/Tag: Challenging Questions
5 06, 2017

Challenging Exponentials

By |2017-06-05T10:50:34+00:00June 5th, 2017|Tags: , , |0 Comments

Challenging Exponentials Find the derivative of $$y=x^x$$. let $$y = {\left( {{e^{\ln x}}} \right)^x}$$ as eln x = x $$y = {e^{x.\ln x}}$$ let y = eu consider separately u = x.ln x $$\frac{du}{dx}=\ln x . 1 + x.\frac{1}{x}$$ $$\frac{du}{dx}=\ln x +1$$ to differentiate y = eu, differentiate [...]

2 11, 2016

Challenging Trig

By |2016-11-06T10:43:10+00:00November 2nd, 2016|Tags: , |Comments Off on Challenging Trig

Challenging Trig Find the exact value of sin x. The x value will be 3/5 and the y value will be 4/5. Use Pythagoras to find the length of the hypotenuse. H2 = 3/5 2 + 4/5 2 H2 = 1 H = 1 use the sum [...]

27 06, 2016

Challenging Questions

By |2016-11-03T17:52:19+00:00June 27th, 2016|Tags: , , , |Comments Off on Challenging Questions

Challenging Questions Find the area of an equilateral triangle with 2cm sides. Form a right triangle from the equilateral, using the perpendicular will bisect the base. Use Pythagoras to find the height of the triangle h2 = 22 - 12 h2 = 3 h = √3 h = 1.73 A = ½bh [...]

14 05, 2016

Challenging Right Trig

By |2016-11-06T11:17:53+00:00May 14th, 2016|Tags: , , |Comments Off on Challenging Right Trig

Challenging Questions Work out the length marked BC in this diagram. sin 48 = $$\frac{AC}{19}$$ AC = 19 sin 48 AC = 14.12cm use this now to find the angle in ΔABC sin B = $$\frac{14.12}{23}$$ B = 37°52' cos 37°52' = $$\frac{BC}{23}$$ BC = 23 × cos 37°52' BC = 18cm [...]

16 03, 2016

Challenging Indices

By |2016-10-21T13:17:06+00:00March 16th, 2016|Tags: , , , , |0 Comments

Challenging Indices Simplify $$\frac{2^{a+3}-4\times 2^a}{2^{2a+1}-4^a}$$. $$= \frac{2^{a+3}-2^2\times 2^a}{2^{2a+1}-(2^2)^a}$$ $$= \frac{2^{a+3}-2^{a+2}}{2^{2a+1}-2^{2a}}$$ $$= \frac{2^a(2^3-2^2)}{2^{2a}(2^1-1)}$$ $$= \frac{2^a(8-4)}{2^{2a}(2-1)}$$ $$= \frac{2^a(4)}{2^{2a}}$$ $$= \frac{2^a\times 2^2}{2^{2a}}$$ $$= \frac{2^{a+2}}{2^{2a}}$$ $$= 2^{a+2-2a}$$ $$= 2^{2-a}$$ Simplify $$\frac{2^{n+1}-2^{n+2}}{2^{n-1}-2^{n-2}}$$. $$=\frac{2^n(2^1-2^2)}{2^n(2^{-1}-2^{-2})}$$ $$=\frac{2-4}{\frac12-\frac14}$$ $$=\frac{-2}{\frac14}$$ = -8 Simplify $$\frac{x^{\frac12}y^{-\frac12}-x^{-\frac12}y^{\frac12}}{x^{-1}y^{-1}}$$. $$=\frac{x^{\frac12}y^{-\frac12}}{x^{-1}y^{-1}}-\frac{x^{-\frac12}y^{\frac12}}{x^{-1}y^{-1}}$$   remembering that when you divide, the indices are subtracted $$=x^{\frac32}y^{\frac12}-x^{\frac12}y^{\frac32}$$ $$=x^{\frac12}y^{\frac12}(x-y)$$ [...]

25 08, 2015

Challenging Speed Questions

By |2016-11-05T18:31:18+00:00August 25th, 2015|Tags: , , , |Comments Off on Challenging Speed Questions

Challenging Questions A riverboat cruise liner boat travels 8km upstream and 8km downstream.The total time for both parts of the trip is 3 hours. The speed of the stream is 2km/h. what is the speed of the boat in still water? let the speed be x upstream x -2  as [...]

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