Checkpoint Unit 1 - 30 Flashcards
These flashcards cover all the theorems, formulae, and concepts you need to know for Units 1 - 30 (91 cards)
1
Q
Indices multiplication rule
A
Add powers
2
Q
Indices division rule
A
Subtract powers
3
Q
Indices bracket rule
A
Multiply powers
4
Q
A number with 0 index = ?
A
1
5
Q
Negative powers mean what?
A
Reciprocal or 1 over
6
Q
How to write in Standard Form?
A
a x 10^n where a is greater than or equal to 1 and less than 10. n is the power and can be positive or negative.
7
Q
Standard form with negative power means?
A
A small number. Less than 1.
8
Q
What do you get with a Standard form number with a power greater than 1?
A
Large number. Greater than 10.
9
Q
Pythagoras formula for finding long length?
A
h = SQRT( a^2 + b^2)
10
Q
Pythagoras formula for finding short length?
A
b = SQRT(h^2 - a^2)
11
Q
How to find height of a equilateral triangle with lengths given?
A
Divide inot 2 right angled triangles and use one to find height with pythagoras.
12
Q
Types of Quantitative data?
A
Discrete and Continuous.
13
Q
Types of Qualitative Data?
A
Ordinal and Nominal
14
Q
Examples of Quantitative data and type.
A
Weight - continuous, Count of something - discrete
15
Q
Examples of Qualitative Data?
A
Hair colour - norminal or categorical. Grades - ordinal.
16
Q
Formula for circumference of a circle?
A
2 x pi x r or pi x D
17
Q
Formula for the area of a circle
A
pi x r^2
18
Q
What does BIDMAS stand for?
A
Brackets, Indices, Division, Multiplication, Addition, Subtraction. Left to Right.
19
Q
How to convert from km to cm?
A
Multiply by 100000
20
Q
Converting 1000 nanometre to metre?
A
Divide by 1000000
21
Q
Converting 10 gigabyte to megabyte?
A
10000 mb
22
Q
What types of correlations can you have?
A
Positive, Negative, or no correlation.
23
Q
Explain weak and strong correlation.
A
Weak - scattered. Strong - close together
24
Q
How to draw a Stem and Leaf Chart
A
Put numbers in order. Create a stem with the largest numbers. Put the leafs in, repeating any that repeat, down the stem.
25
How to find the volume of a prism?
Cross-sectional area multiplied by length.
26
Formula for the area of a triangle?
1/2 x b x h
27
What is a net?
It is the shape you get when you lay a 3d shape out flat.
28
How many sides does a cube have?
6
29
How many surfaces does a cylinder have?
3. 2 circles and a rectangle.
30
How to calculate surface area?
Draw a net. Calculate the area of each part. Add them together. Remember to put units in.
31
What is a rational number?
It can be written as a fraction. It terminates as a decimal or is recurring.
32
What is an irrational number?
One that cannot be written as a fraction, does not terminate. The square root of any non-square number is irrational.
33
What is an independent event?
One that does not depend on the previous event. E.g. tossing a coin.
34
What are mutually exclusive events?
Events that cannot occur at the same time. e.g. getting a heads and a tail.
35
What is a complimentary event?
Refers to the opposing events. Heads is the complimentory event to Tails.
36
What probability do complimentary events add up to?
1 or 100%
37
What is experimental probability?
The probablilty you get from doing an experiment. E.g. tossing a coin 100 times and recording the results.
38
How do you write an inequality for Upper and Lower Limits
25 =< N < 40
N is greater than or equal to 25 (UL) and less than 40 (UL)
39
How would you draw the Upper and Lower limits on a number line.
Full circle is less than or equal to, empty circle is less than.
40
What are the Upper and Lower limits of 10.1?
Lower limit = 10.05
Upper limit = 10.15
41
What is the Mode?
The Statistic with the highest frequency.
42
What is the Median
The middle Statistic. If sample size is even, add both on either side and divide by 2.
43
How do I calculate the Mean?
The overall total statistic divided by the sample number.
44
What are all the headings for a frequency table with a Class Interval?
Class Interval, Mid-interval Value, Frequency, Cumulative Frequency, Mid-interval x Frequency
45
What are congruent parts?
3D shapes that are exactly the same.
46
What is a plane of symmetry?
A plane that cuts a 3D object into two congruent parts.
47
Name 4 types of Transformation.
Rotation, Translation, Reflection, Enlargement.
48
What are the two key bits of information for an Enlargement?
Centre of enlargement and scale factor.
49
What is the rule that makes a fraction a recurring decimal?
A fraction in its lowest terms with a multiple of a Prime number for the denominator, except for 2 or 5 will always produce a recurring decimal.
50
Explain the steps to add or subtract fractions.
Convert factions to the same common denominator. Add or subtract the numerators of the fractions together. Simplify the fraction.
51
Explain the steps to multiply fractions.
Convert to improper fractions if necessary. Multiply numerators, multiply denominators, simplify the fraction.
52
What is a(2a + b)
2a^2 + ab
53
What is (x + 1)(x +3)
x^2 + 4x + 3
54
What is (p +3)(p - 2)
p^2 + p - 6
55
What is the number in front of variables (letters) called?
The coefficient of that variable or letter.
56
What is 2a^8/a^5?
2a^3
57
What is (4b^2 x b^3) / 2b^4?
2b
58
What is [(x + 2)(x - 3)]/(x + 2)
(x - 3)
59
What are combined events?
Two or more events occurijng one after another.
60
What are independent events and give an example?
Combined events where the fist event does not affect subsequent events (the second event is not dependent on what happens in the first event). E.g. tossing a coin or throwing dice.
61
What are the probabilities of combined events called?
Outcomes.
62
How do you canculate the probability of an outcome?
You muliply the probabailities along the branches of that outcome.
63
Only A or B can happen. If the probability of A happening is 23%, what is the probability of B happening>
76%
64
What is the formula for finding the interior angle of a regular polygon?
Interior angle = Sum of Interior Angles / Number of sides. Or 180 - exterior angle.
65
What is the formula for finding the size of an exterior angle of a regular polygon?
Exterior angle = 360/Number of sides, or 180 - interior angle.
66
What does making something the subject of the formula mean?
It means that it becomes the only thing on the left hand side pf the formula and the rest is on the right hand side. E.g. b = 2x + 5, b is the subject of the formula.
67
What is theoretical probability?
What is expected to happen. E.g. the theoretical probability of getting a head in a coin toss is 50%.
68
What is relative frequency? How do you calculate it?
It is the observed frequency of something happening (also known as the experimental probability). If we toss a coin 50 times the relative frequency of heads is the number of times we get heads. Relative frequency = observed frequency / number of trials.
69
What is expected frequency and how doo we calculate it?
It is the number of times we expect something to happen based on theoretical probability. For example, if we toss a coin 50 times, we expect to get 25 heads. Expected frequence = number of trials x theoretical probability.
70
What does a solid circle on a Number Line mean?
Greater than or equal to, or Less than or equal to.
71
What does a hollow circle mean on a number line?
Greater than or less than.
72
Rewrite -2x > 4
- 2 > x or x < - 2
73
In a sequence, how can you tell if it is linear?
The first differences are all constant or the same.
74
In a sequence, how can you tell if it is non-linear.
The first differences are not constant. If the second differences are constant, then the sequence is quadratic.
75
What is the rule in a sequence?
The difference from term to term.
76
Explain how to find the general rule for finding the nth term in a linear sequence, given first difference = D, term = T and number = N.
N = D(T-1) + first number or
N = DT + constant (we canculate)
77
What is the next 2 terms in this sequence?
3, 6, 11, 18?
DIfferences are 3, 5, 7 and the next 2 would be 11 and 13. So, the next 2 terms are 29 and 42.
78
How to increase a number by a percentage?
1 + percentage/100 * number.
79
How to decrease a number by a percentage?
1 - percentage/100 * number.
80
What is compound interest?
It is interest that is accumulated over a period of time. The interest from 1 year is added to the amount that earns interest. So the interest earns interest.
81
How do you calculate compound interest at 5% over 3 years for $100?
100 * (1.05)^3
82
If an object has perimeter P and area A and is increased by a scale factor of 2 what is the new measurements?
Perimeter increases to 2P. and area increases to 4P (we need to square the scale factor). For volume we need to cube it.
83
What sort of graph does a quadratic equation give you?
A quadratic equation has a squared term in it, e.g. x^2. The plot is either a smooth U or a a smooth upside-down U.
84
How do you write a coordinate point?
(x-co-ordinate, Y-co-ordinate)
85
What is the formula for finding mid-points?
((x1 + x2)/2 , (y1 + y2)/2)
86
What is a surd?
It is an irrational number (does not terminate). It is a root of a number that does not produce a integer result. For example the square-root of 4 is 2, so it is not a Surd.
87
What is the equation for a straight line and what is the gradient and y-intercept.
y = mx + c. m is the gradient and is change in y/change in x. c is the y-intercept, and can be 0.
88
Do you work out a bearing?
Start with North, go clockwise, measure the angle using 3-digit numbers.
89
What are the three forms of proportion?
Ratio, Fraction and Percentage.
90
Explain a direct and inverse proportion.
If x and y are proportional then a directly proportion means that when x increases y increases. For a inverse proportionality, as x increases, y decreases.
91
How do you find time when given distance and speed?
Time = distance / speed.
Speed = distance / time.
