Algebra Strategies Flashcards
(59 cards)
1
Q
xy > 0 Implication?
A
x and y are both positive OR both negative
2
Q
xy < 0 Implication?
A
x and y have different signs (one positive, one negative)
3
Q
x² - x < 0 Implication?
A
x² < x, so 0 < x < 1
4
Q
Distance formula?
A
D = RT
5
Q
Relative rates going towards each other?
A
Add the the two rates together to determine collective R
6
Q
Relative rates away from each other?
A
Add the two rates to determine increasing distance R
7
Q
Relative rates going in the same direction?
A
Subtract the two rates, difference is R
8
Q
13²
A
169
9
Q
14²
A
196
10
Q
15²
A
225
11
Q
20²
A
400
12
Q
3⁴
A
81
13
Q
2⁹
A
512
14
Q
2⁸
A
256
15
Q
2⁷
A
128
16
Q
2⁶
A
64
17
Q
2⁵
A
32
18
Q
1/8 FDP?
A
0.125 and 12.5%
19
Q
3/8 FDP?
A
0.375 and 37.5%
20
Q
5/8 FDP?
A
0.625 and 62.5%
21
Q
7/8 FDP?
A
0.875 and 87.5%
22
Q
even +/- even
A
even
23
Q
even +/- odd
A
odd
24
Q
odd +/- even
A
odd
25
odd +/- odd
even
26
even x even
even
27
even x odd OR odd x even
even
28
odd x odd
odd
29
Divisible by 3?
3 if the sum of the integer's digits is a multiple of 3
30
Divisible by 9?
9 if the sum of the integer's digits is a multiple of 9
31
Successive percents?
Multiply each percent change
32
Percent increase and decrease formula?
Percent change = Change in Value/Original Value
33
Compound interest formula?
P (1+ r/n)^nt (P = principal, r = rate, n = number of times per year, t = number of years)
34
Unknown multiplier formula?
X item / Y item = total, or X item / Y item = ratio
35
Average formula?
A = S/N
36
Weighted average formula
Weighted average = weight/sum of weights (data point) then add each additional item
37
"x in terms of y" means?
Isolate x. "x= something containing only y's."
38
(x+y)² equals?
x² + 2xy + y² (square of a sum)
39
(x-y)² equals?
x² - 2xy + y² (square of a difference)
40
(x+y)(x-y) equals?
x² - y² (difference of squares)
41
Units digit?
Take the ones digit of each product and multiply
42
Consecutive integer formula?
The sum of a set = (the mean of the set) x (the number of terms in the set)
43
Average of two large numbers?
Last term vs first term. Divide by two
44
How many integers in a set?
Last - First + 1
45
Consecutive multiples formula?
Last - First / Increment + 1
46
Weighted average formula?
Weighted average = Total sum / Total times
47
Remainders formula?
Dividend = multiple of divisor + remainder
48
Remainders expressed as a fraction formula?
Dividend/Divisor = Quotient + Remainder/Divisor
49
Divisible by 4?
The last two digits are divisible by 4
50
Divisible by 8?
If the last two digits are divisible by 8
51
Divisible by 9?
If the sum of the integer's digits is divisible by 9
52
Greatest common factor?
Everything shared in the venn diagram of primes between two numbers
53
Least common multiple?
All the prime factors of two numbers multiplied together
54
Even / Even?
Even or odd or non-integer
55
Even / Odd?
Even or non-integer
56
Odd / Even?
Non-Integer
57
Odd / Odd?
Odd or non-integer
58
When the numbers don't matter, do what?
Pick numbers
59
First ten prime numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
