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IB APPLICATIONS > 3 DECK SCRAMBLE > Flashcards

3 DECK SCRAMBLE Flashcards

1
Q

what is a coefficient?

A

the number in front of a variable or variables

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2
Q

f(x) = ax^2 + bx + c What is the coefficient of the linear term?

A

b

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3
Q

f(x)= 2(x+4)^2-3 What is vertex and which way does it open?

A

at (-4, -3) and it opens upwards (has min)

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4
Q

why are roots called “zeros”

A

because it is where the height is zero; where the y value is zero; they are the x values that make the y=0

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5
Q

What is the x intercept of a line? (what are the coordinates?)

A

Where the line crosses the horizontal axis, the x axis. The coordinates are ( X, 0 )

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6
Q

how do you find “probability”

A

experimental: (#successes)/(total # tries).
theoretical: (# successful outcomes) / (# total possible outcomes)

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7
Q

When are there no solutions to simultaneous equations?

A

when the lines don’t cross, when they are parallel (no overlap)

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8
Q

When completing the square and “a” is not equal to 1, what do you have to do?

A

divide both sides of equation (every term) by that “a” to turn “a” into “1”

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9
Q

f(x)= -2(x-5)^2- 3What is vertex and is it a min or a max? What is the axis of symmetry?

A

at ( 5, -3) and it is a maximum, the AOS is x=5

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10
Q

what is the constant term’s exponent on the x?

A

0

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11
Q

How do you get the probability of taking a certain route on a tree diagram?

A

multiply the branches along the path till the end. write it at the end of the branch.

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12
Q

How can you tell if the point (5, -3) is a solution to a linear equation?

A

If it “works.” Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.

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13
Q

When is there and infinite number of solutions to simultaneous equations?

A

when they are the same line, then all points on the line satisfy both equations

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14
Q

one out of four is _____ or ____%

A

0.25 or 25%

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15
Q

three out of five is ____ or ____%

A

0.6 or 60%

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16
Q

f(x)= 5 - 2x +3x^2 What is a, b and c ?

A

a = 3, b = -2, c = 5

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17
Q

What are the fractional equivalents of these popular decimals:
0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001

A

1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000

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18
Q

change the probability of 3/5 to a decimal and a percent

A

0.6 or 60%

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19
Q

What is the zero product property?

A

(this)(that)=0 is true when (this)=0 and when (that)=0. this is what we use when solving by factoring.

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20
Q

change the probability 40% to a decimal

A

0.4

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21
Q

Explain what a parabola with two real roots (real zeros) looks like.

A

crosses x axis at those roots, at those x values

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22
Q

How do you solve by isolating the x^2 ? (when can you do it?)

A

When there is no linear term (no x term), simply act like you’re solving for x, but solve for x2 and in the last step, take square root of both sides ( + / - )

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23
Q

change the probability 0.5 to a percent

A

50%

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24
Q

What do we call b^2-4ac

A

the discriminant

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25
Q

can you have more than 100% of something?

A

YES…. if you have more than a whole. (but this can’t be a probability)

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26
Q

what are the decimal equivalents of these popular fractions:

1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000

A

0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001

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27
Q

change the decimal 0.0003 to a percent

A

0.03%

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28
Q

What are the roots of a function? (other names?)

A

the zeros, the x-intercepts, the solutions,where the parabola crosses

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29
Q

f(x) = ax^2 + bx + c What is the constant term?

A

c (it is the y intercept)

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30
Q

If an x intercept is 455, what point is on the line?

A

(455, 0)

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31
Q

what does a slope that is undefined look like?

A

vertical, straight up and down. The y axis has a slope of zero.

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32
Q

why is it called a constant term

A

alone it would be a constant function.. The same height always. a horizontal line with a constant y, a constant height

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33
Q

What is the standard form of a quadratic?

A

ax2+bx+c = 0

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34
Q

How many diamonds in a deck of cards?

A

13

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35
Q

what is the quadratic term’s exponent on the x ?

A

2

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36
Q

f(x)= 3x^2-6x+3 What is the constant term? what is the y intercept?

A

3, it is the also the y intercept

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37
Q

Why can’t you divide by zero? (why can zero be in the top and not the bottom?)

A

10/2 asks “how many times do you add 2 to itself to get to 10?” the answer is 5.
10/0 asks “how many times do you add 0 to istelf to get to 10?” the answer is there is no answer. undefined

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38
Q

where is the vertex located?

A

on the axis of symmetry (highest or lowest point).

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39
Q

What are the three forms of a quadratic that we use?

A

standard: y = ax2-bx-c
factored: y = a (x-r) (x-r)
vertex: a (x-h)2 +k

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40
Q

How can you always get rid of fractions in any equation?

A

Multiply every term by the LCD (plop the LCD in the numerators, then simplify)

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41
Q

What is the gradient of a vertical line?

A

undefined

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42
Q

change the probability 0.04 to a percent

A

4%

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43
Q

one out of three is ____ or ____%

A

about .33 or 33%

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44
Q

how would you solve (3x-2)(x-5)=0 (what are solutions?)

A

set factors = 0 and solve: 3x-2=0 and solve x-5=0 zero product property. The solutions are x = { 5, 2/3}

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45
Q

what is tricky about the vertex form?

A

the -h part.. If its (x+9)2 +8 then h is -9.. remember that x=h is also the AOS !!!

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46
Q

What if you solve simultaneous equations all three ways, what will you notice?

A

they all give the same answer, the same POINT, (x,y)

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47
Q

If the discriminant is zero, what do you know about roots?

A

there is one double root, it is a perfect square, the parabola just touches down x axis without crossing, the vertex is on the x axis.

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48
Q

if there are 10 kids and you are choosing 3 to bring on a trip, how many ways can you do that? (perm or comb?)

A

Combination. nCr with n=10 and r=3

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49
Q

How do you show that a point lies on a line?

A

Show that, when you plug the point in, you get a true mathematical statement.

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50
Q

What are the solutions of a function? (other names)

A

the roots, the x intercepts, the zeros where the parabola crosses

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51
Q

How do you find the vertex of a parabola in standard form? y=ax^2+bx+c

A

the x value is always -b/2a . To get the y value for it, put that x value into the function and solve

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52
Q

what is the tough thing about quadratics?

A

the fact that they are squared.. We have to undo that x2. We want to get it linear!!

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53
Q

What does (A’)’ look like when shading?

A

double negative. (A’)’ = A, so the entire A circle should be shaded.

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54
Q

What is the x coordinate for all y-intercepts?

A

zero. all y intercepts are in the middle, not left or right, because they are on the y axis.

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55
Q

How do you solve by factoring?

A

get stuff all on one side, factor, set each factor = 0, solve each linear equation.

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56
Q

f(x) = a(x-h)^2 + k where it the vertex? what is the Axis of Symmetry?

A

vertex at the point (h, k), the AOS is the vertical line x= h

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57
Q

When you shade a VENN diagram, what does A U B look like?

A

Both circles and the overlap are all shaded (everything inside)

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58
Q

Perpendicular lines have _____ gradients, or slopes

A

OPPOSITE SIGN AND RECIPROCAL

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59
Q

How do you convert from vertex to standard form?

A

square the binomial and combine stuff

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60
Q

What does the discriminant tell us about?

A

about the roots, the zeros, how many x intercepts the parabola has, how many times it crosses the x axis, whether roots are real or imaginary

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61
Q

change the probability of 2/3 to a decimal and a percent

A

about .67 or 67% (.66666666666)

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62
Q

What is the “general” form of a line?

A

Ax + By = C no fractions.

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63
Q

what is the “most popular” form of a line?

A

gradient intercept (slope intercept)

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64
Q

What does the quadratic formula say about finding the x intercepts? (stand where and do what?)

A

stand at the AOS and reach up and down a bit to find the solutions

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65
Q

Geometrically, how is the shape of a parabola made?

A

A parabola is the set of all points equidistant from point, called the focus, and a line, called the directrix.

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66
Q

How many kings in a deck of cards?

A

4

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67
Q

Describe what an axis of symmetry is

A

it is where the parabola can fold onto itself. It is the equation of this vertical line, so you write “x = ___”(-b/2a)

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68
Q

f(x) = a(x-h)^2 + k How do we know if it opens up or down?

A

by the sign of a, if its positive, up, negative , down

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69
Q

what is the slope of a line that goes straight up and down?

A

undefined

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70
Q

when you are given a two way table, what should you always do?

A

PUT IN THE TOTALS ON SIDE and BOTTOM and the OVERALL TOTAL IN THE CORNER

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71
Q

what is the probability of getting 3 tails in a row flipping a coin?

A

1/2 x 1/2 x 1/2 = 1/8

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72
Q

one out of ten is _____ or ____%

A

0.1 or 10%

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73
Q

What are the zeros of y=5(x-3)(2x+1)

A

The zeros, or roots, or x intercepts are at(3, 0) and (-1/2, 0)

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74
Q

What is the discriminant?

A

b2-4ac (notice there is no sq root on it!!)

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75
Q

If the discriminant is zero, how many times does the parabola hit the x axis?

A
  1. hits it and bounces off.
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76
Q

How is the axis of symmetry hidden in the quadratic formula?

A

it is the beginning.. (put both parts over 2a).. -b/2a

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77
Q

What is the quadratic formula?

A

x = -b +- sqroot b squared - 4ac all over 2a (but in formula)

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78
Q

f(x)= 3x^2-6x+3 What is the coefficient of the linear term?

A

-6 this is also known as “b”

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79
Q

What is the gradient-intercept form?

A

y = mx + c

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80
Q

f(x)= 3x^2-6x+3 What is the linear term?

A

-6x

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81
Q

what is the linear term’s exponent on the x ?

A

1

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82
Q

change the probability of 1/4 to a decimal and a percent

A

0.25 or 25%

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83
Q

What is the gradient of a horizontal line?

A

ZERO

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84
Q

How do you solve simultaneous equations by substitution?

A

isolate a variable. SUBSTITUTE into the other equation, solve, then sub back in to find (x,y)

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85
Q

What is the symbol that joins two sets together into one set?

A

A big U , stands for UNION

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86
Q

how can you think of 150% of something?

A

150% of a pizza is one and a half pizzas!! (this can’t be a probability)

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87
Q

What numbers can represent a probability?

A

Always between 0 and 1, examples: 0, .75, .05, 1, .35

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88
Q

change the decimal 0.03 to a fraction

A

3/100

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89
Q

f(x)= -4x^2 + 8 What is a, b and c ?

A

a = -4, b = 0, c = 8

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90
Q

What does A’ mean?

A

The elements not in A

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91
Q

how would you solve 4x^2 - 9 = 13 ? (just say what you’d do)

A

no linear term, so just isolate the x2 and root sides

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92
Q

What is the probability of randomly taking one card and getting a diamond from a deck?

A

13/52 or 1/4

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93
Q

f(x) = ax^2 + bx + c What is the coefficient of the constant term?

A

c (it is the y intercept)

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94
Q

change the decimal 0.0003 to a fraction

A

3/10000

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95
Q

What is the y intercept of a line? (what are the coordinates?)

A

Where the line crosses the vertical axis, the y axis. The coordinates are ( 0, Y )

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96
Q

What is a midpoint?

A

the point halfway along a segment. right in the MIDDLE

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97
Q

f(x)= -4x^2 + 8 What is the axis of symmetry?

A

x= -b/2a = -0/2(-4) = 0/8 = 0. AOS is x=0, which is the y axis!!

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98
Q

change the probability of 1/3 to a decimal and a percent

A

about .33 or 33% (.33333333333)

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99
Q

If the discriminant is negative, what do you know about roots?

A

there are no real roots, 2 imaginary roots, the parabola doesn’t touch x axis

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100
Q

change the probability of 1/2 to a decimal and a percent

A

0.5 or 50%

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101
Q

How do you find the midpoint between two given points?

A

the midpoint has an x and y value, (x,y). the X value is the average of the two x values, and the Y value is the average of the two y values.

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102
Q

change the probability of 2/5 to a decimal and a percent

A

0.4 or 40%

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103
Q

How would you solve 9x^2 - 3x = 0 ? (just say what you’d do)

A

factor out x and set factors=0.. (one solution will be 0)

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104
Q

What is a perpendicular bisector?

A

the line that goes through the midpoint of a segment, and it is also perpendicular to it.

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105
Q

Explain what the graph of a parabola with no real roots (real zeros) looks like.

A

doesn’t touch x axis

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106
Q

If a line as a slope of -5, then any line parallel to it will have a slope of ___ and any line perpendicular to it will have a slope of ___

A

-5 and perp 1/5

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107
Q

why is it called a discriminant?

A

because it discriminates between which type of solutions, roots and zeros you will have (2real, one real or imaginary)

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3
4
5
Perfectly
108
Q

What are the zeros of a function? (other names?)

A

the roots, the x intercepts, the solutions, where the parabola crosses

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109
Q

When is there just one solution to simultaneous equations?

A

when they cross (at one point)

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110
Q

How can you think of %

A

PER 100 (or, divided by 100)

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111
Q

What are the five ways to solve a quadratic?

A

set to zero and factor, complete square, quadratic formula, graph and look for x-intercepts, or when there is no linear term, isolate the x2 and root both sides.

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112
Q

What is the graph of a line showing us? (or a graph of a parabola or any function)

A

It is showing us all of the points, (x,y), that make the equation true. Every dot on the graphed line will make the equation true, they all work.

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113
Q

What is the slope of a line in standard (general) form?

A

-A/B

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114
Q

Are all quadratics similar?

A

YES.. THEY ALL HAVE THE EXACT SAME SHAPE.. They are simply zoom-ins or zoom-outs of eachother..

115
Q

thinking of the quadratic formula, why are there no real roots when you have a negative discriminant?

A

because you have to take the square root of a negative, which is an imaginary number. You end with an imaginary number.. .hence.. Imaginary roots (not real)

116
Q

How do you find the average of two numbers?

A

add them up and divide by 2

117
Q

change the decimal 0.03 to a percent

A

3%

118
Q

If A = { 1, 2 }, how many elements does A have?

A

two

119
Q

When you graph a line or a parabola, what are you actually graphing?

A

THE SOLUTION! Those are all of the points that make the equation true. All of the points that “work”. If you put any other pionts, (x,y) into the equation, they wont work, You will get a false statement.

120
Q

What do students forget about OR ?

A

The OR BOTH part. The union of A and B are all of the elements in A, in B and also the ones that are in BOTH.

121
Q

If we are given an x, like x=5, and need to fine a y that goes with it, how do we find it?

A

substitute the 5 in for the x in the eqution and solve for y, That y value goes with the 5. The point (5, y) will be on the line.

122
Q

How can you tell if the point (5, -3) is on a line or a parabola if you are given the equation?

A

If it “works.” Sub 5 in for the X and -3 in for the Y. Simplify. If the statement is true, then it is a solution. If it is a solution, then it is on the line.

123
Q

Why do parabolas look different if they are all similar?

A

Well…. Simply either imagine zooming way in or zooming way out… this method can always get any 2 parabolas to look the same.

124
Q

If A = { 1, 2, 6} , what is n(A) ?

A

n(A) is the number of elements in A. In this case, n(A)= 3

125
Q

where is the combination button on the calculator?

A

Math > PRB then down to nCr

126
Q

What is the gradient formula? (the slope formula?)

A

m = ( y - y ) / ( x - x )

127
Q

AND goes with ______ [union or intersection]

A

intersection

128
Q

change the probability of 1/5 to a decimal and a percent

A

0.2 or 20%

129
Q

What is solution to:5(x-8)(x+3)=0

A

8 and -3.
(this)(that)=0 situation
this=0 and that=0
we are looking for the x values that make the equation true.. so we want to make x-8=0 and x+3=0

130
Q

Why is it called “gradient-intercept” form? (slope-intercept)

A

There is a gradient and a slope explicitly shown in the formula

131
Q

three out of ten is ____ or ____%

A

0.3 or 30%

132
Q

If the discriminant is positive, how many times does the parabola hit the x axis?

A

2

133
Q

How do you graph a quadratic in standard form?

f(x)=ax^2+bx+c

A

first graph the Axis of symmetry with dotted line, (x= -b/2a) then make a T table and use that x value to find the vertex and use a couple integers near it to find other points. LEAVE SPACE FOR ARITHMETIC. Reflect over the AOS and connect the dots

134
Q

what are the coordinates of a point?

A

(x,y), the x and y value.

135
Q

What is a slightly different form of the general form you may be asked to write an equation in?

A

Ax + By + D = 0 in stead of Ax + By = C

136
Q

What are the fractional equivalents of these popular percents:
50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%

A

1/2, 1/3, 1/4, 1/5, 1/8, 1/10, 1/100, 1/1000

137
Q

If you have 3 pairs of shoes, two pairs of pants and 4 shirts.. how many outfits?

A

324= 24 outfits

138
Q

INTERSECTION goes with _____ [OR or AND]

A

AND

139
Q

If you are given two points and need to find the equation of a line, how do you do it?

A

First, fine the gradient using m=(y-y)/(x-x), then use that gradient and EITHER OF THE POINTS. Put it in point gradient form. (point slope form)

140
Q

How do you know when a parabola is smiling?

A

when a is positive

141
Q

What are the x intercepts of: y=5(x+6)(x-3)

A

at -6 and at 3(they are also called solutions or zeros)

142
Q

If a y intercept is 990, what point is on the line?

A

(0, 990)

143
Q

If the discriminant is positive, what do you know about roots?

A

there are 2 real roots, and the parabola crosses x axis twice..at these roots

144
Q

change the decimal 0.3 to a percent

A

30%

145
Q

f(x)= -4(x-8)^2+6What is vertex and which way does it open?

what is AOS?

A

at (8, 6) and opens downward (has max). The AOS is x=8

146
Q

the number 5/0 is equal to :

A

undefined

147
Q

How many cards in a deck of cards?

A

52

148
Q

What is solution to:g (x+f)(x-w) = 0

A

-f and w(this)(that)=0 situationthis=0 and that=0we want to make equation trueso we solve x+f=0 and x-w=0

149
Q

With two simultaneous linear equations, what are the three options for a solution?

A

No solution, one solution, or an infinite number of solutions.

150
Q

What does (A U B)’ look like when shading?

A

shade just the area outside of the circles.

151
Q

How do you find the max or min value of a quadratic in either form?

A

it is the y value at the vertex. In vertex form, it’s simply k. In standard form, Plug -b/2a into the function to get y.remember to look at “a” + smiles have min.. - frowns have max. OR PUT IN YOUR CALCULATOR AND USE MAX MIN FINDER.

152
Q

If you know that a quadratic has x intercepts at 5 and 3, , what is the factored form?
What is the equation of AOS?

A

factored form: y = a (x-3)(x-5)
aos: x=4
notice aos is average of 3 and 5
(3+5)/2 = 4

153
Q

two out of five is ____ or ____ %

A

0.4 or 40%

154
Q

How do you know when it is a quadratic?

A

when the highest degreed term is the x^2 term (quadrus:square)

155
Q

what completes the square and what is the factored form? x2 + 6x + ____

A

9 completes it and the factored form is (x+3)^2

156
Q

What is the probability of randomly picking one card a red card from a deck?

A

26/52 or 1/2

157
Q

What is the gradient of a flat (horizontal) surface?

A

ZERO

158
Q

How do you solve simultaneous equations by elimination?

A

organize equations so they line up nice. Get coefficients to be opposites. Add equations and solve. Then sub back in to find (x,y)

159
Q

On a number line, what is the midpoint between 8 and 12?

A

at the average: 10. 10 is halfway between 8 and 12. add and divide by 2. 8+12=20. 20/2= 10

160
Q

change the probability 0.8 to a percent and a fraction

A

80% and 4/5

161
Q

What are the decimal equivalences of these popular percents?

50%, 33.3%, 25%, 20%, 12.5%, 10%, 1%, 0.1%

A

0.5 , 0.333, 0.25, 0.2, 0.125, 0.1, 0.01, 0.001

162
Q

Parallel lines have ______ gradients, or slopes

A

the same

163
Q

change the decimal 0.003 to a fraction

A

3/1000

164
Q

two out of three is ____ or ____%

A

about .667 or 66.7%

165
Q

If the discriminant is negative, how many times does the parabola hit the x axis?

A

0

166
Q

If there are 10 kids and you are choosing a president, vp and treasurer, how many ways can you do that? (perm or comb)

A

Permutation. nPr with n=10 and r=3

167
Q

How do you solve simultaneous equations by graphing?

what if they are quadratics?

A

graph both lines and look for the intersection, the solution is the coordinates (x,y) If they are quadratics they could have 2 intersections.

168
Q

Why does AND go with INTERSECTION? A ∩ B = A and B

A

Because you have to be a member of both A and a member of B to be a part of A ∩ B

169
Q

f(x)= 3x - 9 What is a, b and c?

A

a = 0 , b = 3, c = -9..There is no quadratic term..
THIS IS LINEAR!!!
IT’S A LINE!
slope of 3

170
Q

What is the solution to simultaneous equations? (system of equations?)

A

The set of points that satisfies (makes true) all of the equations in the system. In algebra 1, this is just ONE POINT, (x,y), But we will solve quadratic-linear systems that will have 2 solutions.

171
Q

change the probability of 1/10 to a decimal and a percent

A

0.1 or 10%

172
Q

What are the x intercepts of a function? (other names?)

A

the roots, the zeros, the solutions

173
Q

What fractions can represent a probability?

A

Any fraction as long as the top is smaller than the bottom (or equal). IT CAN’T BE TOP HEAVY!

174
Q

When can you just isolate the x^2 and root both sides?

A

when there are no linear terms (only quad and const)

175
Q

What is the symbol that just takes the overlap of two sets?

A

An upside down U, look like this: ∩, INTERSECTION

176
Q

f(x) = ax^2 + bx + c What is the linear term?

A

bx (the term is the whole thing)

177
Q

thinking of the quadratic formula, why are there 2 real roots when the discriminant is positive?

A

because there is a square root of a positive, you will have to + and - that in the top, giving 2 different real solutions.

178
Q

What are the gradients (slopes) of the diagonals of a square?

A

+1 going up L to R, and -1 going down from L to ROW

179
Q

f(x)= 6x^2- 7x What is a, b and c ?

A

a = 6, b=-7, c = 0

180
Q

What is a way to help shading in VENN diagrams?

A

Label the areas 1, 2, 3 and 4. Let A= {1,2} B= {2,3} , intersection is {2} and outside of the circles {4).

181
Q

f(x)= (x+9)^2-8 What is vertex and is it a min or a max?

A

at (-9, -8) and it is a minimum

182
Q

How could simultaneous quadratic equations have no solutions?

A

two parabolas curving away from eachother and never crossing is one possibility.

183
Q

Does “a” have to be equal to 1 when completing a square?

A

YES

184
Q

if you know that the x intercepts of a parabola are at (-3, 0) and (9,0), what is the factored form and what is AOS?

A

factored form: y= a (x+3) (x-9)
aos at x = (-3+9) / 2 = 6/2
aos at x=3

185
Q

What are simultaneous equations? (system of equations)

A

a group of equations

186
Q

f(x)= 3x^2-6x+3 What is the coefficient of the constant term?

A

3 this is also known as “c”

187
Q

What is the probability of randomly taking one card and getting a king from a deck?

A

4/52 or 1/13

188
Q

f(x)= 3x^2-6x+3 What is the quadratic term?

A

3x^2

189
Q

what is point-gradient form? (point slope)

A

A rearrangement of the gradient formula: y-y =m (x-x)

190
Q

How can centimeters and a meter stick help you think of percent?

A

Think of centimeters as “PERCENTIMETERS”.. each one is one percent of a meter. 35cm is 35% of a meter.

191
Q

What are the three ways we solve simultaneous equations?

A

Graphing (and looking for intersection), substitution and elimination

192
Q

How do you know when a parabola is frowning?

A

when a is negative

193
Q

change the probability 0.5% to a decimal

A

0.005

194
Q

How could simultaneous equations have exactly two solutions?

A

Imagine a line and a parabola. the line could cross the parabola twice.

195
Q

What is an interesting fact about slopes between -1 and +1?

A

HALF OF ALL POSSIBLE SLOPES ARE BETWEEN -1 and +1 (and they are perpendicular)

196
Q

When we graph a parabola to solve a quadratic, what do we look for?

A

look for the x intercepts, these are the roots. The zeros, the solutions

197
Q

If a line as a slope of 2/3, then any line parallel to it will have a slope of ___ and any line perpendicular to it will have a slope of ___

A

2/3 and perp -3/2

198
Q

If there is no constant term, what is an easy way to factor?

A

just factor out the x and set the factors to zero (one solution is zero)

199
Q

four out of five is ____ or ____%

A

0.8 or 80%

200
Q

why are they called “quadratics?”

A

from latin “quadrus” which means SQUARE

201
Q

What do the probabilities on the branches leaving a single node in a tree diagram have to add to?

A
  1. If you have two branches, then they should add to 1, if you have five branches from same node, all five added together should equal 1.
202
Q

When you shade a VENN diagram, what does A ∩ B look like?

A

Just the overlap sliver in the middle is shaded.

203
Q

With tree diagrams, what does MA.AD stand for?

A

Multiply across, Add down

204
Q

What is the equation of the y axis?

A

x=0

205
Q

If we are given a Y value, like y-8, and need to find the x that goes with it, how do you do it?

A

substitute the 8 in for the y in the equation and solve for x. That x goes with the 8. the point (x, 8) will be on the line.

206
Q

What are solutions to (x+8)(x-3) = 0

A

x = { -8, 3} this is not a point on the graph, it is a set of two numbers that make the equation true. They are also the x intercepts of the parabola

207
Q

can you have a probability of 5/3?

A

NO… that is more than 1

208
Q

What does it mean to “satisfy” an equation?

A

Make the equation true.

209
Q

What are the three forms of a quadratic function?

A

Standard y=ax^2+bx+c
Vertex y=a(x-h)^2+k
Factored y= a(x-r)(x-r)

210
Q

What is the eqution of a horizontal line that goes through the y axis at 8?
How can you think about it to help you?

A

y = 8. Since y is the height, you can think of it as all of the points that have a height of 8. Also, you can think of it as all of the points that have a y value of 8, so you are a solution if your y value is 8.

211
Q

Why is it called “point-gradient” form?

A

There is a point and a gradient explicitly shown in the form

212
Q

f(x)= 6x^2- 5x What is the axis of symmetry?

A

x= -b/2a = -(-5)/2(6) = 5/12, AOS x= 5/12

213
Q

How do you find the equation of a perpendicular bisector?

A

Find the point and the gradient (slope) and put it in point-gradient form. The point is the midpoint (use averages) and the slope is the RECIPROCAL and OPPOSITE of the slope between the two given points.

214
Q

can you have a probability of 3/5?

A

Yes, that’s 60%

215
Q

thinking of the quadratic formula, why is there only one real root when the discriminant is zero?

A

because the square root of zero is zero, so you are going to + and - zero… the quad formula reduces to -b/2a .. The only root is the axis of symmetry (the vertex is on the x axis)

216
Q

change the probability of 0.45 to a percent

A

45%

217
Q

change the probability 0.04% to a decimal

A

0.0004

218
Q

How do we handle that squared term? how can we undo it?

A

by either splitting the x’s apart by factoring, or by taking a square root somewhere..

219
Q

What is the equation of the axis of symmetry?

A

x = -b / 2a
x= opposite b / twice a
(notice it is the equation of a vertical line)

220
Q

Does “a” have to be equal to 1 when doing quadratic formula?

A

NO

221
Q

How do you know if a parabola in standard form opens upward (smile) or down (frown)?

A

if “a” is pos it opens up. if a is negative, it opens down. Positive people smile, negative people frown.

222
Q

change the probability 0.0003 to a percent

A

0.03%

223
Q

can you have a probability of 0.5?

A

Yes, that’s 50%

224
Q

How do a lot of people think about the gradient

(the slope)?

A

rise/run… or change in y / change in x

225
Q

Can you have a probability of 3.5?

A

NO. probabilities are between 0 and 1

226
Q

change the probability of 3/4 to a decimal and a percent

A

0.75 or 75%

227
Q

What is probability?

A

The likelihood of an event happening.

228
Q

can you have a percent of 5/4 ?

A

YES! that would be 125%….. (this can’t be a probability)

229
Q

one out of five is ____ or ____%

A

0.20 or 20%

230
Q

change the decimal 0.003 to a percent

A

0.30%

231
Q

Explain what a parabola with one real root (real zero) looks like.

A

just touches x axis at one spot, the root (the zero), it doesn’t cross it, it bounces off it, called a “double root”, the vertex is on the x axis

232
Q

How do you know if a parabola has a max or minimum by looking at the function in standard form?

A

if “ a” is pos, it has a min. if ‘a’ is negative, it has a max

233
Q

what completes the square and what is the factored form? x^2 - 8x + ____

A

16 completes it and the factored form is (x-4)^2

234
Q

f(x) = a(x-h)^2 + k
How do we know if it has max or min?
what is the AOS?

A

by the sign of a, if its positive it opens up so it has a MIN, negative it opens down so it has a MAX.
aos at x=h

235
Q

change the probability of 4/5 to a decimal and a percent

A

0.8 or 80%

236
Q

How do you solve by completing the square?

A

get all quadratic and linear term on one side and bring constant term over to other…. Make sure a=1, take half of b and square it, add it to both sides. Factor, root, solve

237
Q

what does a slope of zero look like?

A

horizontal, flat from left to right. The x axis has a slope of zero.

238
Q

What is the gradient of a line?

A

the slope, the steepness

239
Q

UNION goes with ______ [OR or AND]

A

OR

240
Q

What is the the difference between theoretical and experimental probability?

A

theoretical is from thinking of all of the possibilities and doing it with math, experimental is the #successes/total attempts you observe.

241
Q

Why is it called a “linear” term

A

alone its graph would be a straight line

242
Q

What is the y coordinate for all x-intercepts?

A

zero. all x intercepts have a height of zero because they are on the x axis.

243
Q

the number 0/5 is equal to :

A

zero. 0

244
Q

Do all quadratic functions have x intercepts?

A

No, some don’t touch the x axis.. These have imaginary roots and a negative discriminant

245
Q

Difference between a Permutation and a Combination?

A

Permutation is choosing and Placing in a Particular Place, Combinations are just choosing

246
Q

what is difference between (3, -2) and {3, -2}

A

the first is a point on a plane (over 3, down 2) and is in parentheses… The second set are numbers in braces, so it is simply a set containing two values, 3 and -2. It is not a point on a plane, the order does non matter in braces.

247
Q

What is the midpoint of (4, 5) and (6, 15). (think, the average of 4 and 6, and the average of 5 and 15

A

average of 4 and 6 is 5. the average of 5 and 15 is 10. so at (5, 10)

248
Q

f(x) = ax^2 + bx + c What is the coefficient of the quadratic term?

A

a

249
Q

What is the equation of the x axis?

A

y = 0

all horizontal lines are in the form y=something

250
Q

What is a solution to an equation?

A

A solution is the set of values that makes an equation TRUE.

251
Q

How can you find the x intercepts from an equation of a line?

A

Plug zero in for Y, and solve for X. The coordinates will be ( X, 0)

252
Q

How can you find the y intercepts from an equation of a line?

A

Plug zero in for X and solve for Y. The coordinates wll be (0, Y)

253
Q

Why does OR go with UNION, ex. A U B = A or B

A

Because you are part of the union as long as you are a part of A or B or BOTH

254
Q

f(x)= 3x^2-4x+5 What is a, b and c ?

A

a = 3, b = -4, c = 5

255
Q

change the probability 5% to a fraction

A

1/20 (one out of 20)

256
Q

change the decimal 0.3 to a fraction

A

3/10

257
Q

The three forms of equations of a line we use are :

A

point-gradient form, gradient-intercept form, general form

258
Q

f(x) = ax^2 + bx + c What is the quadratic term?

A

ax2

259
Q

f(x)= 3x2-6x+3 What is the axis of symmetry?

A

-b/2a = -(-6)/2(3) = 6/6 = 1

260
Q

What is the vertex form of a quadratic?

A

f(x) = a(x-h)^2 + k

261
Q

If there is no linear term, what is an easy way to solve?

A

simply isolate the x^2 and root both sides.

262
Q

OR goes with______ [union or intersection]

A

union

263
Q

one out of twenty is ____ or _____%

A

0.05 or 5%

264
Q

How can you think of a slope of 1 or -1?

A

A perfect diagonal of a square, 45 degrees!

265
Q

change the probability of 1/8 to a decimal and a percent

A

0.125 or 12.5%

266
Q

In general, what are we looking for with two simultaneous linear equations?

A

THE INTERSECTION! (X, Y) ! the intersection is the solution, it is the point that makes both equations true, it satisfies both equations.

267
Q

What is the equation of a vertical line that goes through the x axis at 7?
How can you think of that line to help make sense of it?

A

x = 7. You can think all of the points that are over 7 to the right.. or “all of the points on this line have an x value of 7, so you are a solution as long as your x=7.

268
Q

where is the permutation button on the calculator?

A

Math > PRB then down to nPr

269
Q

Do all quadratics have a y intercept

A

YES… All quadratics have exactly 1 y-intercept.. (c).. if there is no constant term, the y intercept is 0, so the parabola passes through the origin!!!!

270
Q

f(x)= 3x^2-6x+3 What is the coefficient of the quadratic term?

A

3 this is also known as “a”

notice that 3x^2 is the entire quadratic term, 3 is just he coefficient.

271
Q

change the probability of 6% to a decimal

A

0.06

272
Q

How can you always find the y intercept of a line?

A

plug zero in for x and find the y. y intercept at (0, y)

273
Q

how can you always find the x intercept of a funciton

A

plug zero in for y and find the x or x’s. x intercept at (x,0)

274
Q

what are the three forms of a linear equation?`

A

standard (general): Ax + By + C = 0
slope (gradient) intercept: y = mx + b
point - slope (gradient): y-y = m (x-x)

275
Q

How can you use calculator to find aos?

A

Graph the parabola, then use MAX or MIN. the x value is the AOS.

276
Q

What is a cool feature you can use when tracing along a graph on your calculator?

A

While tracing, you can type any x value and it will give you the y value for that x , and hence, the coordinates (x,y)

277
Q

what does the line y=x look like?

A

an uphill diagonal of a square. It goes from bottom right to top left.

278
Q

what does the line y= - x look like?

A

A downhill diagonal of a square. It goes from top left to bottom right.

279
Q

What does line y= -4 look like?

A

a HORIZONTAL (left to right) line through y=-4. It is below the x axis. All of the points on the line have a y value of -4.

280
Q

What does the line x = 8 look like?

A

a VERTICAL line (up and down) through x = 8. it is to the right of the y axis. All of the points on the line have an x value of 8.

281
Q

what is the equation of the x axis?

A

y = 0 (all of the points on x axis have a y value of zero)

282
Q

what is the equation of the y axis?

A

x = 0 (all of the points on the y axis have an x value of zero)

283
Q

what does y=0 look like?

A

It is the x axis. all of the points on x axis have a y value of zero.

284
Q

what does x=0 look like?

A

It is the y axis. All of the points on the y axis have an x value of zero.

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