Algebra Flashcards
(x+y)^2 - (x-y)^2
4xy
(x+y+z)^2
x^2 + y^2 + z^2 + 2(xy + xz + yz)
x^3 + y^3
(x+y)(x^2 + y^2 - xy)
x^3 - y^3
(x-y)(x^2 +y^2 +xy)
T or F. a^n - b^n is always divisible by a- b
T
a^n - b^n is divisible by a+b if
n is even
a^n + b^n is divisible by a+b if
n is odd
How do you express negative exponents ?
reciprocal of the inside base and turn negative to positive exponent
T or F. if 0^x = 0 = 0^y , x is equal to y
False. 0^4 = 0 = 0^3 but 4 ≠ 3
How do you express exponential growth formula?
y(t) = y(0).k^t
T or F. In GMAT, you should always subtract or divide two inequalities
F. You should never
If 0< G < 1 then how does G^n compare to G (if n is odd/even positive integer)
G^n is less than original G
If 0< G < 1 then how does G^n compare to G (if n is odd/even negative integer)
G^n is larger than original G
If -1< G < 0 then how does G^n compare to G (if n is odd/even positive integer)
G^n is larger than original G
If -1< G < 0 then how does G^n compare to G (if n is odd/even negative integer)
G^n is larger than original G (if n is even)
G^n is smaller than original G (if n is odd)
T or F. If both sides are known to be negative, you can’t flip the inequalities sign when you square
False. You can flip the sign.
Ex: -4 < - 3 then 16 > 9
T or F. If both sides are known to be positive, you don’t flip the inequalities sign when you square
True.
T or F. If one side is positive and one side is negative, the inequality sign stays when you square
False.
it may or may not
T or F. If the signs are unclear, then you cannot square
True.
If x < y, then how does 1/x compare to 1/y when x and y are both positive or both negative?
1/x > 1/y (flip the sign)
If x < y, then how does 1/x compare to 1/y when x is negative and y is positive?
1/x < 1/y
T or F. If you don’t know the sign of x or y, you can still take the reciprocals.
False.
if |x| > a then:
x > a or x < -a
if |x| < a then:
-a < x < a
If |A| = |B| then
A = B or A = - B
What is the equation expression for directional proportionality?
y(1)/ x(1) = y(2)/ x(2)
What is the equation expression for inverse proportionality?
y(1) . x(1) = y(2) . x(2)
When 0< G < 1, G^n < G if
n is positive integer
When 0< G < 1, G^n > G if
n is negative integer
When -1 < G < 0, G^n < G if
n is odd negative integer
When -1< G< 0, G^n > G if
n is positive integer or
n is negative even integer
square root of 2
about 1.4
square root of 3
about 1.7
square root of 5
around 2.25
square root of 121
11
square root of 144
12
13^2
169
square root of 196
14
square root of 225
15
square root of 256
16
square root of 625
25
G^n < G when
0< G < 1
-1 < G < 0 if n is negative odd
G^n > G when
n is negative for 0< G < 1
n is negative even for -1< G < 0
n is positive for -1< G < 0
T or F. Any positive proper fraction raised to a power between 0 and 1 will result in a number larger than the original fraction.
T (problem #3 p. 125 Manhattan)
T or F. Any positive proper fraction raised to a power greater than 1 will result in a number larger than the original fraction.
F.
How do you translate “The retailer has less than twice as many radios as clocks in inventory” in math expression?
r < 2c
How do we know a quadratic function has a solution or not?
if the discriminant (b^2 - 4ac) < 0, = 0 or > 0
If the discriminant is greater than zero, then how many solutions are there?
two
If the discriminant is equal to zero, then how many solutions are there?
one solution
If the discriminant is less than zero, then how many solutions are there?
no solution
The answer (A) in data sufficiency is?
Statement (1) alone is sufficient, but statement (2) is not
The answer (B) in data sufficiency is?
Statement (2) alone is sufficient, but statement (1) is not
The answer (C) in data sufficiency is?
Both statement together are sufficient, but neither statement alone is sufficient
The answer (D) in data sufficiency is?
EACH statement ALONE is sufficient
The answer (E) in data sufficiency is?
Statement (1) and (2) TOGETHER are NOT sufficient.
The trick to translate fractional exponent of a number to a root
denominator OUT
numerator IN
The trick to translate a root to fraction exponent
in NUMERATOR
out DENOMINATOR
Can absolute value result in negative number?
NO. its results are always greater than 0
x^0 = ?
1
0^x = ?
0
proper fraction
a fraction between 0 and 1
How do you express proper fraction with decimals with exponents?
Ex: (0.6)^2 (0.5)^4 (0.1)^5
The decimals move to the left in accordance with the value of exponent after exponent non-zero digits.
Ex: (0.6)^2= 0.36
(0. 5)^2 = 0.0625
(0. 1)^5 = 0.00001
what is the value of 0^0 ?
undefined
T or F. There is no solution for the even root of a negative number
T
What does x^2 - x < 0 imply?
x^2 < x, so 0 < x < 1
square root of 324
18
square root of 289
17
19^2
361
What is the vertex (x,y) of equation:
a(x-h)^2 + k = 0
(h,k)
T or F. Any two points the same distance from the origin along perpendicular lines will have the opposite coordinates from one another - if one point is (a,b), the other will be (b,a)
True.
T or F. In x-y plane, the quadrants is upper shaded area if the inequality is equal to or greater (>=)
True.
T or F. In x-y plane, the quadrants is below shaded area if the inequality is equal to or less (=
True.
