@?a-level

Flashcards 2022-02-10 Where is all radiation emitted from?? An unstable nucleus. What are the four different types of radiation?? Alpha Beta-minus Beta-plus Gamma What particle is emitted in beta-minus radiation?? An electron. What particle is emitted in beta-plus radiation?? A positron. What instrument do you use to detect radiation?? A Geiger-Muller counter. What must you subtract from every Geiger-Muller counter in order to accurately determine the radioactivity of a substance?? The background radiation.

Flashcards 2022-02-07 What are the two types of beta decay?? Beta minus Beta plus How should you write an electron in a beta decay equation?? $$ _{-1}^0 e $$ When denoting particles in a beta decay equation, such as $_y^x \alpha$, what does $y$ represent?? The charge. When denoting particles in a beta decay equation, such as $_y^x \alpha$, what does $x$ represent?? The nucleon number. What two quantities are conserved in a beta decay equation?

See also [[Further Maths - Loci in the Argand Diagram]]S . This diagram shows the loci of points for $|z - (3 + 3i)| = 2$. Visualise the region $|z - (3 + 3i)| \le 2$?? This diagram shows the (poorly drawn) loci of points for $|z| = 3$ and $|z| = 5$. Visualise the region $3 \le |z| \le 5$?? This diagram shows the loci of points for $|z + 6| = |z - 4|$.

What is the definition of an even function?? $$ f(x) = f(-x) $$ What is the definition of an odd function?? $$ -f(x) = f(-x) $$ What is the parity of $x^2$?? Even What is the parity of $x^3$?? Odd What is special geometrically about even functions?? The function is symmetric with the $y$-axis. What is special geometrically about odd functions?? The function has $180^{\circ}$ rotational symmetry with respect to the origin. What is the parity of $\sin x$?

Degrees What is $\sin 0^{\circ}$?? $$ 0 $$ What is $\sin 30^{\circ}$?? $$ \frac{1}{2} $$ What is $\sin 45^{\circ}$?? $$ \frac{\sqrt{2}}{2} $$ What is $\sin 60^{\circ}$?? $$ \frac{\sqrt{3}}{2} $$ What is $\sin 90^{\circ}$?? $$ 1 $$ What is $\cos 0^{\circ}$?? $$ 1 $$ What is $\cos 30^{\circ}$?? $$ \frac{\sqrt{3}}{2} $$ What is $\cos 45^{\circ}$?? $$ \frac{\sqrt{2}}{2} $$ What is $\cos 60^{\circ}$?? $$ \frac{1}{2} $$ What is $\cos 90^{\circ}$?? $$ 0 $$ What is $\tan 0^{\circ}$?? $$ 0 $$

How many radians in a full circle?? $$ 2\pi $$ How many radians in $360^{\circ}$?? $$ 2\pi $$ How many circles in a half turn?? $$ \pi $$ What is $180^{\circ}$ in radians?? $$ \pi $$ What is $\frac{\pi}{2}$ radians in degrees?? $$ 90^{\circ} $$ What is $90^{\circ}$ degrees in radians?? $$ \frac{\pi}{2} $$ What is $\frac{\pi}{3}$ radians in degrees?? $$ 60^{\circ} $$ What is $60^{\circ}$ degrees in radians?? $$ \frac{\pi}{2} $$ What is $\frac{\pi}{6} radians in radians?

The sole purpose of this entry being seperate is so that I don’t have to re-load the other [[Further Maths - Series]]S into Anki because it’s got some formatting issues that are down to underscores inside Latex formulas being recognised as italics rather than subscripts. How can you rewrite $\sum^{n}_{r=1} (r+4)^3$?? $$ \sum^{n+4}{r=1} r^3 + \sum{4}{r=1} r^3 $$ Why can you rewrite $\sum^{n}_{r=1} (r+4)^3$?? Because it’s the same as a $r^3$ sequence starting at $5$.

Conjugates A pair of complex numbers with a different sign but otherwise the same values are called conjugates: $$ 3 + 4i 3 - 4i $$ What are complex conjugates?? A pair of complex numbers with real and imaginary parts equal in magnitude but opposite in sign: $a+bi$ and $a-bi$ What is a pair of complex numbers $a+bi$ and $a-bi$ called?? A complex conjugate. What is the result of multipling complex conjugates?? You get a real number.