@?maths

Flashcards 2022-02-07 What is the first step in using the decimal search method?? Rearranging to get 0 on one side. How can you find a good estimate to start with for decimal search?? Draw a sketch. What should you say when an identifying a root using decimal search?? “Gee wiz! The function $f(x)$ is continuous in the interval $[a, b]$ and there is a change of sign, so a root lies near $x$”. How would you show that $1.

Flashcards 2022-02-07 Can you use SUVAT in two dimensions?? Yes. Backlinks [[Maths - Syllabus]]S Metadata date: 2022-02-07 12:34 tags: - '@?mechanics' - '@?maths' - '@?year-2' - '@?school' - '@?public' title: Mechanics - Further Kinematics

Flashcards 2021-12-05 In what form can you express $a\sin x \pm b\cos x$?? $$ R\sin(x \pm \alpha) $$ In what form can you express $a\cos x \pm b\sin x$?? $$ R\cos(x \mp \alpha) $$ You want to express $$a\sin x \pm b\cos x$$ as $$R\sin(x \pm \alpha)$$ How can you calculate $R$?? $$ R = \sqrt{a^2 + b^2} $$ You want to express $$a\sin x \pm b\cos x$$ as $$R\sin(x \pm \alpha)$$ How can you calculate $\alpha$?

Advanced Problems in Mathematics is a series of books designed to help students work through STEP exam material. Like with [[UKMT Questions]]N and [[MAT Questions]]N, the idea is not to use flashcards to memorise the answers to questions but to help spot common patterns in order to help with problem solving. [[APM - Q2 - Finding a general result]]N Backlinks [[Misc Notes]]N Metadata date: 2021-11-30 07:44 tags: - '@?

[[UKMT Senior Maths Challenge - 2020 - Q14]]?? [[UKMT Senior Maths Challenge - 2019 - Q6]]?? [[UKMT Senior Maths Challenge - 2019 - Q16]]?? [[UKMT Senior Maths Challenge - 2019 - Q1]]?? [[UKMT Senior Maths Challenge - 2019 - Q14]]?? [[UKMT Senior Maths Challenge - 2019 - Q4]]?? Backlinks [[APM Questions]]N [[Misc Notes]]N Metadata date: 2021-11-29 11:56 tags: - '@?

Flashcards 2021-11-25 How would you write the probability that $B$ occurs, given that $A$ has already occurred?? $$ P(B|A) $$ What is true about $P(A|B)$ for independent events?? $$ P(A|B) = P(A|B') = P(A) $$ How would you calculate $P(A | B)$?? $$ \frac{0.15}{0.15 + 0.25} $$ How would you calculate $P(A | A \cup B)$?? $$ \frac{0.15}{0.4 + 0.15 + 0.25} $$ How would you calculate $P(A' | B')$?? $$ \frac{0.2}{1-0.15-0.25} $$ Why do you have to be careful dealing with conditional probabilities involving things like “given $B'$”?

Flashcards 2021-11-20 What is the formula for the maximum friction?? $$ F_\text{max} = \mu R $$ What is $\mu$ when talking about friction?? The coefficient of friction. What is $\mu$ if a surface is described as “smooth”?? $$ 0 $$ If a block is being pushed with a $10\text{N}$ force but there is a $20\text{N}$ max friction, what will happen?? The block will not move. What is the situation called when a block is being pushed with a $20\text{N}$ force but there is a $20\text{N}$ max friction?

See Also [[Further Maths - Radians]]S Flashcards What is the small angle approximation for $\sin \theta$ and $\tan \theta$?? $$ \sin \theta \approx \tan \theta \approx \theta $$ What is the small angle approximation for $\cos \theta$?? $$ 1 - \frac{\theta^2}{2} $$ What is $$\frac{\tan 2\theta}{\sin \theta}$$ for $\theta \approx 0$?? $$ 2 $$ Backlinks [[Maths - Syllabus]]S Metadata date: 2021-11-09 15:30 tags: - '@?public' - '@?

Flashcards 2021-11-02 If you know two roots of a cubic equation $ax^3 + bx^2 + cx + d = 0$, how can you find the final one?? Use the sum of the roots or product of the roots formulas. Backlinks [[MAT Questions]]N Metadata date: 2021-11-02 19:08 summary: "" tags: - '@?public' - '@?mat' - '@?notes' - '@?maths' title: MAT - Paper 2020 - Q2

Flashcards 2021-11-02 When given a seemingly opaque equation like $$\beta^4 + 2\beta^3 - 4\beta - 2$$ what should you do?? Try and plot it. What’s a common technique for showing that if something holds for a special case of a graph/function, it also holds more generally?? The properties are preserved under geometric transformations. Backlinks [[MAT Questions]]N Metadata date: 2021-11-02 18:01 summary: "" tags: - '@?public' - '@?mat' - '@?notes' - '@?maths' title: MAT - Paper 2019 - Q3

what is true about (1 + x)(1 + x^2)(1 + x^3)…

how is true about these three log equations?