# Maths C1 notes

• 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.

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)

• 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…

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# Maths C1 notes

• 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.

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)

• 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…