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ScotlandMaths

Expressions and Functions

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do the laws of logarithms let you solve equations with the unknown in the power, and how do logs reveal hidden relationships in data?

The laws of logarithms and their use in simplifying expressions and solving equations, the relationship between exponential and logarithmic form, and the use of logarithms to find the parameters in experimental laws of the form y equals k x to the n and y equals a b to the x.
A focused answer to the SQA Higher Mathematics exponentials and logarithms content, covering the laws of logarithms, the link between exponential and logarithmic form, solving equations with the unknown in the power, and using logs to find the parameters in experimental power and exponential laws.
9 min answer →

How do functions combine, invert and transform, and how do those operations move and reshape their graphs?

Functions and their domain and range, composite functions, inverse functions, exponential and logarithmic graphs, and the graphs that result from translating, reflecting and stretching a known function.
A focused answer to the SQA Higher Mathematics functions and graphs content, covering domain and range, composite and inverse functions, the shapes of exponential and logarithmic graphs, and how translating, reflecting and stretching transforms the graph of a known function.
9 min answer →

How do you describe a straight line algebraically, and how do gradient and angle let you decide whether lines are parallel, perpendicular or concurrent?

The gradient of a line including the connection to the angle it makes with the x-axis, the equation of a line through a point with a given gradient, parallel and perpendicular lines, and the medians, altitudes and perpendicular bisectors of a triangle.
A focused answer to the SQA Higher Mathematics straight line content, covering gradient and its link to the angle with the x-axis, the equation of a line through a point, parallel and perpendicular lines, and finding medians, altitudes and perpendicular bisectors in a triangle.
9 min answer →

How do you measure angles in radians, read exact trigonometric values, and sketch and transform trigonometric graphs?

Radian measure and the conversion between degrees and radians, exact values of sine, cosine and tangent for the standard angles, the graphs of the trigonometric functions, and the transformations that change their amplitude, period and phase.
A focused answer to the SQA Higher Mathematics trigonometry and radians content, covering radian measure and degree conversion, exact values of sine, cosine and tangent, the trigonometric graphs, and the amplitude, period and phase transformations that reshape them.
9 min answer →

How do you describe position and direction in three dimensions, and how does the scalar product reveal the angle between two vectors?

Vectors in three dimensions, the magnitude and unit vector, addition and scalar multiplication, the section formula and collinearity, and the scalar product including its use to find the angle between two vectors and to test for perpendicularity.
A focused answer to the SQA Higher Mathematics vectors content, covering three-dimensional vectors, magnitude and unit vectors, addition and scalar multiplication, collinearity and the section formula, and the scalar product used to find the angle between vectors and test perpendicularity.
9 min answer →