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ScotlandMaths

Applications

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you use differentiation to find the best possible value in a real situation and to describe how quantities change?

Using differentiation to find the optimal value in optimisation problems, the greatest and least values of a function on a closed interval, rates of change, and the motion of a particle through displacement, velocity and acceleration.
A focused answer to the SQA Higher Mathematics applying differential calculus content, covering optimisation problems, the greatest and least values on a closed interval, rates of change, and the displacement, velocity and acceleration of a moving particle.
9 min answer →

How do you use integration to measure area and volume and to recover a quantity from its rate of change?

Using integration to find the area enclosed between a curve and a line or between two curves, the area below the x-axis, recovering displacement from velocity, and using a definite integral to evaluate an accumulated quantity in context.
A focused answer to the SQA Higher Mathematics applying integral calculus content, covering the area between a curve and a line or between two curves, the area below the x-axis, recovering displacement from velocity, and evaluating an accumulated quantity with a definite integral.
9 min answer →

How do recurrence relations model step-by-step change, and when does such a sequence settle towards a limit?

Recurrence relations of the form u sub n plus 1 equals a u sub n plus b, generating terms, the condition for a limit to exist, finding the limit, and interpreting a recurrence relation in a real context.
A focused answer to the SQA Higher Mathematics sequences and recurrence relations content, covering linear recurrence relations, generating terms, the condition for a limit, finding the limit, and interpreting a recurrence relation in a real-world context.
9 min answer →

How do you describe a circle algebraically, find its centre and radius, and decide how a line meets it?

The equation of a circle with centre the origin and with a general centre, the general equation of a circle, finding the centre and radius, the intersection of a line and a circle, and the equation of a tangent to a circle.
A focused answer to the SQA Higher Mathematics circle content, covering the equation of a circle with any centre, the general equation, finding the centre and radius, the intersection of a line and a circle, and the equation of a tangent to a circle.
9 min answer →