Math Yearly '17

Front 1

Difference of two squares formula

Back 1

(a+b)(a-b) = a^2-b^2

Front 2

Perfect square formula +

Back 2

(a + b)^2 = a^2 + 2ab + b^2

Front 3

Perfect squares formula -

Back 3

(a - b)^2 = a^2 - 2ab + b^2

Front 4

Scientific notation: 6.58 x 10^2 =?

Back 4

658

Front 5

Scientific notation: 6.5 x 10^-4 = ?

Back 5

0.00065

Front 6

What is a quadratic expression

Back 6

Has x^2 at the start. If it has 3 terms it is a trimonial

E.g ax^2 + bx +c

Front 7

What are 2 methods used to factorise monic trimonials?

Back 7

1. Split the middle term: 2 factors that make c and add to b

2. Grouping in pairs

Front 8

How do you factorise a non-monic quadratic trimonial?

Back 8

Multiply the coefficient of x with the last term (c) and continue as you would with a monic trimonial

Front 9

How do you solve an equality/equation

Back 9

As you normally would except if you divide or multiply by a negative number you flip the sign but don't remove the negative

E.g 2x-1 > 5

+1

2x =6

Divide by 2

X = 3

Front 10

What is method 1 to solve simultaneous equations

Back 10

1. Elimination

1.number the equations

2. + or - the equation to make one variable disappear

3. Solve 1 variable

4. Substitute the value back into one of the original equations

5. Solve for next variable

6. Write solution

7. Check

Front 11

What is method 2 to solving simultaneous equations

Back 11

2. Substitution

E.g

Y= x +4.......1

Y= 3x - 2........2

In 1 y = x +4 so sub 1 into 2

2 becomes x+4 = 3x-2

-x

4=2x-2

+2

6=2x

Divide by 2

X=3

Sub back into 1 then 1 is y=3+4=7

Then x=3, y=7

Then check

Front 12

What are the 3 methods to solve quadratics?

Back 12

1. Factorisation

2. Completing the square

3. Quadratic formula

Front 13

What is the quadratic formula

Back 13

X = -b (+/-) the square root of b^2 -4ac

(all over) /2a

Front 14

Probability language

Back 14

1. Impossible, unlikely, even chance, likely, certain

2. If, then, given, knowing that

Front 15

Theortical probably of rolling a two on a six sided die

Back 15

P(2)= 1/6

Front 16

Relative frequency of an event is 46/80 the experimental probability is

Back 16

46/80

Front 17

The experimental probability is 46/80, if we were to do the experiment 750 times, the expected number would be

Back 17

46/80 X 750 =431.25

=431

Front 18

Simple interest formula

Back 18

I = PRN

Front 19

Compound interest formula

Back 19

A = P(1 + R)^n

Front 20

Depriciation formula

Back 20

Value (v)= P(1+R)^n

Front 21

Define bivariate data

Back 21

2 variables with a relationship

Front 22

Define univariate data

Back 22

1 variable with no relationship

Front 23

Five number summary

Back 23

1. Lower extreme: lowest score

2. 1st quartile (Q1) : middle score of first half of scores

3. Median (Q2) :

4. 3rd quartile (Q3) : middle score of second half of scores

5. Upper extreme : highest score

Front 24

Interquartile range

Back 24

IQR = Q3 - Q1

A measure of spread

Shows middle 50%

Front 25

Define 3 different skewness

Back 25

1. Negative (tail pointing to origin)

2. Positive (tail pointing away from origin

3. Symmetrical

Front 26

What is standard deviation

Back 26

Average distance of scores from the mean

Symbol is sigma

Front 27

Frequency histogram

Back 27

1/2 column before start at end

Frequency (f) on y axis

Score (x) on x axis

Columns n a line (polygon) goes to middle of column

Front 28

Define prism

Back 28

A solid with a uniform cross section where the cross section is a polygon

Front 29

Area of right angled triangle

Back 29

A = 1/2bh

Front 30

Area of parallelogram

Back 30

A = bh

Base x perpendicular height

Front 31

Area of trapezium

Back 31

A = 1/2(a+b)h

Front 32

Area of rhombus or kite

Back 32

A = 1/2xy

Xy = product of diagonals

Front 33

Area of circle

Back 33

A = Pi r^2

Front 34

Surface area of a closed cylinder

Back 34

SA = 2(pi)rh + 2(pi)r^2

Front 35

Surface area of a 1/2 open cylinder

Back 35

SA = 2(pi)rh + (pi)r^2

Front 36

Surface area of an open cylinder

Back 36

SA = 2(pi)rh

Front 37

Surface area of a cone

Back 37

SA = (pi)r^2 + (pi)rh

(h= slant height)

Front 38

Surface area of a sphere

Back 38

SA = 4(pi)r^2

Front 39

Surface area of a hemisphere

Back 39

SA = 1/2[4(pi)r^2] + (pi)r^2

= 3(pi)r^2

Front 40

Volume formula

Back 40

V = Ah

Front 41

Congruency (3horizontallines) proofs

Back 41

Sss

Sas

Aas

Rhs

Front 42

Angle sum of an n sided polygon

Back 42

(n-2)180(degrees)

Front 43

Interior angle of a regular polygon

Back 43

(n-2)180 divided by n

Front 44

Exterior angle sum of convex polygon

Back 44

360 degrees

Front 45

Exterior angle of a regular n sided convex polygon

Back 45

360 divided by n

Front 46

Exterior angle of a triangle =

Back 46

Sum of opposite interior angles

Front 47

Similar figures scale factor

Back 47

Side length of image

-----------------------------

Matching side of original

Front 48

Trapezium properties

Back 48

1 pair of sides parallel

Front 49

Kite properties

Back 49

-2 pairs of adjacent sides equal

- diagonals cross at 90 degrees

-only one diagonal is bisected by the other

Front 50

Parallelogram properties

Back 50

-Opposite sides equal

-pairs of parallel sides

-adjacent angles supplementary (180)

-diagonals bisect and create congruent triangles

-if one angle is 90 all angles r 90 n it becomes a rectangle

Front 51

Rhombus properties

Back 51

Parallelogram with perpendicular diagonals

Front 52

Rectangle properties

Back 52

Paralellogram with all angles equal (90 degrees)

Front 53

Square properties

Back 53

Rectangle + rhombus

-equal sides and angles

Front 54

Cos rule to find an angle

Back 54

CosA = b^2 + c^2 - a^2

---------------------

2bc

Front 55

Cos rule to find a side

Back 55

C^2 = a^2 + b^2 - 2abCosC

Front 56

Sine rule

Back 56

a b c

---- = ------- = --------

SinA SinB SinC

Front 57

Area of non right triangle

Back 57

A = 1/2abSinC

Front 58

Trig ratios of complementary angles in right angled triangles

Back 58

(add up to 90)

SinA = a/c

Cos B = a/c

/////

SinA =CosB

=Cos(90-A)

--

CosA =SinB

=Sin(90-A)

Front 59

Exact values tan

Back 59

Tan30 = root3/2

Tan45= 1

Tan60 = root3

Front 60

Exact values tan x =

Back 60

Sin x

Tan x = -------

Cos x

Front 61

Volume vs capacity

Back 61

Volume: amt of space a 3d object occupies

units3

Capacity: amount a 3d object holds

mL, L etc

Front 62

Gradient formula(m) (given 2 points)

Back 62

Y2- Y1 Rise

m = ---------- ---------

X2 - X1 run

Front 63

Midpoint (M) of an interval

Back 63

M = (average of x values , average of y values)

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

Front 64

Distance between two points

Back 64

D = (root everything)

(x2 -x1)^2 + (y2 - y1)^2

Front 65

To find x or y intercept

Back 65

Sub 0 into x n solve

Front 66

Volume of a sphere

Back 66

V= 4/3 (pi) r^3

Front 67

Gradient intercept equation

Back 67

Y = mx +b

X n y r random points on the line

M is gradient

B is y intercept

Front 68

Point gradient form: equation for finding the equation of a line if we know the gradient and a point (x1, y1)

Back 68

m = y-y1

-------

X - x1

Or

Y- y1 = m(x-x1)

Front 69

A line parallel to another has the same.....formula

Back 69

Same gradient

Formula: m1=m2

Then sub into y -y1 = m(x-x1) to solve

Front 70

Perperdincular lines meet at .... And gradients.....formula:

Back 70

Meet at 90 degrees

Gradients are negative reciprocal of each other

-1

Formula: m2 = ----

m1

Or m1, m2 =-1

Then sub into y-y1 = m (x-x1) and solve

Front 71

Speed =

Back 71

Speed = distance/time

Front 72

Direct porportion

Back 72

Y = kx

K is a constant (bigger than 0) and is gradient

K must be straight and pass thru origin

Front 73

Simple parabolas formula

Back 73

Y = ax^2 + c

A is the curvature

C is where the vertex minimum/maximhm point lies (0,C)

Front 74

If the a in simple parabolas are + or - what happens to the parabola

Back 74

Positive: concave up

Negative: concave down

Front 75

Hyperbola formula

Back 75

K

Y = ----- + c

x

K increases the graph gets further away from the centre

C is centre

K is + first n third

K is - 2nd n 4th

Front 76

Exponential graphs

Back 76

Y=a^x

Never negative

X is + increases to right: growth

X is - decreases ro right: decay

As a increases the graph gets steeper

Front 77

Circle formula with a centre (0,0)

Back 77

X^2 + y^2 = r^2

Front 78

Circle with centre (h,k)

Back 78

(x-h)^2 + (y-k)^2 = r2