Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

MATHS 12 > Exam Revision > Flashcards

Exam Revision Flashcards

Revise for exams

1
Q

N = ?

A

the set of positive integers and zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Z = ?

A

the set of all integers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Z+ = ?

A

the set of positive integers without zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Q = ?

A

the set of all rational numbers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Q+ = ?

A

the set of positive rational numbers without zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

R = ?

A

every number

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

R+ = ?

A

any number greater than zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Irrational = ?

A

infinite numbers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

How to solve simultaneous equations

A

SSLE or graphing intersection

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Solution of quadratic equations ?

A

If x^2 = k, then = +/- SqRt (k)
= x-axis
= solutions of polynomials

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Does x,y satisfy the equation? how does this work

A

substitue x and y into the equation and then compare answer to equation on the graph –> is there a point with those values

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

how to find y-intercept

A

let x = 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

how to find x-intercept

A

let y = 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Finding the quadratic equation from a graph

A

Factorised form = x-intercept + point –> y = (x-a)(x-b)
Expanded form = any 3 points –> y = ax^2 + bx + c
–> substitute x-intercept values for a + b
–> add lettered variable “k” after y
–> solve for “k”
–> rearrange equation to y = k(x-a)(x-b)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

Finding the quadratic equation in expanded form

A 
3 points
enter coordinates in SPREADSHEET
label columns
menu-->Stats-->stat calcs--> option 6
Sub in
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

finding the equation of a line

A

the gradient + point on the line

two points on the line

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

R- = ?

A

all numbers less than zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Z- = ?

A

negative integers without zero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

representing number of elements in a set

A

n(A) = 6

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

what is a subset

A

If p and q are two set and all of the elements of p are in q then
–> (2,4,6)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

Intersection

A

elements that are COMMON in both sets

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Union

A

all elements in both sets

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Disjointed sets

A

neither sets have elements in common

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

How do you writie set notation

A
  • X < 3 = (-infinity, 3]
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

what is the compliment

A

the compliment of A is everything not in A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

how many mm–>cm–>m–>km

A

mm x10 = cm x100 = m x1000 = km

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

Area conversions mm^2 –> cm^2 –> m^2 –> ha

A

x100 –> x10,000 –> x10,000 –> x100

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

Volume conversions mm^3 –> cm^3 –> m^3 –> km^3

A

x10 = x100 = 1000

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

How to solve right angle triangle with 1 angle + 1 side

A

If side = 20cm and angle = 59 degrees

then –> nSolve (Sin/Tan/Cos (59) = 20/x,x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

Finding the area of a triangle

A

If we have Height + Base = 1/2bh

If we have 2 side + included anngle = 1/2(a)(b)Sin(C)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

Cosine rule - what and when

A

Used for NON RIGHT-ANGLE TRIANGLES
When 2 side + included angle = A^2 formula
When 3 sides = Cos(A) formula

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

Sine rule - what and when

A

Used for NON RIGHT-ANGLE TRIANGLES
When 2 angles + 1 side –> a/SinA formula to find side
When 2 sides + non-included angle –> SinA/a formula to find angle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

common difference

A

d = U1 + 1 - Un

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

Arithmatic mean

A

b = A+C/2

35
Q

Common ratio

A

Un + 1 / Un

36
Q

Geometric mean

A

b^2 = (a)(c)

37
Q

what is a relation

A

a finite number of ordered pairs

or - any set of powers which connect two variables (e.g: x and y)

38
Q

what is a function

A

a relation in which no two different ordered pairs have the same x co-ordinate

39
Q

how to test for a function

A

if we draw a vertical line on the graph the relation is a function if each line cuts the graph no more than once

40
Q

what is a domain

A

the set of x-values in the relation

41
Q

what is a range

A

the set of y-values in the relation

42
Q

Domain and range notation

A

Domain x E (-1,infinity)

Range y E (-3, infinity)

43
Q

equation of an exponential function

A

y = ka^x + c

44
Q

Key features that must be shown when sketching all graphs

A
  1. x-intercept + y-intercept (co-ordinates)
  2. turning points
  3. asymptotes –> horizontal + vertical
  4. state any restrictions on domain and range
45
Q

Catagorical data

A

divided into catagories

e.g: male + female

46
Q

numerical data

A

data has a numerical value

47
Q

Discrete data

A

an exact value and is often the result of counting

48
Q

Continuous data

A

can take any numerical value within a range and is often a result of measuring

49
Q

Measures of spread

  • range
  • IQR
  • Standard deviation
A

range = max value - min value
IQR = Upper quartile - lower quartile
Standard deviation = use calc

50
Q

how to make Line of Best Fit by eye

A
  1. calculate mean of x and mean of y
  2. plot the mean point of x-mean and x-y on a scatter plot
  3. draw a line through mean point which best fits the trend of the data
51
Q

Null Hypothesis

A 
H0 = x and y are independant
H1 = x and y are not independant
52
Q

Expected values

A

Var = stat exp.matrix

53
Q

When do you reject or accept the hypothesis?

A

If chi>k –> reject H0

If chi accept H0

54
Q

When are two events independent

A

If Pr (A ^ B) = Pr (A) x Pr (B)

55
Q

When are two events dependant

A 
If Pr (A then B) = Pr (A) x Pr (B given A has occured)
--> Pr (B/A) = Pr (B intersection A) / Pr (A)
56
Q

What is Pr (AuB) equal to

A

Pr (AuB) = Pr (A) + Pr (B) - Pr (A ^ B)

57
Q

Formula for conditional probability

A

Pr (A/B) = Pr (A ^ B) / Pr (B)

58
Q

Logical propositions

A

can be true / false / indeterminate

59
Q

Compound propositions

A

propositions that include ‘and’ + ‘or’

60
Q

What is a conjunction

A

symbol is ^ and the word used is ‘and’

61
Q

What is a disjunction

A

symbol is upside down ^ and the word used is ‘or’

62
Q

What is exclusive disjunction

A

True if –> x or y but not both

symbol is upside down ^ with underline

63
Q

What is a tautology

A

a tautology is a compound proposition if all the values in the truth table column are true

64
Q

Logical contradiction

A

a logical contradiction is a compound proposition if all the values in the truth table column are false

65
Q

What is logical equivalent

A

when both columns in a truth table are identical

66
Q

Converse of a statement

A

q –> p

p –> q (converse)

67
Q

Inverse of a statement

A

q –> p

-q –> -p (inverse)

68
Q

Calculus: Average rate of change

A

gradient of a line between 2 points

y2-y1 / x2-x1

69
Q

Contrapositive of a statement

A

q –> p

-p –> -q

70
Q

Derivative function

A

gives the gradient of a function at a point

71
Q

How to find the equation of a tangent

A

find a point
substitute x value into derivative to find gradient
nSolve for C

72
Q

How to find equation of the normal (perpendicular) to an equation

A

find point
substitute x value into derivative to find gradient
reverse the gradient
Nsolve for C

73
Q

when does a stationary point occur

A

when the gradient = 0

74
Q

types of stationary points

A

maximum, minimum, inflexion

75
Q

global maximums + global minimums

A

the maximum / minimum for the entire domain

76
Q

local maximum + local minimum

A

occur at turning points

77
Q

two ways to find stationary points

A
  1. graph the function and find the max / min

2. find derivative of the function –> solutions of polynomials –> substitute x value into equation for y value

78
Q

what does dy/dx give other than derivative

A

rate of change

–> gives the rate of change in y with respect to x

79
Q

how to apply differential calculus (derivative) and find the time rate of change?

A
  1. find dy/dx
  2. substitute value in for x
  3. if dy/dx is > 0 then it is increasing
    - – if dy/dx is < 0 then it is decreasing
80
Q

general rates of change

A

other rate problems can be treated the same way as those involving time
–> E.g: the cost of manufacturing x items has the cost function of C (x) dollars.

81
Q

How to work out optimisation problems

A
  1. draw a large clear diagram of the situation (shape)
    - -> create a formula for the volume of the shape
    - –> E.g: 4000 = x^2y
  2. construct a formula with the variable to be optimised as the subject
    - -> E.g: A(x) = x^2 + 16000x^-1
  3. Find the derivative and fine the value of x where it is zero
    - -> E.g: A’(x) = 2x - 16000x^-2
    - -> E.g:
  4. show using a sign diagram or a graphical test that you have a maximum or a minimum
82
Q

What is the equation of normal distribution?

A

(x ~ N (u, 6^2)
u = mean
6^2 = standard deviation

83
Q

What are the normal distribution boundaries

A
  1. 13%
  2. 15%
  3. 59%
  4. 13%
84
Q

What are the mean boundaries for normal distribution

A

-36
-26
-6
0
+6
+26
+36

MATHS 12 (2 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions