@?maths

This is a method that’s super difficult to describe. Backlinks [[Maths - Syllabus]]S Metadata date: 2021-03-22 18:05 tags: - '@?maths' - '@?public' title: Maths - Algebraic Long Division

See Also Flashcards What is hypothesis testing?? Determining how likely observed data occured by chance. What is the notation for the null hypothesis?? $$ H_0 $$ What is the notation for the alternate hypothesis?? $$ H_1 $$ What is a population parameter?? A statistic that summarises some information about a population. In the A-level, what’s the definition of a hypothesis?? Some statement made about a population parameter. In a binomial distribution, what is the population parameter?

$$(a + b)^12$$ What would you use to expand this?? The binomial theorem. What is the $r$-th term in the binomial expansion of $(a + b)^n$?? $$ \left(\begin{matrix} n \\ r \end{matrix}\right) a^n b^{n - r} $$ $$1 \quad 5 \quad 10 \quad 10 \quad 5 \quad 1$$ What is the next row of Pascal’s triangle?? $$ 1 \quad 6 \quad 15 \quad 20 \quad 15 \quad 6 \quad 1 $$ What does the $n$-th row of Pascal’s triangle start with (ignoring the top)?

What is always true about two radii and a chord in a circle?? They always make an isoceles triangle. What is always true about the perpindicular bisector of a chord in a circle?? It always passes through the centre of the circle. What is true about angles created from the same arc (think slice of pie)?? They are equal. What is true about angle C, the angles formed by drawing lines from the ends of a diameter to the circumference?

What is $\csc\theta$?? $$ \frac{1}{\sin\theta} $$ What is $\sec\theta$?? $$ \frac{1}{\cos\theta} $$ What is $\cot\theta$?? $$ \frac{1}{\tan\theta} $$ What is $\csc\theta$ in terms of triangle sides?? $$ \frac{\text{hyp}}{\text{opp}} $$ What is $\sec\theta$ in terms of triangle sides?? $$ \frac{\text{hyp}}{\text{adj}} $$ What is $\cot\theta$ in terms of triangle sides?? $$ \frac{\text{adj}}{\text{opp}} $$ 2021-02-22 $$\cos^2 x + \sin^2 x = 1$$ What do you get if you divide both sides by $\cos^2 x$?? $$ 1 + \tan^2 x = \sec^2 x $$

See Also [[Maths - Differentiation]]S [[Maths - Chain Rule]]S Flashcards If $y = uv$, what is $\frac{dy}{dx}$?? $$ u\frac{dv}{dx} + v\frac{du}{dx} $$ If $f(x) = g(x)h(x)$, what is $f'(x)$?? $$ g(x)h'(x) + h(x)g'(x) $$ How would you explain the product rule in English?? To find the derivative of two things multiplied together, add the products of the pairs of each function and its opposite’s derivative. This diagram represents $h(x) = f(x)g(x)$.

Circles are like smooth squares. Flashcards What’s the gradient of the line passing through the centre?? $$ \frac{2-5}{3-2} = -\frac{3}{2} $$ If the gradient of the line passing through the centre is $-\frac{3}{2}$, what is the gradient of the tangent?? $$ \frac{2}{3} $$ Backlinks [[Maths - Syllabus]]S Metadata date: 2021-02-05 13:27 tags: - '@?maths' - '@?public' title: Maths - Circles Attachments circle-tangent.png

See Also [[Maths - Differentiation]]S https://betterexplained.com/articles/derivatives-product-power-chain/ Flashcards What is the chain rule?? $$ \frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx} $$ What new variable do you introduce when using the chain rule?? $$ u $$ When do you apply the chain rule?? When you have composite functions. $$y = (3x + 4)^5$$ What substitution would you make in order to differentiate?? $$ u = 3x + 4 \\ y = u^5 $$ $$y = u^5$$ What is $\frac{dy}{du}$?

See Also [[Maths - Differentiation]]S Flashcards $$y = a^x \ y = a^{-x}$$ What is true about these two graphs?? They are reflections of each other in the $y$-axis. $$y = a^x$$ What is the $y$-intercept of this graph?? $$ 1 $$ $$\log_a b = c$$ If this is true, what is also true?? $$ a^c = b $$ $$3^x = 9$$ What would you do to both sides to make $x$ the subject?

See Also [[Maths - Differentiation]]S Flashcards Visually, if $y = f(x)$ is a maximum or minimum, what does the curve $y = f'(x)$ do?? Cuts the $x$-axis. Visually, if $y = f(x)$ is a point of inflection, what does the curve $y = f'(x)$ do?? Touches the $x$-axis. Visually, if $y = f(x)$ has a positive gradient, where is the curve $y = f'(x)$?? Above the $x$-axis. Visually, if $y = f(x)$ has a negative gradient, where is the curve $y = f'(x)$?

What would the differential be called for $A = \pi r^2$?? $$ \frac{dA}{dr} $$ $$A = \pi r^2 \ \frac{dA}{dr}$$ How would you describe the differential?? The rate of change of area with respect to radius. Can you differentiate $V = \frac{4}{3} \pi r^3$?? $$ \frac{dV}{dr} = 4\pi r^2 $$ $$V = \frac{4}{3} \pi r^3 \ \frac{dV}{dr} = 4\pi r^2$$ How could you explain “the rate of change of volume with respect to radius”?? How much additional volume you gain for a small change in the radius.

What is the transformation as a vector for $y = f(x) + a$?? $$ \left(\begin{matrix} 0 \\ a \end{matrix}\right) $$ What does the transformation $y = f(x) + a$ mean in simple terms?? Move the graph up by $a$. What is the transformation as a vector for $y = f(x + a)$?? $$ \left(\begin{matrix} -a \\ 0 \end{matrix}\right) $$ What does the transformation $y = f(x + a)$ mean in simple terms?? Move the graph back horizontally by $a$.