Maths 101

Question 1

How to solve simultaneous equations

Answer 1

SSLE or graphing intersection

Question 2

Solution of quadratic equations ?

Answer 2

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

Question 3

Finding the quadratic equation from a graph

Answer 3

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)

Question 4

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

Answer 4

x100 –> x10,000 –> x10,000 –> x100

Question 5

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

Answer 5

x10 = x100 = 1000

Question 6

Cosine rule - what and when

Answer 6

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

Question 7

Sine rule - what and when

Answer 7

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

Question 8

common difference

Answer 8

d = U1 + 1 - Un

Question 9

Arithmatic mean

Answer 9

b = A+C/2

Question 10

Common ratio

Answer 10

Un + 1 / Un

Question 11

Geometric mean

Answer 11

b^2 = (a)(c)

Question 12

Domain and range notation

Answer 12

Domain x E (-1,infinity)

Range y E (-3, infinity)

Question 13

equation of an exponential function

Answer 13

y = ka^x + c

Question 14

Key features that must be shown when sketching all graphs

Answer 14

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

Question 15

Discrete data

Answer 15

an exact value and is often the result of counting

Question 16

Continuous data

Answer 16

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

Question 17

how to make Line of Best Fit by eye

Answer 17

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

Question 18

Null Hypothesis

Answer 18

H0 = x and y are independant
H1 = x and y are not independant

Question 19

When are two events independent

Answer 19

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

Question 20

When are two events dependant

Answer 20

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

Question 21

What is Pr (AuB) equal to

Answer 21

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

Question 22

Formula for conditional probability

Answer 22

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

Question 23

Derivative function

Answer 23

gives the gradient of a function at a point

Question 24

How to find the equation of a tangent

Answer 24

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

Question 25

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

Answer 25

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

Question 26

what does dy/dx give other than derivative

Answer 26

rate of change

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

Question 27

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

Answer 27

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

Question 28

What is the equation of normal distribution?

Answer 28

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

Question 29

What are the normal distribution boundaries

Answer 29

0. 13%
1. 15%
2. 59%
3. 13%

Question 30

What are the mean boundaries for normal distribution

Answer 30

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