Semester exam Flashcards
Which is the dependent variable?
‘Y’ is the dependent variable
what is line Y = 4X + 15 and Y = 4X + 45’s relationship ?
Parallel lines
How do we get a perpendicular line?
Slope 1 x Slope 2 = -1
or (-1 / Slope 1) = Slope 2
what is line y = 2x + 1 and y = −0.5x + 4’s relationship?
Perpendicular lines
what does BIDMAS stand for?
Brackets, Indecies, Division, Multiplication, Addition, Subtraction
What two parts of BIDMAS go in order by left to right instead of over-riding each other?
Division is not more prioritized than multiplications
neither is addition over subtraction
they both go ‘left to right’
X-intercept is?
the value of X when Y = 0
Y-intercept is?
The value of Y when X = 0
What does the big ‘n’ stand for/do in set theory?
n = intersection. It describes the variables that fit both groups ( Chickens fit the intersection of the groups: “bird’s” and “farm animal’s”)
What does the big ‘U’ stand for/do in set theory?
U= unison. It describes the variables that are in either groups (Peacocks and Cows fit either groups: “birds” or “farm animal’s”)
What does the big ‘⊆’ stand for/do in set theory?
⊆= sub set. It describes how one group is a more specific set inside a bigger group. (“birds” are a subset of “animals” = “Birds” ⊆ “Animals))
What is the formulae for a percent?
percent (in decimal form) times by whole number = peice of whole. 0.5 X 6 = 3. 3 is 50% of 6
OR
percent / 100 = part / whole
What is the formulae for ‘change in percent?’
change in value times divided by original amount times by 100 = change in percent.
(-2/50) = -0.04 x 100 = -4% = change in percent.
Graphing Midpoint Formulae?
X= X1 + X2 divided by 2. Y= Y1 + Y2 divided by 2.
(2,4) and (8,5) midpoint?
= 8+2 = 10/2 = 5 = x value
=5+4 = 9/2 = 4.5 = y value
= (5,4.5)= midpoint
Direct Variation Formulae?
Y = KX
Y = dependent variable X = independent variable K = constant variable
Graphing: x-value reflection transformation?
Y = MX + B to Y = -M(X) + B
Graphing: y-value reflection transformation?
Y = MX + B to Y = M(-X) + B
Graphing: translation?
Y = MX + B to Y = MX + (B+A)
what could distance formulae help calculate in the test?
triangles (other shapes)
How do you calculate the longer/sloped side of the triangle?
you square the other two lines and add them together
(AxA) + (BxB) = (CxC)
find square root of result
= C
How to find distance of one point of a slope to the other?
the distance of two points is the distance of X squared
plus the distance of Y squared
and taking the result and then fining the square root of the answer
(X2-X1)= A
(Y2-Y1)=B
(AxA) + (BxB) = (CxC)
find square root of result
= C
C = distance
What is an arithmetic sequence?
An infinitely going sequence of numbers that is calculated with a constant:
1, 4, 7, 10, 13, 16, 19, 22, 25, …
A+ (0xD) = 1, A+(1xD) = 4, A+(2+D)…
the distance between each number is 3 (D = 3)
the starting point is 1 (A = 1)
N is a shifting state (N = 1, 2, 3, 4, 5…)
The formulae is = Xn = A + D(n-1)
How does an arithmetic sequence work?
The formulae is = Xn = A + D(n-1)
N is the step the sequence is in
(N = 1, 2, 3, 4, 5, 6…)
X is the product of the formulae, the N next to it specifies which ‘step’ the number is
A is constant, it is the starting point in the sequence
D is the number that the sequence shifts in each time
(n-1) is the step the number is on. shifted one down to eliminate the first because it’s is just ‘A’
Identify the solutions of the inequality 11 ≤ p + 5.
all real numbers greater than or equal to 6
Carpenter A charges $50 an hour. Carpenter B charges $20 to visit your home plus $45 for each hour. For how many hours will the total cost for each carpenter be the same? How much will that cost be? If a customer thinks they need a carpenter for 3 hours, which carpenter should be hired?
4 hrs; $200
carpenter A is cheaper for less than 4 hours
Juliet went to the mall to buy clothes for the new school year. Shirts cost $15 and pants cost $40. If Juliet bought 10 items of clothing for a total of $225, how many shirts and pants did she buy?
7 shirts and 3 pants
What is an integer?
A whole counting number including negatives and zero
-infinity)…-3, -2, -1, 0, 1, 2, 3…(+infinity
What are whole numbers?
positive counting numbers (positive integers)
starting: 0, 1, 2, 3, 4, 5 (+infinity)
What are rational numbers?
Numbers that can be described properly as a fraction including: integers, decimals;
numbers that are not rational are numbers that cannot be described in a finite amount of numbers or any fraction, there fore needing a symbol
irrational numbers: ( √2, π, e, and φ)
What are real numbers?
any number that can be on the number line
1, 1.000~1, 1.000~2 (so-on) 2, 2.00~1, 2.00~2 –infinity
this is all rational numbers, irrational numbers, integers, and whole numbers
What are imaginary numbers?
Pfft, I dunno
0, sometimes, if it wants to be… (?)
Would integers be a subset of whole numbers
nope.
whole numbers are positive integers
can irrational numbers be a subset of real numbers
yes, real numbers are any numbers that you can interpret on the number line
what quadrant would (4.-4) be in?
quadrant IV or quadrant 4
What quadrant would (-6, 7) be in?
quadrant II or quadrant 2
What quadrant would (7, 7) be in?
quadrant I or quadrant 1
What quadrant would (-1,-1) be in?
quadrant III or quadrant 3
What is the domain?
usually the independent variable or X
What is the range?
usually the dependent variable Y. product of the domaine in the relationship
What is the range in a function?
The product of X after going through a function, yielded exclusively by it’s own Xn
What is a function?
Function: A function is a set of ordered pairs in which each x-element has only ONE y-element associated with it.
What is a linear function?
A straight slope that each X has it’s own exclusive Y
so not anything with a slope like: 5/0 or 0/5
what would f(X)=7x + 3 be translated across the X-axis
g(X)= -7X - 3
what would f(X)=7x + 3 be translated across the Y-axis
g(X) = -7x + 3
Find the equation of the straight line that has slope m = 4 and passes through the point (–1, –6).
y = 4x – 2
process
y1 = -6
X1 = -1
y – y1 = m(x – x1) y – (–6) = (4)(x – (–1)) y + 6 = 4(x + 1) y + 6 = 4x + 4 y = 4x + 4 – 6
y = 4x – 2
How do you find the equation of the straight line that has slope m = 4 and passes through the point (–1, –6).
y – y1 = m(x – x1) y – (–6) = (4)(x – (–1)) y + 6 = 4(x + 1) y + 6 = 4x + 4 y = 4x + 4 – 6
to keep consistent, you need to take the first step of Y from the Y value. same with X.
the numerical value that is left next to the X afterwards is the Y-intercept
Arithmetic sequence formulae question:
What is the A in “Xn= A + D(n -1)?”
A is the value that the arithmetic sequence starts off with
in
3, 4, 5, 6, 7, 8
A = 3
Arithmetic sequence formulae question:
What is the D in “Xn = A + D(n - 1)?”
The amount that the arithmetic sequence progresses in each step
in
3, 6, 9, 12, 15, 18
D = 3
