can do. But Sometimes MORE IS BAD. For example, imagine we're sharing a dinner. The more people we have, the less food each person gets. Set a equal equation: '# of ppl x time = # of ppl x time If a water supply can last 30 people 12 days, how long would the water supply last if 40 people were present? Assume each person drinks the same amount of water each day. 30 ppl x 12 days = 40 ppl x time 30 x 12 = 40 x t→time = 360 ÷ 40 = 9 days

Answer 11

An ordered list usually but not always, comprised of numbers. **Arithmetic:** * succeeding term is obtained by adding or subtracting a certain number from the previous term: 2, 4, 6, 8→2, 4(2**+2**), 6(4**+2**), 8(6**+2**) **Geometric:** * each succeeding term is obtained by multiplying or dividing a certain number from the previous term: 5, 10, 20, 40→5, 10(5**x2**), 20(10**x2**), 40(20**x2**) **Quadratic:** * The "second difference" of the terms is the same: 1, 12, 36, 73, 123 →First difference: 11, 24, 37, 50: 1, 12(1+11), 36(12+24), 73(36+37) →2nd difference: 13, 13, 13: 11, 24(24-11=**13**), 37(37-24=**13**), 50(50-37=**13**) **Harmonic:** * Where the reciprocal of the terms is an arithmetic sequence: ½, ⅓, ¼

Answer 12

* aₙ can be written as n itself. (1st term = a₁, 2nd term =a₂) * aₙ can be written as previous terms of the sequence (Previous term = aₙ₋₁, 2 terms previous =aₙ₋₂) * aₙ can be written as exceeding terms of the sequence (Next term = aₙ₊₁, 2 terms after =aₙ₊₂)

Answer 13

* The sum of the first n terms of a sequence Sequence: 1, 2, 3, 4 Series: 1 + 2 + 3 + 4

Answer 14

A common way to represent a series is by the summation operator, Σ. m Σ aₙ = aₓ + aₓ₊₁ + aₓ₊₂...+aₘ n=x * Σ (Sigma): The summation operator itself. * m: The upper index. This is the last value to be added * n=x: The lower index. This is the starting value. * aₙ (or other expression): The term to be summed. 6 Σ aᵢ i=3 If aₙ = 2n, the sequence will be 2 (1x2), 4 (2x2), 6 (3x2), 8 (4x2) 6 Σ 2ᵢ = 6(starting index is 3)+8+10+12 (ending index is 6) = 36 i=3 Keep in mind that you won't be expected to know the summation operator for the GRE and hence the above section can be considered as optional. ETS will instead describe the same thing without using the operator, so in the above example, one way they could phrase this would be "If the nth term of a sequence is 2n, what is the sum of the third through the sixth term of the sequence?"

Answer 15

* A type of sequence where the terms cancel out in such a way that it becomes quite easy to find the series. * The nth term of a telescoping sequence would look something like this: aₙ = ¹⁄ₙ - ¹⁄ₙ₊₂ Suppose we need to find the sum of the first 100 terms of the sequence. Try writing down the first few terms 　1st　　 2nd　　3rd　　4th (¹⁄₁ - ⅓) + (½ - ¼) + (⅓ - ⅕) + (¼ - ⅙) 1. Terms that cancel out (⅓,¼) 1. Terms don't cancel out? ¹⁄₁, ½, -⅕, -⅙ (last 2 terms to subtract) 1. In terms of 100, the last 2 terms to subtract will be: -¹⁄₁₀₁, -¹⁄₁₀₂, so the formula for the sum of the first 100 terms will be: ¹⁄₁ + ½ - ¹⁄₁₀₁ - ¹⁄₁₀₂

Algebra Flashcards

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