Collection of questions on factorising quadratics with a=1.

Factorise a quadratic equation of the form $x^2+bx+c$ with one positive and one negative root.

Factorise a quadratic equation of the form $x^2+bx+c$ with one positive and one negative root.

Factorise a quadratic equation of the form $x^2+bx+c$ with two positive roots

Factorise a quadratic equations of the form $x^2+bx+c$ with 2 negative roots.

Factorising without powers

Factorise an expression of the form $ax^n+bx^m$.

Factorise an expression of the form $ax+bxy$ for variables $x$ and $y$.

Factorise an expression of the form $-ax-b$ for numbers $a,b$

Substituting a values of $x$ and $z$ into $\frac{ax+bz}{c}$

Substituting a values of $x$ and $z$ into $a(x+z)$

Solving linear equations with unknowns on both sides

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Recovering original function given some information such as derivative and value at some point.

More work on differentiation with trigonometric functions

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

Simplifying single term expressions involving more than one letter.

Performing calculations with numbers in standard form

A set of questions practicing finding equivalent fractions with an emphasis on simplifying.

spot use of a multiplier to get equivalent fractions with larger denominators.

Simplifying a fraction with many factors up to cubed primes in common.

Simplifying a fraction with a common factor up to a square.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

Draw Shear and Bending Moment Diagrams for a simply supported beam with triangular loading

Find the centroid and the centroidal moments of inertia for a beam composed of a flat plate and two angle sections.

Calculate the centroidal moment of intertia of a rectangle with a excentric rectangular hole.

Find moment of inertia of a composite shape consisting of a rectangle and two triangles with respect to the x-axis. Shapes rest on the x-axis so the parallel axis theorem is not required.

Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.

Questions testing understanding of the precedence of operators using BIDMAS, applied to integers. These questions only test DMAS. That is, only Division/Multiplcation and Addition/Subtraction.