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09MATC 2023 > Checkpoint Unit 1 - 30 > Flashcards

Checkpoint Unit 1 - 30 Flashcards

These flashcards cover all the theorems, formulae, and concepts you need to know for Units 1 - 30

1
Q

Indices multiplication rule

A

Add powers

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2
Q

Indices division rule

A

Subtract powers

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3
Q

Indices bracket rule

A

Multiply powers

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4
Q

A number with 0 index = ?

A

1

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5
Q

Negative powers mean what?

A

Reciprocal or 1 over

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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.

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7
Q

Standard form with negative power means?

A

A small number. Less than 1.

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8
Q

What do you get with a Standard form number with a power greater than 1?

A

Large number. Greater than 10.

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9
Q

Pythagoras formula for finding long length?

A

h = SQRT( a^2 + b^2)

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10
Q

Pythagoras formula for finding short length?

A

b = SQRT(h^2 - a^2)

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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.

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12
Q

Types of Quantitative data?

A

Discrete and Continuous.

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13
Q

Types of Qualitative Data?

A

Ordinal and Nominal

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14
Q

Examples of Quantitative data and type.

A

Weight - continuous, Count of something - discrete

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15
Q

Examples of Qualitative Data?

A

Hair colour - norminal or categorical. Grades - ordinal.

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16
Q

Formula for circumference of a circle?

A

2 x pi x r or pi x D

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17
Q

Formula for the area of a circle

A

pi x r^2

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18
Q

What does BIDMAS stand for?

A

Brackets, Indices, Division, Multiplication, Addition, Subtraction. Left to Right.

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19
Q

How to convert from km to cm?

A

Multiply by 100000

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20
Q

Converting 1000 nanometre to metre?

A

Divide by 1000000

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21
Q

Converting 10 gigabyte to megabyte?

A

10000 mb

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22
Q

What types of correlations can you have?

A

Positive, Negative, or no correlation.

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23
Q

Explain weak and strong correlation.

A

Weak - scattered. Strong - close together

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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.

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25
Q

How to find the volume of a prism?

A

Cross-sectional area multiplied by length.

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26
Q

Formula for the area of a triangle?

A

1/2 x b x h

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27
Q

What is a net?

A

It is the shape you get when you lay a 3d shape out flat.

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28
Q

How many sides does a cube have?

A

6

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29
Q

How many surfaces does a cylinder have?

A
  1. 2 circles and a rectangle.
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30
Q

How to calculate surface area?

A

Draw a net. Calculate the area of each part. Add them together. Remember to put units in.

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31
Q

What is a rational number?

A

It can be written as a fraction. It terminates as a decimal or is recurring.

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32
Q

What is an irrational number?

A

One that cannot be written as a fraction, does not terminate. The square root of any non-square number is irrational.

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33
Q

What is an independent event?

A

One that does not depend on the previous event. E.g. tossing a coin.

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34
Q

What are mutually exclusive events?

A

Events that cannot occur at the same time. e.g. getting a heads and a tail.

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35
Q

What is a complimentary event?

A

Refers to the opposing events. Heads is the complimentory event to Tails.

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36
Q

What probability do complimentary events add up to?

A

1 or 100%

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37
Q

What is experimental probability?

A

The probablilty you get from doing an experiment. E.g. tossing a coin 100 times and recording the results.

38
Q

How do you write an inequality for Upper and Lower Limits

A

25 =< N < 40
N is greater than or equal to 25 (UL) and less than 40 (UL)

39
Q

How would you draw the Upper and Lower limits on a number line.

A

Full circle is less than or equal to, empty circle is less than.

40
Q

What are the Upper and Lower limits of 10.1?

A

Lower limit = 10.05
Upper limit = 10.15

41
Q

What is the Mode?

A

The Statistic with the highest frequency.

42
Q

What is the Median

A

The middle Statistic. If sample size is even, add both on either side and divide by 2.

43
Q

How do I calculate the Mean?

A

The overall total statistic divided by the sample number.

44
Q

What are all the headings for a frequency table with a Class Interval?

A

Class Interval, Mid-interval Value, Frequency, Cumulative Frequency, Mid-interval x Frequency

45
Q

What are congruent parts?

A

3D shapes that are exactly the same.

46
Q

What is a plane of symmetry?

A

A plane that cuts a 3D object into two congruent parts.

47
Q

Name 4 types of Transformation.

A

Rotation, Translation, Reflection, Enlargement.

48
Q

What are the two key bits of information for an Enlargement?

A

Centre of enlargement and scale factor.

49
Q

What is the rule that makes a fraction a recurring decimal?

A

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
Q

Explain the steps to add or subtract fractions.

A

Convert factions to the same common denominator. Add or subtract the numerators of the fractions together. Simplify the fraction.

51
Q

Explain the steps to multiply fractions.

A

Convert to improper fractions if necessary. Multiply numerators, multiply denominators, simplify the fraction.

52
Q

What is a(2a + b)

A

2a^2 + ab

53
Q

What is (x + 1)(x +3)

A

x^2 + 4x + 3

54
Q

What is (p +3)(p - 2)

A

p^2 + p - 6

55
Q

What is the number in front of variables (letters) called?

A

The coefficient of that variable or letter.

56
Q

What is 2a^8/a^5?

A

2a^3

57
Q

What is (4b^2 x b^3) / 2b^4?

A

2b

58
Q

What is [(x + 2)(x - 3)]/(x + 2)

A

(x - 3)

59
Q

What are combined events?

A

Two or more events occurijng one after another.

60
Q

What are independent events and give an example?

A

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
Q

What are the probabilities of combined events called?

A

Outcomes.

62
Q

How do you canculate the probability of an outcome?

A

You muliply the probabailities along the branches of that outcome.

63
Q

Only A or B can happen. If the probability of A happening is 23%, what is the probability of B happening>

A

76%

64
Q

What is the formula for finding the interior angle of a regular polygon?

A

Interior angle = Sum of Interior Angles / Number of sides. Or 180 - exterior angle.

65
Q

What is the formula for finding the size of an exterior angle of a regular polygon?

A

Exterior angle = 360/Number of sides, or 180 - interior angle.

66
Q

What does making something the subject of the formula mean?

A

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
Q

What is theoretical probability?

A

What is expected to happen. E.g. the theoretical probability of getting a head in a coin toss is 50%.

68
Q

What is relative frequency? How do you calculate it?

A

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
Q

What is expected frequency and how doo we calculate it?

A

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
Q

What does a solid circle on a Number Line mean?

A

Greater than or equal to, or Less than or equal to.

71
Q

What does a hollow circle mean on a number line?

A

Greater than or less than.

72
Q

Rewrite -2x > 4

A
  • 2 > x or x < - 2
73
Q

In a sequence, how can you tell if it is linear?

A

The first differences are all constant or the same.

74
Q

In a sequence, how can you tell if it is non-linear.

A

The first differences are not constant. If the second differences are constant, then the sequence is quadratic.

75
Q

What is the rule in a sequence?

A

The difference from term to term.

76
Q

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.

A

N = D(T-1) + first number or
N = DT + constant (we canculate)

77
Q

What is the next 2 terms in this sequence?
3, 6, 11, 18?

A

DIfferences are 3, 5, 7 and the next 2 would be 11 and 13. So, the next 2 terms are 29 and 42.

78
Q

How to increase a number by a percentage?

A

1 + percentage/100 * number.

79
Q

How to decrease a number by a percentage?

A

1 - percentage/100 * number.

80
Q

What is compound interest?

A

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
Q

How do you calculate compound interest at 5% over 3 years for $100?

A

100 * (1.05)^3

82
Q

If an object has perimeter P and area A and is increased by a scale factor of 2 what is the new measurements?

A

Perimeter increases to 2P. and area increases to 4P (we need to square the scale factor). For volume we need to cube it.

83
Q

What sort of graph does a quadratic equation give you?

A

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
Q

How do you write a coordinate point?

A

(x-co-ordinate, Y-co-ordinate)

85
Q

What is the formula for finding mid-points?

A

((x1 + x2)/2 , (y1 + y2)/2)

86
Q

What is a surd?

A

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
Q

What is the equation for a straight line and what is the gradient and y-intercept.

A

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
Q

Do you work out a bearing?

A

Start with North, go clockwise, measure the angle using 3-digit numbers.

89
Q

What are the three forms of proportion?

A

Ratio, Fraction and Percentage.

90
Q

Explain a direct and inverse proportion.

A

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
Q

How do you find time when given distance and speed?

A

Time = distance / speed.
Speed = distance / time.

09MATC 2023 (1 decks)

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