Simplifying single term expressions involving more than one letter.

Simplifying coefficients and establishing the standardized order of writing expressions.

Difference of two squares - where one square has a coefficient

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.

Solving factorised quadratics with leading coefficient NOT 1

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

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

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

Students are supposed to use Excel (or similar) to find the answers (e.g., enter coordinates of two points then plot and add trendline).

Uses an embedded Geogebra graph of a line $y=mx+c$ with random coefficients set by NUMBAS.

Given the following three vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\textbf{v}_{r}=p\textbf{v}_{s}+q\textbf{v}_{t}$ for suitable $r,\;s,\;t$ and integers $p,\;q$.

Algebra:  Quadratic Factorisation.

              Coefficient of squared term is 1.

Differentiate a polynomial expression involving coefficients and, negative and fractional indices. 

Factorise a quadratic equation where the coefficient of the $x^2$ term is greater than 1 and then write down the roots of the equation

Solving a quadratic equation via factorisation (or otherwise) with the $x^2$-term having a coefficient of 1.

Fiind the Highest Common Factor of two algebraic expressions involving a coefficient and powers of $x$ and $y$.

Solving a quadratic equation via factorisation, with the $x^2$-term having a coefficient of 1.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

Factorising a quadratic expression with the $x^2$-term having a coefficient of 1.

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Calculate the Pearson correlation coefficient on paired data and comment on the significance.

rebelmaths

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Real numbers $a,\;b,\;c$ and $d$ are such that $a+b+c+d=1$ and for the given vectors $\textbf{v}_1,\;\textbf{v}_2,\;\textbf{v}_3,\;\textbf{v}_4$ $a\textbf{v}_1+b\textbf{v}_2+c\textbf{v}_3+d\textbf{v}_4=\textbf{0}$. Find $a,\;b,\;c,\;d$.

This question tests the students ability to factorise simple quadratic equations (where the coefficient of the x^2 term is 1) and use the factorised equation to solve the equation when it is equal to 0.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients

More work on differentiation with fractional coefficients and powers

More work on differentiation with fractional coefficients.