By failing to prepare, you are preparing to fail.

# Junior

/Tag: Junior
16 06, 2017

Point Gradient Formula y – y1 = m(x – x1) worked examples Find the equation of the line passing through  (2, -4) and (-3, 6).  $m=\frac{6-(-4)}{-3-2}$ $=\frac{10}{-5}$ m = -2  x1 = 2, y1 = -4 x2 = -3, y2 = 6 find gradient first using gradient formula [...]

16 06, 2017

## Two Point Formula

By |2017-06-16T12:10:57+10:00June 16th, 2017||Comments Off on Two Point Formula

Two Point Formula $\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$  worked examples Find the equation of the line passing through (2, -4) and (-3, 6).   $\frac{y-(-4)}{x-2}=\frac{6-(-4)}{-3-2}$  x1 = 2, y1 = -4, x2 = -3, y2 = 6 substitute into the formula $\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$ $\frac{y+4}{x-2}=\frac{10}{-5}$ $\frac{y+4}{x-2}=-2$ simplify y + 4 = -2(x -2) multiply both sides by (x - [...]

4 12, 2016

## Expanding Perfect Squares

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” = [...]

4 12, 2016

## Difference Of Two Squares

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 [...]

30 11, 2016

## Single Stage Events

By |2016-11-30T07:24:02+10:00November 30th, 2016||Comments Off on Single Stage Events

Single Stage Events worked examples A spinner with the numbers 1 to 8 is spun. What is the probability of getting a. An even number? b. A prime number? c. A number that is even or less than 4? d. A number that is even or less than 4? a. P(even) [...]

28 11, 2016

## Dividing Logs

Dividing Logs worked examples Simplify $\frac{\log16}{\log8}$.  $=\frac{\log2^4}{\log2^3}$ there is no log law to allow us to directly divide logs, so we are going to rewrite them with the same numbers as powers consider what both 16 and 8 can be written to the power of 16 = 24 and [...]

28 11, 2016

## Factor Theorem

Factor Theorem P(a) = 0 then (x - a) is a factor of P(x) worked examples Is x + 2 a factor of x2 + 11x + 18? P(-2) = (-2)2 + 11 × -2 + 18 substitute x = -2 in the function, remembering that if (x - a) [...]

28 11, 2016

## Expanding Surds

Expanding Surds worked examples Expand and simplify √3(10 - √2). = 10√3 - √6 multiply √3 by 10, remembering that if you multiply a number by a surd the number part stays out front of the surd, similar to 10 × y = 10y so 10 × √3 = 10√3 multiply √3 by √2, remembering [...]

28 11, 2016

## Dividing Surds

Dividing Surds $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$ worked examples Simplify √10 ÷ √2. $\sqrt{10\div2}$ = √5 divide the surds part to form single surd and then simplify. Simplify 15√12 ÷ 3√6. = 5√2 think of this as two separate questions: divide the number parts by each other and then divide the surd parts [...]
Multiplying Surds $\sqrt{a}\times\sqrt{b}=\sqrt{ab}$ $\sqrt{a}\times\sqrt{a}=a$ $\sqrt{a}^2=a$ worked examples Simplify √3 × √3.  = √9 = 3 multiply the things in the surds togetther as a single surd and then simplify. Simplify √3 × √5. $=\sqrt{3\times5}$ = √15 multiply the surds together and if they can't be simplified, then [...]