Maths C1 notes

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

• 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…