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Math > Semester exam > Flashcards

Semester exam Flashcards

1
Q

Which is the dependent variable?

A

‘Y’ is the dependent variable

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2
Q

what is line Y = 4X + 15 and Y = 4X + 45’s relationship ?

A

Parallel lines

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3
Q

How do we get a perpendicular line?

A

Slope 1 x Slope 2 = -1

or (-1 / Slope 1) = Slope 2

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4
Q

what is line y = 2x + 1 and y = −0.5x + 4’s relationship?

A

Perpendicular lines

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5
Q

what does BIDMAS stand for?

A

Brackets, Indecies, Division, Multiplication, Addition, Subtraction

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6
Q

What two parts of BIDMAS go in order by left to right instead of over-riding each other?

A

Division is not more prioritized than multiplications
neither is addition over subtraction
they both go ‘left to right’

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7
Q

X-intercept is?

A

the value of X when Y = 0

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8
Q

Y-intercept is?

A

The value of Y when X = 0

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9
Q

What does the big ‘n’ stand for/do in set theory?

A

n = intersection. It describes the variables that fit both groups ( Chickens fit the intersection of the groups: “bird’s” and “farm animal’s”)

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10
Q

What does the big ‘U’ stand for/do in set theory?

A

U= unison. It describes the variables that are in either groups (Peacocks and Cows fit either groups: “birds” or “farm animal’s”)

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11
Q

What does the big ‘⊆’ stand for/do in set theory?

A

⊆= sub set. It describes how one group is a more specific set inside a bigger group. (“birds” are a subset of “animals” = “Birds” ⊆ “Animals))

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12
Q

What is the formulae for a percent?

A

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

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13
Q

What is the formulae for ‘change in percent?’

A

change in value times divided by original amount times by 100 = change in percent.

(-2/50) = -0.04 x 100 = -4% = change in percent.

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14
Q

Graphing Midpoint Formulae?

A

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

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15
Q

Direct Variation Formulae?

A

Y = KX

Y = dependent variable
X = independent variable
K = constant variable
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16
Q

Graphing: x-value reflection transformation?

A

Y = MX + B to Y = -M(X) + B

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17
Q

Graphing: y-value reflection transformation?

A

Y = MX + B to Y = M(-X) + B

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18
Q

Graphing: translation?

A

Y = MX + B to Y = MX + (B+A)

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19
Q

what could distance formulae help calculate in the test?

A

triangles (other shapes)

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20
Q

How do you calculate the longer/sloped side of the triangle?

A

you square the other two lines and add them together

(AxA) + (BxB) = (CxC)

find square root of result

= C

21
Q

How to find distance of one point of a slope to the other?

A

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

22
Q

What is an arithmetic sequence?

A

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)

23
Q

How does an arithmetic sequence work?

A

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’

24
Q

Identify the solutions of the inequality 11 ≤ p + 5.

A

all real numbers greater than or equal to 6

25
Q

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?

A

4 hrs; $200

carpenter A is cheaper for less than 4 hours

26
Q

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?

A

7 shirts and 3 pants

27
Q

What is an integer?

A

A whole counting number including negatives and zero

-infinity)…-3, -2, -1, 0, 1, 2, 3…(+infinity

28
Q

What are whole numbers?

A

positive counting numbers (positive integers)

starting: 0, 1, 2, 3, 4, 5 (+infinity)

29
Q

What are rational numbers?

A

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)

30
Q

What are real numbers?

A

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

31
Q

What are imaginary numbers?

A

Pfft, I dunno

0, sometimes, if it wants to be… (?)

32
Q

Would integers be a subset of whole numbers

A

nope.

whole numbers are positive integers

33
Q

can irrational numbers be a subset of real numbers

A

yes, real numbers are any numbers that you can interpret on the number line

34
Q

what quadrant would (4.-4) be in?

A

quadrant IV or quadrant 4

35
Q

What quadrant would (-6, 7) be in?

A

quadrant II or quadrant 2

36
Q

What quadrant would (7, 7) be in?

A

quadrant I or quadrant 1

37
Q

What quadrant would (-1,-1) be in?

A

quadrant III or quadrant 3

38
Q

What is the domain?

A

usually the independent variable or X

39
Q

What is the range?

A

usually the dependent variable Y. product of the domaine in the relationship

40
Q

What is the range in a function?

A

The product of X after going through a function, yielded exclusively by it’s own Xn

41
Q

What is a function?

A

Function: A function is a set of ordered pairs in which each x-element has only ONE y-element associated with it.

42
Q

What is a linear function?

A

A straight slope that each X has it’s own exclusive Y

so not anything with a slope like: 5/0 or 0/5

43
Q

what would f(X)=7x + 3 be translated across the X-axis

A

g(X)= -7X - 3

44
Q

what would f(X)=7x + 3 be translated across the Y-axis

A

g(X) = -7x + 3

45
Q 
Find the equation of the straight line that has slope m = 4 and passes through
the point (–1, –6).
A

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

46
Q 
How do you find the equation of the straight line that has slope m = 4 and passes through
the point (–1, –6).
A 
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

47
Q

Arithmetic sequence formulae question:

What is the A in “Xn= A + D(n -1)?”

A

A is the value that the arithmetic sequence starts off with

in
3, 4, 5, 6, 7, 8
A = 3

48
Q

Arithmetic sequence formulae question:

What is the D in “Xn = A + D(n - 1)?”

A

The amount that the arithmetic sequence progresses in each step

in
3, 6, 9, 12, 15, 18
D = 3

Math (10 decks)

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