Maths C1 notes

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  • Created by: reannew
  • Created on: 14-03-16 14:07

1. Powers & surds     | meaning root of        / meaing divided        * meaning multiplied

Surds 

  • Simplified by finding a square number that multiplies into this surd. E.G |50 = 5|2
  • Only like surds can be added or subtracted
  • When multiplying surds:
    • |a * |b = |axb  
    • |a * |a = a
  • When rationalising denominators: 
    • Always write in the form a |b / c where all a, b and c are integers.
    • E.G   2 / |5  =  2 |5 / |5 * |5  =  2 |5 / 5

Indicies                            ^x meaning to the power of             ^3| meaning cube root of 

  • Basic indicies  - 2^3 = 2 * 2 * 2 = 8
  • Fractional indicies - 
    • 4^1/2 = |4 = 2 
    • 64^2/3 = 2 * (^3|64) = 4 * 2 = 8 
  • Negative indicies 
    • 2^-3 = 1 / 2^3 = 1 / 8
    • (25 / 16)^-1/2 = (16 / 25)^1/2 = 4 / 5 
    • find the recipricol of the integer and root it or times it accordingly.
  • Adding terms with indicies
    • Only like terms with the same power can be added or subtracted
  • Multiplying powers
    • If 2 like terms with powers are multiplied then the power in the answer can be found by adding the powers in the question but the term remains the same 
  • Powers in brackets
    • When in brackets, multiply the 2 powers together. E.G (x^2)^4 = x^8
  • Dividing powers 
    • When 2 like terms with powers are divided, the power in the answer is found by subtracting the powers in the question. 

2. Quadratics 

Factorising qudratics

  • Either;
    • Take out the highest factor possible as a coeffcient of the bracket. OR
    • Find 2 numbers that add to make the coeffcient of x and times to make the constant (in the case of a coeffcient of x^2, first times this by the constant)

Quadratic functions 

  • Using quadratics to draw graphs; 
    • 1st factorise f(x)
    • Solve the equation to find the solution(s) to x. These are the x-axis intercepts.
    • Find y when x = 0. This gives the y-axis intercept(s)
    • Sketch the U shaped parabola, showing all intercepts.

Solving quadratics using the formula 

  • The formula is

        Image result for quadratic equation

  • It's used when quadratic equations wont factorise with whole numbers.
  • If a question states "leave in exact answer" it means to use this method, and give the simplified surd answer. 

Completing the square

  • "write in the worm a(x+b)^2 + c
  • To solve; 
    • Factorise by halfing the co-effcient of x, put into brackets with x, and square the bracket.
    • Square the factorised constant, and subtract from the factorised x bracket.
    • Add/subtract the constant from the orginal equation and simplify
  • When sketching graphs; 
    • The constant in the original equation shows the y intercept.
    • In completed squared form, the constant in the bracket shows the line of symmetry when the sign is changed, and…

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