. Flashcards
A^0
1
A^-n
1/a^n
A^1/n
N root a
A^m/n
(N root a) ^m
A^-1
1/a
A^1/2
Root a
Power law fractions
Apply the power to the top and bottom
(15/7)^2 = 15^2/7^2
Power law negative power
Turn it upside down and take the positive power
E.g. (5/8)^-2=8^2/5^2
Trapezium area
1/2(a+b)h
Prism volume
Area of cross section x length
Cylinder volume
Pi r^2 h
Pyramid volume
1/3 x area of base x h
Speed
Distance/time
Density
Mass/volume
Pressure
Force/area
Pythagoras
A2+b2=c2
Sin area of a triangle
1/2ab sinC
Cosine rule
a2 = b2+c2-2bc(cosA)
CosA = b2+c2-a2
————
2bc
Co interior angle
180 degrees total
Corresponding angle
Same angle
Alternate angle
Congruent
Same shape and size but not facing the same way
Similar
Same shape but different size
Percentage change
(Difference/original) x 100
Difference of 2 squares
A2-b2=(a+b)(a-b)
State whether the following expressions represent length, area or volume
A) 2(x+y+z) b)xyz c)x2+z2
A) length
B) volume
C) area
Inequality
Same as normal equation
If you multiply/divide by negative number remember to flip inequality sign
Multiplying 2 powers
Add them
Dividing 2 powers
Subtract them
Raising 1 power to another (4^3)^4=4^12
Multiply them
Anything to the power of 1
Is itself
Anything to the power of 0
Is 1
1 to the power of anything
Is 1
Circle labelled
frequency polygon
Find the midpoint of the category. 2to4 = 3
Multiply the midpoint and frequency. Frequency=6 3x6=18
Plot the points (midpoint,frequency) and join them up with a straight line (3,6)
Midpoint of a line
(X1+x2. Y1+y2)
——— , ———
2. 2
Completing the square
X2+bx+c = (x+b/2)^2 - (b/2)^2 + c
Turning point
Once you’ve complete square turning point equals b/2 with a reverse sign so + if it was - and vice versa
Y=(b/2)^2 + c
E.g. (x-3)^2 - 16 = 0
Turning point: (3,-16)
Inequalities square roots
2 solutions!
X2<36=-6
Compound growth decay
No(1+-r/100)^n
No = initial amount
+ or - depends if increase or decrease
R= percentage
N= number of periods
When products of factors = 0
At least one factor is 0
Quadratic factorising
Ax^2 + bx + c =0
Add to make b and multiply to make c
When a = 1
(X ) (x ) = 0
When a>1
(Ax ) (x ) = 0
Vector in opposite direction
Put a ‘-‘ infront
X1. X2
+
Y1. Y2
X1+x2
Y1+y2
X1. X2
-
Y1. Y2
X1-x2
Y1-y2
C(x1
Y1)
Cx1
Cy1
Simultaneous equations elimination
- rearrange both equations so they’re in the format ax + by = c
- multiply+eliminate+solve
Substitution simultaneous equations
Make either x or y the subject of one of these two formulas and sub into the other equation
Direct proportion
Y=kx
Class width
Upperclass - lowerclass
CLass boundaries
-value in between each interval
I.e 41-50 = 50.5
51-60 = 60.5
61-70= 70.5
Simultaneous equations graphically
- draw both graphs
- where they intersect = solution
Frequency density
Frequency / class width
Angle in a semi circle is 90 degrees
Circle theorems - circumference centre
Angle at circumference is half the angle at the centre
Radius tangent circle theorem
Angle between radius and tangent is 90 degrees
Alternate segment circle theorem
Angle between chord and tangent is equal to opposite angle inside the triangle
Same segment from chord circle theorem
angles in the same segment from a common chord are equal
Cyclic quadrilateral circle theorem
Opposite angles in a cyclic quadrilateral add up to 180
Tangent circle theorem
Radius chord circle theorem
Histogram
Looks like a bar chart
Frequency of histogram
Area of bar
What are the x and y axis in a histogram
X= height Y= frequency density
Median histogram
add up all the frequencies and add one then divide by 2. You then see what region that is in for which frequency column. You then see how many numbers in the frequency it is out of the total. Divide that by the total to give a percent. As a percentage of the width. Use class width and find the percentage of that is. Add that to the starting bit of the like total width
Quartile ranges for histogram
Same as median
Mean of histogram
multiply midpoint of each group by the frequency. Add them all together and divide by the total frequency.
Assumptions in similar triangles
All of the angles are the same
If triangles are similar then the corresponding sides are in the same ratio
Iterations between x=0 and x=1
show tht the first x is too low and the second x is too high.
Average speed
Total distance/ total time
Dividing 2 fractions
Flip 2nd fractions so it’s multiplying and you can cross cancel numerator of one with the denominator of the other
Product rule for counting
find the total number of outcomes for two or more
events, multiply the number of outcomes for each event
together.
If it’s like how many of them will have different digits
So number of options first time and then minus one and that’s the number of options next then minus one for number of options for the 3rd digit and then multiply them together
E.g. how many possible three digit numbers have 3 different digits from 5 options
= 5 x 4 x 3
Ratio dependent probability 1
2
3
Vectors a whengiven coordinates
Working out vectors as column vectors from grids
