Maths Mutt Publications

These notes are primarily designed for the SQA Higher Mathematics course.

• Derivative of \(f(x) = ax^n\)
• Sum Rule
• Derivative of \(f(x) = (x + a)^n\)
• Derivative of \(f(x) = (ax + b)^n\)
• The Chain Rule
• Trig functions
• Logarithms and exponentials

A quick revision guide to basic integration, designed for the SQA Higher Mathematics course, with additional material extending into Advanced Higher.

• Integral calculus
• Basic rules of integration
• Fundamental theorem of calculus
• Trig functions
• Logarithms and exponentials
• Integration by substitution
• Common forms
• Areas on graphs
• Newton’s equations of motion
• Areas under curves
• Integration and the area function
• Area between curve and the y‑axis
• Areas enclosed by the graph and the x‑axis
• Area between two graphs

These notes are designed as a revision aid for differentiation by first principles, covering core rules and trigonometric derivatives derived from limits.

• Derivative of \(f(x) = g(x) + h(x)\)
• Derivative of \(f(x) = ax^n\)
• Derivative of \(f(x) = (x + a)^n\)
• Derivative of \(f(x) = (ax + b)^n\)
• The Chain Rule
• Finding trigonometric derivatives by first principles
• Derivative of \(f(x) = \sin x\)
• Derivative of \(f(x) = \sin(ax)\)
• Derivative of \(f(x) = \cos x\)
• Derivative of \(f(x) = \tan x\)
• Product Rule
• Quotient Rule

A collection of forty questions with full worked solutions, covering key techniques in integration and differential equations.

Questions include:

• Variables separable
• First‑order differential equations
• Second‑order differential equations
• Partial fractions
• Integration by parts
• Integration by substitution