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Mathematics > Formulae > Flashcards

Formulae Flashcards

1
Q

basic weekly wage

A

basic wage * hours worked

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2
Q

overtime wage

A

basic wage * 1.5 (time and a half or double time) * hours worked

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3
Q

Calculating cost price given profit%

A

(SP)$/(SP profit)%* 100= CP

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4
Q

Calculating cost price given loss%

A

(SP)$/(SP loss)% * 100= CP

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5
Q

finding % profit

A

P/CP*100

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6
Q

finding % loss

A

L/CP*100

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7
Q

Calculating selling price given profit %

A

percent added to 100/100 * CP

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8
Q

Calculating selling price given loss %

A

percent subtracted from 100/100 * CP

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9
Q

simple interest

A

SI= P * R * T/100

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10
Q

Principal

A

P= SI * 100/R * T

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11
Q

Rate

A

R= SI * 100/P * T

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12
Q

Time

A

T= SI * 100/P * R

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13
Q

Final Amount for Simple Interest

A

P+ SI

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14
Q

Compound Interest

A

Amount accruing(A)= P (1+r/100)^n

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15
Q

Final amount for Compound Interest

A

Amount accruing - Principal

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16
Q

equation of a line

A

y=mx+c

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17
Q

length of a line

A

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

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18
Q

m/gradient

A

y2 - y1 / x2 - x1

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19
Q

mid point/M

A

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

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20
Q

completing the square

A

h= b/2a

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21
Q

completing the square

A

k= 4ac-b^2/4a

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22
Q

quadratic expressions where h and k are constant

A

a (x+h)^2 +k

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23
Q

When to use SINE rule

A

Two angles, one side
OR
two sides, and a non-included angle

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24
Q

When to use COS rule

A

Three sides
OR
Two sides and the included angle.

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25
Q

Pythagoras Therom

A

c² = a² + b²
c² being the hypotenuse

a² = c² - b²
b²= c² - a²

SQUARE ROOT AFTER

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26
Q

When are phythagoras therom and the trigonometric ratios used?

A

RIGHT ANGLED TRIANGLES ONLY

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27
Q

BEARINGS

A
  • Try and draw it
  • Always have 3 digits
  • Start from NORTH, THEN MOVE
  • Alternate angles (form a z) and corresponding angles (parallel) r equal
  • Straight line and interior angles are equal to zero
  • Bearings move in a CLOCKWISE DIRECTION ONLY
  • horizontal plane simply means flat surface CHILL 😎
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28
Q

ANGLE or point or vertices

A

CAPITAL LETTERS

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29
Q

Length of a side or side or length

A

common letters

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30
Q

If x = to a constant/a whole number the line is…

A

Vertical and parallel to the x-axis

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31
Q

If y is equal to a whole number or constant it is…

A

Horizontal and parallel to the x-axis

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32
Q

(x, y)

A

(-h, k)

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33
Q

If the line is the perpendicular bisector…

A

The gradient is the negative reciprocal

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34
Q

When to use cosine, tangent and sine

A

SOH
CAH
TOA

theta

35
Q

Calculating area of an irregular shape

A
  1. Separate into two shapes maybe more
  2. Calculate areas of individual shapes
  3. Add to get total area
  4. Area equals to ?, possibly given area
  5. Area equals to 0? Transpose
36
Q

Identity Matrix

A

1 0
0 1

37
Q

Identify Matrix Rules

A

I × A= A
A × I= A
A × A inverse = I

38
Q

Solving simultaneous equations using matrices

A
39
Q

Singular matrix

A

Is a matrix whose determinant is 0

40
Q

If you have to square root a number of a matrix there is…

A

Two values negative and positive

41
Q

Matrix multiplication and addition and subtraction etc

A

Addition and subtraction: must be the same size matrix
Scalar Multiplication: multiply each number in the matrix by the scalar
Multiplication and Divsion:
The number of columns of the first matrix must be equal to the number of rows in the second matrix

42
Q

The axis of symmetry

A

The middle of the graph where,
x =

43
Q

To solve a graph using an equation

A

Look for where the graph crosses the x-axis

44
Q

Roots of a graph/equation

A

Where the line crosses the x-axis

45
Q

Y intercept

A

Where it corsses the y axis

46
Q

Minimum and maximum value is also known as

A

The turning point

-h, k

or
x,y

47
Q

Maximum point

A

Negative coefficient frown or n shape

48
Q

Minimum point

A

Postive coefficient smile shape u shaped

49
Q

Angles in a quadrilateral are equal to

A

360 degrees

50
Q

Simultaneous equations ELIMINATION

A
  1. Label the equations 1 and 2
  2. CHOOSE WHICH VALUE U WANT TO ELMIANTE AND WHICH VALUE U WANT TO SOLVE FIRST
  3. MULTIPLY TO GET LCM
  4. SUBTRACT BOTH EQUATIONS
    SUBSTITUTE
51
Q

Mean

Median

A

£ fx / £f

N/2

52
Q

Matrix simultaneous equations

A

Multiply each side by it’s inverse

53
Q

Inverse of a matrix

A

1/the determinant adjoins matrix

54
Q

Undefined function

A

When the denominator is equal to 0

55
Q

When doing compound shapes or anything with unknown variables..

A

ALWAYS BUT BRACKETS

56
Q

When dividing by a negative number, switch the inequality in other words try not to divide by a negative number

A
57
Q

Show that means

A

Literally just calculate

58
Q

Exterior angles of a polygon add up to..

A

360 degrees

59
Q

A chord

A

A line connected to two ends of the circumference of a circle

60
Q

Radius

A

Perpendicular to the diameter

61
Q

SUM OF INTERIOR ANGLES Triangles
Quadrilateral
Pentagon
Hexagon

A

180 degrees
360 degrees
540 degrees
720 degrees

62
Q

In functions,

A

The inside part goes first
e.g.
fh(x)
f[h×)

63
Q

Length and perimeter same thing essentially

A

USE FORMUAL SHEET

64
Q

Circumference

A

C = 2TTr

65
Q

r

A

r= C/2TT

66
Q

Height of a cone when it is right-angled

A

Phythora’s theorm

67
Q

The equation of the axis of symmetry especially when it is 1 mark is usually

A

X =

68
Q

Values of x ARE

A

where the curve/parabola intersects the x-axis

69
Q

how to calculate a transformation..

A

Multiply the matrix (FIRST) by a made up vector
THEN
Create a sketch and describe it

70
Q

y= -x

A

\

71
Q

Enlargement

A

Centre of enlargement
Angle
Scale factor which is k

72
Q

For center of enlargement or center of rotation

A

DRAW CONSTRUCTION LINES PAST THE POINTS WHERE THE LINES INTERSECT IS THE CENTRE OF ENLARGEMENT OR ROTATION

73
Q

Rotation

A

Angle (use protractor)
Centre of rotation (CONSTRUCTION LINES)

74
Q

Bearings

A

USUALLY Sine rule / cosine rule or angles such as interior

75
Q

ax² + bx + c

A

Three terms
THE TWO NUMBERS WHEN ADDED OR SUBTRACTED MUST GIVE U BACK BX
(ax+ )(x+ )

76
Q

Difference of two squares

A

a²-b²
OR
(a-b)²

(a-b)(a+b)

77
Q

Factorization by grouping

A

Four terms

mx - my + nx - ny
m(x-y) + n(x-y)

BRACKETS FIRST
(x-y) (m+n)

78
Q

Roots of an equation

A

In the formula sheet and in graph, where the line crosses the x-axis

79
Q

Congruent

A

Angles with the same size/measure
Lengths are the same

80
Q

Vectors

A

Usually added together
Usually only two positions vectors
Usually start the ‘‘working out’’ from the beginning vector
Usually end at the end vector
e.g.
AB BX
AX = AB + BX

THE TWO MIDDLE LETTERS MUST ALWAYS BE THE SAME
AND THE ENDING LETTERS MUST MATCH THE VECTOR’S LETTERS UR LOOKING FOR

81
Q

Magnitude of a vector

A

|AB| = x² + y² square rooted

82
Q

Cos rule

A

ASS
SSS

83
Q

Sine rule

A

Matching pairs

Mathematics (3 decks)

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