Formulae Flashcards
basic weekly wage
basic wage * hours worked
overtime wage
basic wage * 1.5 (time and a half or double time) * hours worked
Calculating cost price given profit%
(SP)$/(SP profit)%* 100= CP
Calculating cost price given loss%
(SP)$/(SP loss)% * 100= CP
finding % profit
P/CP*100
finding % loss
L/CP*100
Calculating selling price given profit %
percent added to 100/100 * CP
Calculating selling price given loss %
percent subtracted from 100/100 * CP
simple interest
SI= P * R * T/100
Principal
P= SI * 100/R * T
Rate
R= SI * 100/P * T
Time
T= SI * 100/P * R
Final Amount for Simple Interest
P+ SI
Compound Interest
Amount accruing(A)= P (1+r/100)^n
Final amount for Compound Interest
Amount accruing - Principal
equation of a line
y=mx+c
length of a line
(x2 - x1)^2 + (y2 - y1)^2 square rooted
m/gradient
y2 - y1 / x2 - x1
mid point/M
(x2 + x1 /2), (y2 + y1 /2 )
completing the square
h= b/2a
completing the square
k= 4ac-b^2/4a
quadratic expressions where h and k are constant
a (x+h)^2 +k
When to use SINE rule
Two angles, one side
OR
two sides, and a non-included angle
When to use COS rule
Three sides
OR
Two sides and the included angle.
Pythagoras Therom
c² = a² + b²
c² being the hypotenuse
a² = c² - b²
b²= c² - a²
SQUARE ROOT AFTER
When are phythagoras therom and the trigonometric ratios used?
RIGHT ANGLED TRIANGLES ONLY
BEARINGS
- 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 😎
ANGLE or point or vertices
CAPITAL LETTERS
Length of a side or side or length
common letters
If x = to a constant/a whole number the line is…
Vertical and parallel to the x-axis
If y is equal to a whole number or constant it is…
Horizontal and parallel to the x-axis
(x, y)
(-h, k)
If the line is the perpendicular bisector…
The gradient is the negative reciprocal
When to use cosine, tangent and sine
SOH
CAH
TOA
theta
Calculating area of an irregular shape
- Separate into two shapes maybe more
- Calculate areas of individual shapes
- Add to get total area
- Area equals to ?, possibly given area
- Area equals to 0? Transpose
Identity Matrix
1 0
0 1
Identify Matrix Rules
I × A= A
A × I= A
A × A inverse = I
Solving simultaneous equations using matrices
Singular matrix
Is a matrix whose determinant is 0
If you have to square root a number of a matrix there is…
Two values negative and positive
Matrix multiplication and addition and subtraction etc
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
The axis of symmetry
The middle of the graph where,
x =
To solve a graph using an equation
Look for where the graph crosses the x-axis
Roots of a graph/equation
Where the line crosses the x-axis
Y intercept
Where it corsses the y axis
Minimum and maximum value is also known as
The turning point
-h, k
or
x,y
Maximum point
Negative coefficient frown or n shape
Minimum point
Postive coefficient smile shape u shaped
Angles in a quadrilateral are equal to
360 degrees
Simultaneous equations ELIMINATION
- Label the equations 1 and 2
- CHOOSE WHICH VALUE U WANT TO ELMIANTE AND WHICH VALUE U WANT TO SOLVE FIRST
- MULTIPLY TO GET LCM
- SUBTRACT BOTH EQUATIONS
SUBSTITUTE
Mean
Median
£ fx / £f
N/2
Matrix simultaneous equations
Multiply each side by it’s inverse
Inverse of a matrix
1/the determinant adjoins matrix
Undefined function
When the denominator is equal to 0
When doing compound shapes or anything with unknown variables..
ALWAYS BUT BRACKETS
When dividing by a negative number, switch the inequality in other words try not to divide by a negative number
Show that means
Literally just calculate
Exterior angles of a polygon add up to..
360 degrees
A chord
A line connected to two ends of the circumference of a circle
Radius
Perpendicular to the diameter
SUM OF INTERIOR ANGLES Triangles
Quadrilateral
Pentagon
Hexagon
180 degrees
360 degrees
540 degrees
720 degrees
In functions,
The inside part goes first
e.g.
fh(x)
f[h×)
Length and perimeter same thing essentially
USE FORMUAL SHEET
Circumference
C = 2TTr
r
r= C/2TT
Height of a cone when it is right-angled
Phythora’s theorm
The equation of the axis of symmetry especially when it is 1 mark is usually
X =
Values of x ARE
where the curve/parabola intersects the x-axis
how to calculate a transformation..
Multiply the matrix (FIRST) by a made up vector
THEN
Create a sketch and describe it
y= -x
\
Enlargement
Centre of enlargement
Angle
Scale factor which is k
For center of enlargement or center of rotation
DRAW CONSTRUCTION LINES PAST THE POINTS WHERE THE LINES INTERSECT IS THE CENTRE OF ENLARGEMENT OR ROTATION
Rotation
Angle (use protractor)
Centre of rotation (CONSTRUCTION LINES)
Bearings
USUALLY Sine rule / cosine rule or angles such as interior
ax² + bx + c
Three terms
THE TWO NUMBERS WHEN ADDED OR SUBTRACTED MUST GIVE U BACK BX
(ax+ )(x+ )
Difference of two squares
a²-b²
OR
(a-b)²
(a-b)(a+b)
Factorization by grouping
Four terms
mx - my + nx - ny
m(x-y) + n(x-y)
BRACKETS FIRST
(x-y) (m+n)
Roots of an equation
In the formula sheet and in graph, where the line crosses the x-axis
Congruent
Angles with the same size/measure
Lengths are the same
Vectors
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
Magnitude of a vector
|AB| = x² + y² square rooted
Cos rule
ASS
SSS
Sine rule
Matching pairs
