3.1 Functions 1. Recap, Domain and Range - Higher Maths Lessons - @MrThomasMaths SQA {Restrictions}

Here is Higher Maths Chapter 3 – Functions.
Lesson 1 of 7: Recap, Domain and Range.

I am using a mix of mainly the Heinemann and Maths in Action Higher textbooks throughout the course. For a few lessons I also dive into the TJ book.
A special thanks must go to Grace, Ryan and Connor for kindly providing me with a unique musical intro…
123 videos have now been uploaded to guide you through Higher Maths and each video includes an explanation along with plenty of worked examples to help you gain a solid understanding.
Here is a list of both the chapters and the individual lessons to allow you to target specific outcomes. Enjoy!

CHAPTERS
1. Straight Line
2. Recurrence Relations
3. Functions
4. Graph Transformations
5. Trig Graphs & Equations
6. Differentiation
7. Polynomials
8. Quadratics
9. Integration
10. Circles
11. Double Angle & Addition Formulae
12. Wave Function
13. Vectors
14. Further Calculus
15. Logs and Exponentials


LESSONS

1. STRAIGHT LINE
1.1. Revision of Gradient
1.2. Collinearity
1.3. Gradient = Tan θ
1.4. The Distance Formula
1.5. ax + by + c = 0
1.6. y - b = m(x - a)
1.7. Perpendicular Lines
1.8. Midpoints
1.9. Medians
1.10. Altitudes
1.11. Perpendicular Bisectors
1.12. Points of Intersection
1.13. Chapter Review

2. RECURRENCE RELATIONS
2.1. nth Term & Recurrence Relations Introduction
2.2. Worded Recurrence Relations
2.3. Limits
2.4. Finding A and B
2.5. Chapter Review

3. FUNCTIONS
3.1. Recap, Domain & Range
3.2. Notation & Graphs of Functions
3.3. Composite Functions
3.4. Inverse Functions
3.5. Graphs of Inverse Functions
3.6. Exponential & Logarithmic
3.7. Chapter Review

4. GRAPH TRANSFORMATIONS
4.1. Shapes of Graphs
4.2. y = f(x) ± a
4.3. y = f(x ± a)
4.4. y = -f(x)
4.5. y = f(-x)
4.6. y = kf(x)
4.7. y = f(kx)
4.8. Composite Functions
4.9. Log & Exponential
4.10. Chapter Review

5. TRIG GRAPHS & EQUATIONS
5.1. Radians
5.2. Exact Values
5.3. Trig Graphs - Period & Amplitude
5.4. Trig Graphs - Max / Min
5.5. Solving Trig Equations 1 - Basic & Multiple Angles
5.6. Solving Trig Equations 2 - Squared and Factorising
5.7. Solving Trig Equations 3 - Phase Angle
5.8. Chapter Review

6. DIFFERENTIATION
6.1. Introduction: Notation & Basic
6.2. Indices Revision
6.3. Fractional & Negative Indices
6.4. Further Differentiation
6.5. Gradient of a Tangent / Curve
6.6. Increasing & Decreasing Functions
6.7. Stationary Points & their Nature
6.8. Curve Sketching
6.9. Max & Min in a Closed Interval
6.10. Optimisation
6.11. Displacement, Velocity & Acceleration
6.12. Sketching the Derivative
6.13. Chapter Review

7. POLYNOMIALS
7.1. Introduction & Previous Knowledge
7.2. Nested Form
7.3. Synthetic Division
7.4. Factor Theorem
7.5. Solving Equations / Roots
7.6. Missing Coefficients
7.7. Functions from Graphs
7.8. Curve Sketching
7.9. Chapter Review

8. QUADRATICS
8.1. Sketching a Parabola
8.2. Completing the Square
8.3. Max and Min Values
8.4. Solving Equations
8.5. Solving Inequations
8.6. The Discriminant
8.7. Tangents to a Curve
8.8. Chapter Review

9. INTEGRATION
9.1. Introduction
9.2. Solving Differential Equations (Finding C)
9.3. Definite Integrals (Area Under a Curve)
9.4. Areas Above & Below the x-axis.
9.5. Area Between 2 Curves
9.6. Chapter Review

10. CIRCLES
10.1. x2 + y2 = r2
10.2. (x - a)2 + (y - b)2 = r2
10.3. x2 + y2 + 2gx + 2fy + c = 0
10.4. Equation of a Tangent
10.5. Intersection of a Line and a Circle
10.6. Chapter Review

11. DOUBLE ANGLE & ADDITION FORMULAE
11.1. Cos(A ± B)
11.2. Sin(A ± B)
11.3. Applications of Addition Formulae (Harder Problems)
11.4. Sin 2A & Cos 2A
11.5. Trig Equations involving Double Angles
11.6. Chapter Review


12. WAVE FUNCTION
12.1. kcos(x - α)
12.2. Other Forms
12.3. Multiple Angles
12.4. Max & Min Values
12.5. Solving Trig Equations
12.6. Chapter Review

13. VECTORS
13.1. Recap from National 5
13.2. Unit Vectors
13.3. Parallel Vectors
13.4. Collinearity
13.5. Section Formula
13.6. Vector Diagrams
13.7. The Scalar Product
13.8. The Angle Between Two Vectors
13.9. Properties of the Scalar Product
13.10. Chapter Review

14. FURTHER CALCULUS
14.1. Differentiating Sinx and Cosx
14.2. The Chain Rule
14.3. The Chain Rule with Trig.
14.4. Further Integration
14.5. Integrating Sinx and Cosx
14.6. Integrating Sin(ax + b) & Cos(ax + b)
14.7. Chapter Review

15. LOGS & EXPONENTIALS
15.1. Surds & Indices Recap
15.2. Exponentials & 'e'
15.3. Logarithms
15.4. Log Rules
15.5. Solving Log Equations
15.6. Natural Logs (ln)
15.7. Experimental Data
15.8. Sketching Log Graphs
15.9. Chapter Review

• #education
• #mrthomasmaths
• #mrthomasmaths