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

Solving a pair of linear simultaneous equations, giving answers as integers or fractions.

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

Rewriting fractions involving surds by rationalising the denominator.

Rewriting fractions involving surds by rationalising the denominator.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Rewriting fractions of the form $\frac{\sqrt[m]{x^n}}{\sqrt[p]{x^q}}$ to $x^{\frac{n}{m}-\frac{q}{p}}$.

Rewrite the expression $\frac{{m}x^2+{n}x+{p}}{x+a}$ as partial fractions in the form $\frac{A}{x+a}+Bx+C$.

Rewrite the expression $\frac{{m}x^2+{n}x+{p}}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+C$.

Rewrite the expression $\frac{mx+a}{nx+b}$ as partial fractions in the form $A+\frac{B}{nx+b}$.

Rewrite the expression $\frac{x+a}{x+b}$ as partial fractions in the form $A+\frac{B}{x+b}$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rewrite the expression $\frac{nx+k}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rewrite the expression $\frac{n}{(x+a)(x^2+bx+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{Bx+C}{x^2+bx+c}$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x+b)^2}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{(x+b)^2}$.

Rewrite the expression $\frac{mx^2+nx+k}{(x+a)(x+b)(x+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Rewrite the expression $\frac{nx+k}{(x+a)(x+b)^2}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{(x+b)^2}$.

Rewrite the expression $\frac{nx+k}{(x+a)(x+b)(x+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Rewrite the expression $\frac{cx+d}{(kx+a)(x+b)}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$.

Rewrite the expression $\frac{n}{(x+a)(x+b)^2}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{(x+b)^2}$.

Rewrite the expression $\frac{n}{(x+a)(x+b)(x+c)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}+\frac{C}{x+c}$.

Used for LANTITE preparation (Australia). NC = Non Calculator strand. NA = Number & Algebra strand. Students are given a proportion of students who DO speak a language other than English at home, and are asked to find the percentage who do NOT. The fraction denominator is either 20 or 25, and the numerator is randomised.

Divisor is double digit. There is a remainder which we express as a fraction. 

Divisor is single digit. There is a remainder which we express as a fraction. 

Divisor is single digit. There is a remainder which we express as a decimal by continuing the division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

Rewrite the expression $\frac{cx+d}{kx^2+mx+n}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$, where the quadratic $kx^2+mx+n=(kx+a)(x+b)$.

Rewrite the expression $\frac{cx+d}{x^2+mx+n}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$, where the quadratic $x^2+mx+n=(x+a)(x+b)$.

Rewrite the expression $\frac{cx+d}{(x+a)(x+b)}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$.

Part of HELM Book 1.2

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.