Just what the title says, I guess.

Just what the title says, I guess.

Transposition of formulae. Changing the subject of an equation. 

rebel rebelmaths

Solving quadratic equations using a formula

Solving quadratic equations using a formula,

Solving quadratic equations using a formula,

Given some random finite subsets of the natural numbers, perform set operations $\cap,\;\cup$ and complement.

Writing ratios in the form n:1 or 1:n

Laplace from tables: e^(at), cos(bt), sin(bt).

rebelmaths

Graphing $y=ab^{\pm x+d}+c$

Graphing $y=ab^x+c$

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Graphing $y=a\log_{b}(\pm x+d)+c$

Graphing $y=a\log_{b}(x)+c$

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

The easiest type of exponential to graph where the base is greater than 1 and no transformations take place.

Solve quadratic equations using formula.

Quiz covering basic arithmetic with complex numbers, solving a quadratic with complex solutions and converting to/from polar and rectangular forms.

Selection of Quadratic Equations to Solve

The student is asked to factorise a quadratic $x^2 + ax + b$. A custom marking script uses pattern matching to ensure that the student's answer is of the form $(x+a)(x+b)$, $(x+a)^2$, or $x(x+a)$.

To find the script, look in the Scripts tab of part a.

Using Jsxgraph to draw the vector field for a differential equation of the form $\frac{dy}{dx}=f(x,y)=x^2-y^2$, and also by moving the point $(x_0,y_0)$ you can see the solution curves going through that point.

If you want to modify $f(x,y)$ simply change the definition of  $f(x,y)$ and that of the variable  str in the user defined function testfield in Extensions and scripts. You have to use javascript notation for functions and powers in the definition of $f(x,y)$.

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Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}e $ where each of $a, \;b,\;c,\;d,\;e$ can be one the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4}$ one of $\lor,\;\land,\;\to$.

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

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

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 $\neg q \to \neg p$.

Algebra:  Quadratic Factorisation.

              Coefficient of squared term is 1.