Divisor is single digit. There is a remainder which we express as a decimal by continuing the long 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.

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.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

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

End of chapter exercises for Engineering Statics: Open and Interactive 

Friction

Friction

Friction

Counting the number of significant figures. 

Pythagoras' Theorem and naming sides of right angled triangle

rebelmaths

Solving factorised quadratics with leading coefficient NOT 1

Solving equations involving algebraic fractions which simplify into quadratics

Solving quadratics which need simplifying first.

quadratic solving using difference of two squares

Factorising and solving a quadratic with a=1

intorductory question on multiplying algebraic fractions. Just multiplying nuerators and denominators required.

Simultaneous equations with at least one non-linear equation

Questions on combining and simplifying algebraic fractions

Simplifying first is essential in terms of managing expressions that might need factorising.

No description given

Manipulate fractions in order to add and subtract them. The difficulty escalates through the inclusion of a whole integer and a decimal, which both need to be converted into a fraction before the addition/subtraction can take place. 

Dividing algebraic fractions question where the result does not require any cancellation

(ax+b)/(mx+n)+(cx+d)/(px+q)

Adding algebraic fractions with linear expressions in the numerators

simplifying pL1^a/n+kL2^bL1^c/m

Adding two algebraic fractions with the same variable in the numberators.

Solving a pair of simultaneous equations of the form $a_1x+b_1y=c_1$ and $a_2 x^2+b_2y^2=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1x+y=c_1$ and $a_2x^2+b_2xy=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1xy=c_1$ and $a_2x+b_2y=c_2$ by forming a quadratic equation.

Questions for practising algebraic methods for solving linear simultaneous equations