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ScotlandMaths

Expressions and Formulae

7 dot points across 7 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you expand brackets and factorise algebraic expressions, including common factors, the difference of two squares and trinomials?

Expanding brackets (including the product of two brackets) and factorising algebraic expressions using a common factor, the difference of two squares, and trinomials with unitary and non-unitary leading coefficients.
A focused answer to the SQA National 5 Mathematics algebra content, covering expanding single and double brackets, and the three factorising methods examined: common factor, difference of two squares, and factorising trinomials with both unitary and non-unitary leading coefficients.
10 min answer →

How do you simplify, add, subtract, multiply and divide algebraic fractions?

Working with algebraic fractions: simplifying by factorising and cancelling, and adding, subtracting, multiplying and dividing algebraic fractions.
A focused answer to the SQA National 5 Mathematics algebraic fractions content, covering simplifying by factorising and cancelling, multiplying and dividing fractions, and adding and subtracting with a common denominator.
9 min answer →

How do you find the length of an arc, the area of a sector, and the volume of standard solids?

Calculating the length of an arc and the area of a sector of a circle, and calculating the volume of standard solids including the prism, cylinder, pyramid, cone and sphere.
A focused answer to the SQA National 5 Mathematics measure content, covering the length of an arc and the area of a sector as fractions of a circle, and the volume formulae for the prism, cylinder, pyramid, cone and sphere.
10 min answer →

How do you write a quadratic expression in the completed-square form, and what does that form tell you about the graph?

Writing a quadratic expression of the form x squared plus bx plus c in the completed-square form (x plus p) squared plus q, and using it to identify the turning point of the parabola.
A focused answer to the SQA National 5 Mathematics completing-the-square content, covering how to write a quadratic in the form (x + p) squared plus q, the link to the turning point and minimum value of the parabola, and how the method is used in Paper 1 non-calculator work.
9 min answer →

How do you calculate the gradient of a straight line from two points, and what does the sign and size of a gradient tell you?

Calculating the gradient of a straight line from two points using the gradient formula, and interpreting positive, negative, zero and undefined gradients.
A focused answer to the SQA National 5 Mathematics gradient content, covering the gradient formula for the slope between two points, interpreting positive, negative, zero and undefined gradients, and the link to steepness and direction.
8 min answer →

How do you write very large and very small numbers in scientific notation, and how do you calculate with numbers in that form?

Writing numbers in scientific notation (standard form), converting between ordinary and scientific notation, and multiplying and dividing numbers written in scientific notation.
A focused answer to the SQA National 5 Mathematics scientific notation content, covering writing large and small numbers in standard form, converting back to ordinary numbers, and multiplying and dividing in scientific notation using the laws of indices.
8 min answer →

How do you simplify and combine surds, rationalise a denominator, and apply the laws of indices including negative and fractional powers?

Simplifying and working with surds (simplifying, adding and subtracting, expanding brackets, rationalising the denominator) and applying the laws of indices including negative and fractional indices.
A focused answer to the SQA National 5 Mathematics surds and indices content, covering simplifying surds, adding and subtracting like surds, expanding brackets, rationalising the denominator, and the laws of indices including negative and fractional powers for exact non-calculator work.
9 min answer →