@?maths

how can we find dates that don’t have any repeating numbers?

lets do some stuff with inequalities and trig functions because we hate fun

Flashcards $$\sqrt{3 - 2\sqrt{2}}$$ How can you simplify this?? Rewrite as $$ \sqrt{2}^2 - 2\cdot\sqrt{2}\cdot + 1^2 $$ and complete the square. 2022-01-19 How could you find the area of the shaded region?? Split it up into a sector and a right-angled triangle. 2022-02-02 Given a parametric curve $$(x(t), y(t))$$ how can you work out the parametric curve for rotating it by an angle $\theta$?? $$ \left(\begin{matrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{matrix}\right) $$

Flashcards What does $fg(x)$ mean?? $$ f(g(x)) $$ What does $f^2(x)$ mean?? $$ f(f(x)) $$ What does $\alpha \circ \beta (x)$ mean?? $$ \alpha(\beta(x)) $$ If the domain for $g(x) = x^2 - 3$ is $$x \in \mathbb{R}, x \ge 0$$ What is the domain for $gf(x)$ where $f(x) = 5x - 2$?? $$ x \ge \frac{2}{5} $$ Backlinks [[Maths - Syllabus]]S Metadata date: 2021-07-05 11:15 tags: - '@?maths' - '@?

Flashcards What is the domain of a function?? The set of all possible inputs. What is the range of a function?? The set of all possible outputs. What is the range of a function sometimes called?? The codomain. What is a mapping?? A transformation from one set of numbers into a different set of numbers. When is a mapping a function?? When every input has a distinct output. Other than a one-to-one function, what’s another type of mapping that is also a function?

See Also [[Maths - Proof by Contradiction]]S [[Maths - Proof Roots of Primes are Irrational]]S Backlinks [[Maths - Proof by Contradiction]]S [[Maths - Syllabus]]S Metadata date: 2021-06-06 11:39 tags: - '@?public' - '@?school' - '@?maths' - '@?proof' title: Maths - Proof

See Also [[Maths - Proof Roots of Primes are Irrational]]S [[Maths - Proof]]S Flashcards How can you prove a statement is FALSE by contradiction?? Find a counterexample. How can you prove a statement is TRUE by contradiction?? Negate the statement and assume it’s false. Prove this leads to a contradiction. What would be the negated statement for “if $n^2$ is even, $n$ must be even”?? “there exists an odd number $n$ such that $n^2$ is even”

See Also [[Maths - Integration]]S [[Maths - Differentiation]]S Flashcards What type of answer do you normally get for differential equation questions?? A family of curves. What’s the general process for solving a differential equation question like $$\frac{dy}{dx} = \frac{y + 1}{x}$$?? Seperate the two variables and put them on either side of the equation. Integrate both sides with respect to $x$. Rearrange. $$\int \frac{1}{y + 1} \frac{dy}{dx} dx$$ What does this simplify down to?

See Also [[Maths - Integration]]S [[Maths - Integration by Substitution]]S [[Further Maths - Integrating and Differentiating Inverse Trig Functions]]S Flashcards $$\int u \frac{dv}{dx} dx$$ How can you rewrite this?? $$ uv - \int v \frac{du}{dx} $$ What table of $4$ variables should you create when doing integration by parts?/ $$ u, v, \frac{du}{dx}, \frac{dv}{dx} $$ $$\int x e^x dx$$ What are the variables you’d use for integration by parts?

See Also [[Maths - Integration]]S Flashcards $$\int (x+2)^5 dx$$ What subsitution could you make in terms of $u$?? $$ u = x + 2 $$ If $u = x + 2$, what is $\frac{du}{dx}$?? $$ \frac{du}{dx} = 1 $$ If $u = x + 2$ and $\frac{du}{dx} = 1$, what is $dx$?? $$ du $$ $$\int (x+2)^5 dx$$ If $u = x+2$ and $du = dx$, how could you rewrite the integral?

Flashcards 2021-03-24 If $f(x)$ is a polynomial and $f(p) = 0$, what must be true?? $(x - p)$ is a factor of $f(x)$. If $f(x)$ is a polynomial and $(x-p)$ is a factor of $f(x), what must bbe true?? $$ f(p) = 0 $$ 2021-03-26 If $f(x)$ is a polynomial and $f\left(\frac{b}{a}\right) = r$, what must be true?? Dividing $f(x)$ by $(ax - b)$ has remaineder $r$. If $f(x)$ is a polynomial and dividing by $(ax - b)$ has remainder $r$, what must be true?

See Also [[Maths - Differentiation]]S [[Maths - Product Rule]]S [[Maths - Chain Rule]]S Flashcards What is the Quotient Rule used for?? Finding the derivative of two things being divided. $$\frac{d}{dx}\left(\frac{u}{v}\right)$$ What is this equal to?? $$ \frac{v \cdot \frac{du}{dx} - u \cdot \frac{dv}{dx}}{v^2} $$ What is important you remember about the product rule?? The order. Where does the $v^2$ bit come from in the product rule?? It’s actually the product rule with $v^{-1}$, which goes to $\frac{1}{v^2}$