SQA Advanced Higher Mathematics

Flashcards for SQA Advanced Higher Mathematics (C847 77), following the course specification (version 2.0, 2019, still current under Qualifications Scotland). Split into the specification's three areas, Calculus, Algebra proof and number theory, and Matrices vectors and complex numbers, then by topic in that order. A card's extra note says whether a result is printed on the formulae list or has to be recalled.

Adding it gives you your own copy, with every subdeck below. Each card then comes back just before you would forget it, and every one you get right or wrong counts towards your mastery of its topic. You can delete or suspend the parts you are not studying once it is yours.

Some of its cards

• What is a vertical asymptote of a rational function?

  A value of $x$ where the denominator is zero and the numerator is not, so the function is undefined and $y$ tends to $\pm\infty$ there.
• What is $\frac{d}{dx}(\sin^{-1}x)$?

  $\dfrac{1}{\sqrt{1-x^2}}$
• What form does a partial fraction decomposition take for a denominator with two distinct linear factors $(x-a)(x-b)$?

  $\dfrac{A}{x-a}+\dfrac{B}{x-b}$
• How do you add the complex numbers $a+bi$ and $c+di$?

  $(a+c)+(b+d)i$
• What matrix represents an anticlockwise rotation through angle $\theta$ about the origin?

  $\begin{pmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{pmatrix}$
• What is the formula for the vector product $a\times b$?

  $|a||b|\sin\theta\,\hat n$
• What is a direct proof?

  A proof that starts from known facts or definitions and reasons forward, in a chain of steps, to the required result.
• What is the order of a matrix with $m$ rows and $n$ columns?

  $m\times n$
• What is the Maclaurin expansion of $f(x)$?

  $f(x)=f(0)+f'(0)x+\dfrac{f''(0)}{2!}x^2+\dfrac{f'''(0)}{3!}x^3+\dfrac{f^{(4)}(0)}{4!}x^4+\dots$
• What is the formula for the $n$th term of an arithmetic sequence with first term $a$ and common difference $d$?

  $a+(n-1)d$

And 454 more once you add the deck.