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