Finding unknown sides/angles in right-angled triangles.

Version 1: b,c known

Version 2: a,x known

Version 3: a,y known

Version 4: b,x known

Version 5: b,a known

Version 6: c,a known

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

Missing: Application with bacteria, turning points, difficult chain rule

Manipulate surds and rationalise the denominator of a fraction when it is a surd.

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

Question on drug calculations

Question on drug calculations

Question on drug calculations

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Given a dose and available tablets, determine the best combination of tablets, to minimise the number of tablets and avoid dividing tablets. Uses 20, 40 and 150 mg.

Given a dose and available tablets, determine the best combination of tablets, to minimise the number of tablets and avoid dividing tablets. Uses 10, 50 and 200 mg.

Question on drug calculations

Reduced or simplified form of a fraction by cancelling the greatest common divisor (gcd) of numerator and denominator (i.e dividing out by it)

The greatest common factor are designed to be one of the following 2,4,5,10,20,25,50,100,125,250

Couting application where repitition is allowed and order does not matter.

Applicaiton of the pigeonhole principle

Definition of the pigeonhole principle, and some examples

Simple counting exercise. Students are encouraged to look for the smart way of counting.