17 results authored by Hannah Aldous - search across all users.

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• Factorising Quadratic Equations with $x^2$ Coefficients of 1

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.

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• Pure mathematics
• Algebra

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• Find and use the formula for a geometric sequence

Find the common ratio of a given geometric sequence, write down the formula for the nth term and use it to calculate a given term in the sequence.

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• Identifying different types of sequences

Differentiate between linear and quadratic sequences and arithmetic and geometric sequences through a series of multiple choice questions. Spot different patterns in sequences like the triangle sequence, square sequence and cubic sequence and then use this pattern to find the next three terms in each of the sequences.

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• Using Laws for Addition and Subtraction of Logarithms

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

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• Combining Logarithm Rules to Solve Equations

Apply and combine logarithm laws in a given equation to find the value of $x$.

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• Pure mathematics
• Arithmetic

Key Stage 4 / GCSE, A-Level, Transition to university

• Factorising Quadratic Equations with $x^2$ Coefficients Greater than 1

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

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• Completing the square

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

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• Using the Quadratic Formula to Solve Equations of the Form $ax^2 +bx+c=0$

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.

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• Using the Logarithm Equivalence $\log_ba=c \Longleftrightarrow a=b^c$

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

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• Pure mathematics
• Arithmetic

Key Stage 4 / GCSE, A-Level, Transition to university

• Use the quadratic formula to solve an equation in terms of an unknown variable

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

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