Math Basics

Math Basics

FACTORS
1. whole numbers that divide exactly into the number (1& itself)
2. common factor- a number that is a factor of two or more numbers
3. prime factor- a number bigger than 1 which whole numbers divide exactly into the number
PRIME
1. whole number greater than 1, only factors are 1 and itself
2. prime factor- a factor that is also a prime number
MULTIPLE
1. common multiple- a number that is a multiple of two or more numbers
2. results of multiplying the number by a positive whole number
EVEN NUMBERS
1. 2,4,6,8,10,12,14,16,18,20...
ODD NUMBERS
1. 1,3,5,7,9,11,13,15,17,19...
LCM (LOWEST COMMON MULTIPLE)
1. the lowest multiple that is common to two or more numbers
  1. e.g LCM of 6 & 8 = listing the 6 and 8 times table till you find the lower of the two common multiples = 24
2. HCF (HIGHEST COMMON FACTOR)
  1. the highest factor that is common to two or more numbers
    1. HCF of 36 and 24= writing the prime factors that are most common between both numbers
      1. e.g- find what numbers (that are factors) form that whole number and the sum of the most common to both are the HCF
        36- 2 x 2 x 3 x 3 24- 2 x 2 x 2 x 3
        2 x 2 x 3 = 12
ALGEBRA
1. to multiply the powers of the same number add the indicies
  1. any letter raised the the power of 1 is equal to the letter itself...
    1. e.g- x1 = x
    2. any letter raised to the power of 0 is equal to 1...
      1. e.g- x0 = 1
FRACTIONS
1. DECIMALS
  1. per cent= out of 100
  2. percentage- 1% 10% 25% 50% 75%
    1. decimal- 0.01 0.1 0.25 0.5 0.75
      1. fraction- 1/100 1/10 1/4 1/2 3/4
  3. to work out the percentage of a quantity using a fraction:
    1. write the percentage as a fraction then multiply the fraction by that quantity
      1. to find a percentage of a quantity using decimals:
        write the percentage as a decimal then...
        multiply the decimal by the quantity
        two methods to increase an amount by a percentage
        1. find the percentage of that number then add this to the starting number
        or you can use a multiplier
        two ways to decrease an amount by a percentage
        you can find the percentage of that number and then subtract this from the starting number or you can use a multiplier
2. equivalent fractions- multiply both numerator and denominator by the same whole number
  1. simplest form- divide the numerator and denominator by the same common factor
    1. to find a common denominator you need to find a common multiple of both numbers
      1. an improper fraction can be written as a mixed number with a whole number part and a proper fraction part
        to multiply two fractions multiply the numerators together and the denominators together
        to find a fraction of a quantity multiply the fraction by the quantitty
        you can convert a fraction into a decimal by doing the division
BRACKETS
1. RE-ARRANGING FORMULAE/Nth TERM
  1. variable= something that can change and is often written as a letter
  2. Brackets Indicies Division Multiplication Addition Subtraction
    1. to expand a bracket you multiply everything inside the bracket by what is outside
  3. multiplying out a bracket is called factorising
    1. putting in a bracket is called factorising
PLACE VALUE
1. multiply= left/ divide= right
SQUARES AND CUBES
1. square- the result of multiplying a whole number by itself
  1. 4 x 4 (the square of 4) =16
2. SQUARE ROOTS AND CUBE ROOTS
  1. square roots- a number which when multiplied by itself gives you the its root
    1. cube roots- a number which when multiplied by itself, then multiplied by itself again
3. cube- comes from multiplying a number by itself and then multiplying the result by the original number
  1. 4 x 4 x 4 (4 cubed) = 64
PERCENTAGE CHANGE
RATIO
1. ratios are used to compare quantities
  1. they can be simplified like fractions
    1. to do so you divide each of its numbers by a common factor
GRAPHS
1. gradient
  1. lines that slant upwards have a positive gradient
    1. lines that slant downwards have a negative gradient
2. midpoint
  1. is halfway along the line
    1. to find it: (+ x-coordinates, ÷ by 2 and + the y-coordinates and ÷ by 2
3. across= x, upwards= y
SHAPES
1. circles
  1. circumference= outside (perimeter)
  2. diameter= middle
    1. radius= a section of the line across the middle (diameter)
  3. (Area= 3.142squared) A=πr2
2. prisms
  1. volume= area of cross section x length
3. pythagoras
  1. a2+ b2 = c2
    1. c2= n, n√
4. rectangle
  1. perimeter= l + w + l + w
  2. area= l x w
5. square
  1. area= a measure of the amount of space within a shape e.g- a 1cm by 1cm square is 1cm2
  2. area= l x l
6. parallelogram area= base x height
7. triangle area= 1/2 x b x h
8. trapezium area = 1/2 (a + b lengths of parallel sides) x h
LOCI
1. CONSTRUCTIONS
  1. perpendicular bisector of a line segment
    1. the locus of a point which moves so that it's an equal distance from two points (A&B) is the perpendicular bisector of the line joining A and B
    2. perpendicular= at right angles to
      1. bisector= cut in half
        BISECTING AN ANGLE
        after drawing an angle at the corner labelled V would be the angle to bisect
        placing your compass on V, draw an arc that crosses both sides of the angle
        label those points A and B
        place your compass on point A and draw an arc between the two sides of the angle
        then, without moving the compass place it on point B and draw another arc that cuts through the previous, label this C
        draw a straight line through point V to C
        the line VC bisects the angle
  2. to do so you draw a line segment XY (the numbers at either end)
    1. put you compass on X, set halfway along the line, then draw an arc proceed to do the same from the opposite end close to Y but halfway along (they should cross)
      1. label the two points A and B, draw a straight line through A and B where lines X and Y , A and B cross within the middle of the arcs, along the right angle label M ad draw a box
      2. the point M where the lines cross is the midpoint of XY and AB is perpendicular to XY
2. the locus of a point moves so that it is always a set distance from a fixed point
  1. the locus of a point moves so that it is a set distance from the line between points P and Q which will be at opposite ends of said line
    1. after measuring a set distance from the line to the measurement provided using a compass you should draw around the line
CORRELATION
1. correlation is positive when the values increase together
  1. correlation is negative when one value decreases as the other increases
    1. 0 is no correlation (the values will appear to not link at all)
    2. -1 is a perfect negative correlation
      1. the value shows how good the correlation is not how steep the line is and if it is positive or negative
  2. 1 is a perfect correlation
PIE CHARTS
1. when given survey results that may be presented in a table to show this within a pie chart with the numbers still in a table you then divide each value by the total and multiply by 100 to get a percentage
  1. comedy:4 action:5 romance:6 drama:1 sci-fi:4 total=20
    1. 4/20= 20% 5/20= 25% 6/20=30% 1/20=5% 4/20=20% total=100%
      1. 4/20 x 360 = 72 5/20 x 360 = 90 6/20 x 360 =108 1/20 x 360 = 18 4/20 x 360 =72 total=360
PROBABILITY
1. probability of an outcome= number of ways the outcome can happen ÷ total number of possible outcomes

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