## Number Patterns

Number Patterns Go to the Forum to see more questions or ask your own Worked examples Show that the number pattern 1, 4, 9, 16 ... can be expressed as n², for n = 1, 2, 3 ... and hence find the 100th term. n = 1 n2 = [...]

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12, 2018

Number Patterns Go to the Forum to see more questions or ask your own Worked examples Show that the number pattern 1, 4, 9, 16 ... can be expressed as n², for n = 1, 2, 3 ... and hence find the 100th term. n = 1 n2 = [...]

3
12, 2018

Fraction & Negative Indices Go to the Forum to see more questions or ask your own Formulas used in Fraction & Negative Indices $$x^{-1}=\frac{1}{x}$$ $$x^{-2}=\frac{1}{x^2}$$ a negative index means a fraction $$x^{\frac12}=\sqrt{x}$$ $$x^{\frac13}=\sqrt[3]{x}$$ a fractional index means a root Worked examples Evaluate 49½ [...]

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12, 2018

Indices Go to the Forum to see more questions or ask your own Formulas used in Indices $$x^{a}\times x^{b}=x^{a+b}$$ $$x^{a}\div x^b=x^{a-b}$$ $$(x^{a})^b=x^{a\times b}$$ $$(x^{0})=1$$ Worked examples Simplify x2 × x4. x2 × x4 = x2 + 4 = x6 since we are multiplying, the indices (the little powers) [...]

3
12, 2018

Expanding Brackets Go to the Forum to see more questions or ask your own Worked examples Simplify 2(x - 1) - 3(x - 3) we must be especially careful when expanding with a negative sign = 2x - 1 - 3x + 9 2(x - 1) = 2 × × + [...]

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06, 2018

Formulae & Equations Go to the Formulae & Equations Forum to see more questions or ask your own Topics Covered in Formulae & Equations Substitution Expanding Brackets Indices Fraction & Negative Indices Changing The Subject Equations Equations with Indices Distance, Speed, Time [...]

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03, 2018

Completing the Square Half and square worked examples Complete the square for x2 + 6x. = x2 + 6x + 9 - 9 consider the coefficient of the x term: 6 find half of 6 = 3 and then square it 32 = 9 and add 9 to the [...]

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03, 2017

Proving Inequalities worked examples Prove $$\left( {a + b} \right)\left( {\frac{1}{a} + \frac{1}{b}} \right) \ge 4$$ for a > 0 and b > 0. Consider (√a – √b)2 ≥ 0 since all square numbers are positive, it is a true statement to say that any perfect square will be larger than [...]

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12, 2016

Expanding Perfect Squares (a + b)2 = a2 + 2ab + b2 (a – b)2 = a2 – 2ab + b2 worked examples Expand: (x + 1)2. = x2 + 2 × x × 1 + 12 “square the first + double the product + square the second” = [...]

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12, 2016

Difference Of Two Squares (a – b)(a + b) = a2 – b2 worked examples Expand: (a – 7)(a + 7). = a2 – 72 since this is the difference of two squares then just - “square the first – square the second” = a2– 49 usually you would [...]

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11, 2016

Equations With Indices worked examples Given $${2^{{2^x}}}=1024$$ = 1024, solve for x, correct to 3 decimal places. $${2^{{2^x}}}=2^{10}$$ rewrite 1024 as 2 to the power of something - guess and check until you find 210 = 1024 2x = 10 since they are now both to the base of [...]