Untitled Deck

Question 1

I know how to find bounds

Answer 1

Upper bound: Add half of the place value getting rounded.
Lower bound: Subtract half of the place value getting rounded.

NOT IN FORMULA BOOKLET

Question 2

I know how to round to significant figures (s.f.)

Answer 2

Rules:
1. All non-zero numbers are always significant.
Example: 123 has 3 significant figures.
2. Any zeros between non-zero numbers are also significant.
Example: 1003 has 4 significant figures.
3. Leading zeros (zeros before non-zero numbers) are not significant.
Example: 0.0045 has 2 significant figures (only the 4 and 5).
4. Trailing zeros (zeros after non-zero numbers) are: Significant ONLY if there is a decimal point.
Example: 3.400 has 4 significant figures.

Note: All answers should always be written in 3 s.f., unless stated otherwise.

NOT IN FORMULA BOOKLET

Question 3

I know how to express numbers in scientific notation

Answer 3

a × 10ᵏ, where 1 ≤ a < 10, k ∈ ℤ
1) a should be one digit long (not including decimal places)
2) k should be an integer (zero or a positive whole number [no decimal places])

NOT IN FORMULA BOOKLET

Question 4

I know how to calculate absolute error

Answer 4

Absolute Error = |Measured Value - True Value|
1) Values from this formula always come out positive
2) Measured value is also known as approximate value or experimental value
3) True value is also known as actual value or theoretical value

NOT IN FORMULA BOOKLET

Question 5

I know how to calculate percentage error

Answer 5

Use the formula given in the AI SL formula booklet (SL 1.6)
Directly plug in the values

IN FORMULA BOOKLET

Question 6

I know how what a percentage is!

Answer 6

A ratio that can be expressed as a fraction of 100
Thus: 0.06% = 0.06/100 = 0.0006

The “swapping trick” for percentages: Finding x% of y is the same as finding y% of x:
79% of 50 = 50% of 79
(due to the commutative properties of multiplication as:
79/100 × 50 = 50/100 × 79)

NOT IN FORMULA BOOKLET

Question 7

I know what is an arithmetic sequence and series are.

Answer 7

Sequence is defined as an arrangement of numbers in a particular order
Series is defined as the sum of the elements of a sequence.
1) U1 is first term
2) d is common difference between two consecutive terms (the constant value added added/subtracted to each term to obtain the next term in the sequence)
3) n is the number of terms
4) Un is the nth term
5) Sn is the sum of the first n terms

IN FORMULA BOOKLET

Question 8

I know what is an geometric sequence and series are.

Answer 8

Sequence is defined as an arrangement of numbers in a particular order
Series is defined as the sum of the elements of a sequence.
1) U1 is first term
2) r is common ratio between two consecutive terms (the constant value added multiplied/divided to each term to obtain the next term in the sequence)
3) n is the number of terms
4) Un is the nth term
5) Sn is the sum of the first n terms

IN FORMULA BOOKLET

Question 9

I know how Sigma Notation works!

Answer 9

Also known as summation notation
Way of expressing the sum of a series of terms concisely using the Greek letter sigma (Σ) - without displaying all the terms in a series

1) Σ is the Greek letter Sigma, indicating summation (addition of all terms)
2) r or k (on the bottom of the Σ symbol, as r = m or k = m [any variable can be used]) is the index of summation (the variable that changes in the sum, the limits set).
Index of summation is the variable that takes on each integer value between the lower and upper limits (inclusive). In each term of the summation, this index is plugged into the function or expression.
3) Lower limit: m (the starting value of r or k) which is the lower limit of summation (the first term added)
Remember: doesn’t always start from U1!
4) Upper limit: n (on the top of Σ symbol) is the upper limit of summation (the final value of r or k, the last term added).
5) (next to the Σ symbol), the general expression of the series being summed (like: 2r + 7 or 8k + 9)

Rules:
1) A summation can be broken into smaller parts, spliting the sum of two expressions into two separate sums.
2) Constants can be factored out from the summation

NOT IN FORMULA BOOKLET

Question 10

I know what exponents are!

Answer 10

Rules:
1) a⁰ = 1
2) a¹ = a
3) aᵐ × aⁿ = a⁽ᵐ⁺ⁿ⁾
4) aᵐ ÷ aⁿ = a⁽ᵐ⁻ⁿ⁾
5) a⁻ᵐ = 1/aᵐ OR 1/a⁻ᵐ = aᵐ
6) a⁽ᵐ⁾ⁿ = a⁽ᵐ ˣ ⁿ⁾
7) (a × b)ᵐ = aᵐ × bᵐ
8) (a/b)ᵐ = aᵐ/bᵐ

NOT IN FORMULA BOOKLET

Question 11

I know what an loan & annuity is

Question 12

I know what interest is and how to find total interest

Question 13

I know what compounding interest is

Question 14

I know how to set up and use the TVM solver on my calculator

Question 15

I know that in finance questions I give my answers to 2 decimal places with the relevant currency, unless stated otherwise

Question 16

I know what a linear equation is

Question 17

I know what a system of linear equations is

Question 18

I know how to set up a system of three linear (or less) equations when I am given the necessary information

Question 19

I know how to solve a system of three (or less) linear equations when I have the system available using a GDC

Question 20

I know that a function relies on inputs and outputs

Question 21

I know how a function can be represented by a graph

Question 22

I know how intersections of graphs can reveal solutions

Question 23

I know how to graph on my GDC (Graphing Display Calculator)

Question 24

I understand what a linear equation is

Question 25

I know the 3 ways of writing a linear equation

Question 26

I understand what the gradient means

Question 27

I know how to calculate the gradient of a line when two points of the line are given

Question 28

I understand what the y-intercept means

Question 29

I know how to calculate the y-intercept given the equation of the straight line

Question 30

I know how to read the gradient and y-intercept of a line when given its equation in gradient - intercept form

Question 31

I know how to find the equation of a straight line when knowing its gradient and a point on the line

Question 32

I understand what it means about the gradient of two lines when they are parallel to each other

Question 33

I understand what it means about the gradient of two lines when they are perpendicular to each other

Question 34

I know how to describe the domain and range of a function

Question 35

I know how to find vertical and horizontal asymptotes

Question 36

I know that the input of a function is the output of the inverse function and vice versa

Question 37

I know that the domain of a function is the range of the inverse function and vice versa

Question 38

I know what a quadratic equation is

Question 39

I know the important features of a quadratic curve

Question 40

I know how to find the y-intercept of a quadratic/cubic equation

Question 41

I know how to find the x-intercepts/zeros of a quadratic/cubic equation

Question 42

I know how to find the vertex/vertices of a quadratic/cubic equation

Question 43

I know how to find the axis of symmetry of a quadratic equation

Question 44

I know what a cubic equation is

Question 45

I understand that the methods of finding the important feature of a cubic function are the same as the ones for a quadratic function

Question 46

I know the important features of a cubic curve

Question 47

Logarithms and Exponentials

Question 48

I know what the general form looks like for an exponential function

Question 49

I know how the constants k,a,c influence the graph of the exponential function

Question 50

I know how to solve simple exponential equations and how to solve complicated exponential equations using graphing

Question 51

I know what e means

Question 52

I know how to identify if an exponential function is growing or decaying and I am familiar with growth/decay type problems

Question 53

I know how to use logarithms

Question 54

I know what the graph of a logarithmic function looks like

Question 55

I know how to solve complicated exponential function using logarithms

Question 56

I know that a trigonometric function is given by f(x) = a*cos(bx)+d or f(x)=a*sin(bx)+d

Question 57

I understand what the amplitude of a trigonometric function is

Question 58

I know how to calculate the amplitude using its formula

Question 59

I know that ampltiude = |a| in a trigonometric function

Question 60

I understand what the period of a trigonometric function is

Question 61

I know how to use the formula to find the period when I know the value of b, and vice versa

Question 63

I know what the principal axis of a trigonometric function means

Question 64

I know how to find the principal axis of a trigonometric function using its formula

Question 65

I know that equation of principal axis is y = d in a trigonometric function

Question 66

I know how to determine the sign of "a" in a trigonometric function

Question 67

I know how to find bearings and bearings between two points

Question 68

I know how to find the distance between points in 2d and 3d space

Question 69

I know what a right angled triangle is

Question 70

I understand what SOHCAHTOA means

Question 71

I know how to use SOHCAHTOA to find missing angles or lengths of a right-angled triangle

Question 72

I know what angle of depression and angle of elevation means

Question 73

I know how to use the cosine rule for non-right-angled triangles given in the formula booklet

Question 74

I know how to use the sine rule for non-right-angled triangles given in the formula booklet

Question 75

I know how to find the area of a triangle using the formula given in the formula booklet

Question 76

I understand that in the formula booklet, A is the angle opposite to side a, B the angle opposite to side b, and C the angle opposite to side c

Question 77

I understand what a right pyramid is and know how to find its volume using its relevant formula

Question 78

I understand what a right cone is and know how to find its volume using its relevant formula

Question 79

I understand what the curved part of a cone refers to and know how to find its surface area using its relevant formula

Question 80

I understand what a sphere is and know how to find its volume and surface area using their respective formulas

Question 81

I understand what an arc is and know how to find its length using its relevant formula

Question 82

I understand what a sector is and know how to find its area using its relevant formula

Question 83

I understand what mean is and know how to find it

Question 84

I understand what median is and know how to find it

Question 85

I understand what mode is and know how to find it

Question 86

I understand what range is and know how to find it

Question 87

I understand what quartiles are and know how to find them

Question 88

I understand what the Interquartile Range (IQR) is and know how to find it using the upper and lower quartiles.

Question 89

I understand what outliers are and know how to check if my data set has outliers

Question 90

I understand what variance and standard deviation tells me about my data

Question 91

I understand what a frequency distribution table shows

Question 92

I understand what a cumulative frequency distribution table shows and know how to calculate quartiles and percentiles from it

Question 93

I understand what a histogram shows

Question 94

I understand what a box & whisker plot shows and know how to produce one if I am given the relevant data/values