All prime numbers end in either 1, 3, 5 or 7.
If asked whether a number is prime or not, then there are certain rules to help you figure it out:
- it must end in 1, 3, 5 or 7.
- it won't divide by any of the primes below the value of its own square root.
1) Does it end in 1, 3, 5 or 7? = YES
2) Find it's square root = 15.264
3) List all the primes that are less than its square root = 2, 3, 5, 7, 11 and 13.
4) Divide all of these primes into the number you're testing.
5) NONE of them divide cleanly so it IS a prime number.
Recurring Decimals into Fractions
First you find the length of the sequence. So for 0.234234234 (which we can abbreviate to 'r') the length is after the first '234' move the decimal point to after this.
Because it has moved 3 decimal places, we have multiplied it by 1000. This then gives us 1000r (234.234234234).
Now we want to work out 1000r - 'r' which we can call 999r. In this case it is 234.
Then simply divide 999r by 999. So 234/999 = 26/111.
Compound Growth & Decay
You can't do this without the formula:
N = No (1 + r/100) x n
What the letters stand for:
- N = the existing amount, at this time.
- No = initial amount
- r/100 = percentage change per day/month/year
- n = number of days/months/years
There are four easy rules:
- when multiplying, you ADD the powers.
- when dividing, you SUBTRACT the powers.
- if there is a power inside the bracket, and one outside, you MULTIPLY them.
- if there'd is a fraction inside the bracket and a power outside, you apply the power to
the top and bottom of the fraction.
And two not so easy rules...
- if the power is negative you turn it upside down, you put the number under 1, and
still apply the power to it, but now it is positive.
- if the power is a half, you square root it. If it is a third, you cube root it. If it is a
quarter you fourth root it etc.
1) Convert each inequality into an equation, by replacing the < or > with =.
2) Draw the graph for each equation
3) Work out which side of each line you want (put x=0 and y=0 into the inequality
To see if the origin is on the correct side
4) Shade in the area.
'Proportional to' is represented by a symbol that looks like that Christian fish. So if the question states 'a is proportional to b x 6' you would write:
a (then the funky fish thing) 6b
Then you replace the funky fish thing with =K, to form an equation:
a = K 6b
Then substitute in the values the question will give you.
Then rearrange to find K.
Finding the Gradient
Gradient = change in y/ change in x
However sometimes the graph is not drawn, and you have to find the gradient from the coordinate.
- find the diffence between the y coordinates
- divide that total by the difference between the x coordinates
y = mx + c
- m = the gradient of the line
- c = the 'y' intercept
Finding the equation of a straight line:
- identify the two variables (e.g for a speed/time graph they would be S & t.
- find the gradient and the y intercept.
- then use these values to sub into y = mx + c
The formula is: dy/dx
If you have an indicie, you move it Infront of the number and reduce the value of the original indicie by 1.
E.g. y = x5 goes to 5x4
When there is already a number Infront you times it by the indicie, and still reduce the indicie value by 1.
When there is no indicie, you simply take away the x.
E.g. y = 24x goes to 24.
Interior and Exterior angles
Exterior angle = 360/n (n being the number of sides the shape has)
Interior angle = 180 - exterior angle.
Sum of exterior angles = 360
1) a tangent always makes 90° with the radius
2) The angle at the centre is twice the angle at the circumference.
3) the angle in semicircle is 90°.
4) Angles in the same segment are equal.
5) Opposite angles in a cyclic quadrilateral add up to 180°
6) The lengths of the two tangents from a point to a circle are equal.
Quartiles and Interquartile range & Cumulative fre
Quartiles divide the data into four equal groups: the lower quartile (25%), the median (50%) and the upper quartile (75%).
- add a third row to the table
- add up the top numbers from each column
If the chart has equal class widths, the frequency will be on the y axis.
If they have unequal class widths then the frequency density will be on the y axis and the AREA will equal the frequency.
Frequency Density = Frequency / Class Width
The OR rule:
The probability of EITHER event A or event B happening is the two separate probabilities ADDED together.
- P(A or B) = P(A) + P(B)
THe AND rule:
The probability of event A AND event B BOTH happening is equal to the two separate probabilities MULITPLIED together.
- P(A and B) = P(A) x P(B)
Expected frequency can be worked out by multiplying the number of times you are doing it (trials) by the probability of the outcome happening.