By failing to prepare, you are preparing to fail.
/Tag: Extension
22 03, 2017

## Proving Inequalities

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 [...]

8 02, 2017

## Zeroes & Multiplicity

By |2019-04-25T07:53:53+10:00February 8th, 2017|Tags: , , |0 Comments

Zeroes/Roots & Multiplicity Go to the Forum to see more questions or ask your own Formulas Used in Roots & Multiplicity zeroes, are the roots, or solutions to the equation P(x) Number of Roots The maximum number of roots a Polynomial can have is equal to the degree of that polynomial [...]

22 12, 2016

## Inverse Differentials

Inverse Differentials $\frac{dx}{dy}\times\frac{dy}{dx}=1$ worked examples For the function y = 2x + 4, find: a. the inverse function b. $\frac{dy}{dx}$ of the inverse function c. $\frac{dx}{dy}$ of the inverse function d. Show that $\frac{dx}{dy}\times\frac{dy}{dx}=1$ a. x = 2y + 4 x - 4 = 2y f-1: y = ½x - 2 rewrite [...]

26 11, 2016

Inverse Trig Domain & Range y = sin-1 x Domain: -1 ≤ x ≤ 1 Range: $-\frac{\pi}2\leq y \leq \frac{\pi}2$ y = cos-1 x Domain: -1 ≤ x ≤ 1 Range: $0\leq y \leq \pi$ y = tan-1 x Domain: all real x Range: $-\frac{\pi}2\leq [...] 25 11, 2016 ## Long Division By |2019-02-11T15:29:55+10:00November 25th, 2016||0 Comments Long Division Go to the Forum to see more questions or ask your own Worked examples Find the linear factors of 6x3 – 23x2 – 5x + 4. P(1) = 6 - 23 - 5 + 4 ≠ 0 P(2) = 48 - 92 - 10 + 4≠ 0 P(4) = 384 [...] 25 11, 2016 ## Cyclic Quadrilaterals By |2016-11-25T16:02:03+10:00November 25th, 2016||0 Comments Cyclic Quadrilaterals opposite angles of a cyclic quadrilateral are equal In the diagram, 0 is the centre of the circle and AB║AD and BC meet at P. Prove: a. CP = DP b. DABP is isosceles c. OAPC is a cyclic quadrilateral. a. ∠PCD = ∠ABC (corresponding [...] 25 11, 2016 ## Arranging In A Row By |2019-03-01T15:50:41+10:00November 25th, 2016||0 Comments Arranging In A Row Go to the Forum to see more questions or ask your own Formulas used in Arranging In A Row Arranging n things in a row: n! Arranging n things in a row with repeats$\frac{n!}{p!q!...}$where p, q,... are the number of repeats Worked examples [...] 24 11, 2016 ## Vertical Asymptote By |2016-11-26T10:20:45+10:00November 24th, 2016||0 Comments Vertical Asymptote worked examples Write the equation of the vertical asymptote of$y = \frac{x}{{2(1 - x)}}$. 2(1 - x) = 0 1 - x = 0 x = 1 to find the vertical asymptote, we need to find the value for which the function is undefined, which is [...] 24 11, 2016 ## Standard Integrals By |2016-11-24T11:16:34+10:00November 24th, 2016||0 Comments Standard Integrals$\int {\sec \,ax\,\tan \,x\,dx\, = \frac{1}{a}\sec \,ax\, + \,c}\int {\frac{1}{{\sqrt {{x^2} - {a^2}} }}\,dx = \ln \left( {x + \sqrt {{x^2} - {a^2}} } \right) + c} \int {\frac{1}{{\sqrt {{x^2} + {a^2}} }}\,dx = \ln \left( {x + \sqrt {{x^2} + {a^2}} } \right) + [...]
Arranging Letters Go to the Forum to see more questions or ask your own Formulas used in Arranging Letters With no repeats: $n!$ With repeats: $\frac{n!}{p!r!...}$ Grouping letters together: to count the placement of the grouping (n - g + 1), where n is the number, g is the number [...]