Higher Mathematics - Video Lessons
Below you will find video lessons for the Higher Mathematics course that can be shared with your pupils.
You may wish to use these lessons in a variety of ways;
1. For Flipped Learning
2. To help pupils catch up on work missed through absence
3. Revision for assessments
4. Help with homework
Simply copy and paste the URL's into your desired platform, e.g. Google Classroom, Show my Homework, Glow, Edmodo, etc.
Each video lesson contains worked examples and questions for the pupils to try. Pupils should copy the worked examples and attempt the questions. They are then provided with the answers and should correct their work. They could then bring in any questions they have about the video lesson to ask their teacher.
This resource covers the full CfE course but is aligned to the "old Higher" - feel free to choose your own order!
The lessons are set at 3 levels of difficulty; bronze, silver and gold. Feel free to choose the appropriate level(s) to meet the needs of your pupils.
|
Higher Mathematics
|
||||
|
Topic 1 – The Straight Line |
||||
|
1∙1 |
Bronze Outcome 1 |
The gradient of a straight line – whole numbers |
Video 1 |
|
|
1∙1 |
Silver Outcome 2 |
The gradient of a straight line – fractions |
Video 2 |
|
|
1∙1 |
Gold Outcome 3 |
Finding a point when given the gradient |
Video 3 |
|
|
1∙2 |
Bronze Outcome 1 |
Equation of line when given point & gradient |
Video 4 |
|
|
1∙2 |
Silver Outcome 2 |
The equation of a line when given 2 points |
Video 5 |
|
|
1∙2 |
Gold Outcome 3 |
The equation of a line - with fractions |
Video 6 |
|
|
1∙3 |
Bronze Outcome 1 |
Calculating the gradient when given an angle |
Video 7 |
|
|
1∙3 |
Silver Outcome 2 |
Calculating an angle when given the gradient |
Video 8 |
|
|
1∙3 |
Gold Outcome 3 |
Calculating the gradient/angle – exact values |
Video 9 |
|
|
1∙4 |
Outcome 1 |
Calculating the distance between 2 points |
Video 10 |
|
|
1∙5 |
Bronze Outcome 1 |
Calculating the Midpoint – positive numbers |
Video 11 |
|
|
1∙5 |
Silver Outcome 2 |
Calculating the Midpoint – negative numbers |
Video 12 |
|
|
1∙5 |
Gold Outcome 3 |
Calculating an end-point when given Midpoint |
Video 13 |
|
|
1∙6 |
Bronze Outcome 1 |
Parallel gradients |
Video 14 |
|
|
1∙6 |
Silver Outcome 2 |
Perpendicular gradients |
Video 15 |
|
|
1∙6 |
Gold Outcome 3 |
Gradients with exact values |
Video 16 |
|
|
1∙7 |
Outcome 1 |
Collinearity |
Video 17 |
|
|
1∙8 |
Bronze Outcome 1 |
Equation of the median |
Video 18 |
|
|
1∙8 |
Silver Outcome 2 |
Equation of the altitude |
Video 19 |
|
|
1∙8 |
Gold Outcome 3 |
Equation of a perpendicular bisector |
Video 20 |
|
|
1∙9 |
Bronze Outcome 1 |
Point of intersection between 2 lines – positive ‘x’ |
Video 21 |
|
|
1∙9 |
Silver Outcome 2 |
Point of intersection between 2 lines – negative ‘x’ |
Video 22 |
|
|
1∙9 |
Gold Outcome 3 |
Points of intersection – with fractions |
Video 23 |
|
|
Topic 2 - Recurrence Relations |
||||
|
2∙1 |
Bronze Outcome 1 |
Calculating terms in recurrence relations – with whole numbers |
Video 24 |
|
|
2∙1 |
Silver Outcome 2 |
Calculating terms – fractions & decimals |
Video 25 |
|
|
2∙1 |
Gold Outcome 3 |
Calculating terms – working backwards |
Video 26 |
|
|
2∙2 |
Bronze Outcome 1 |
Calculating the limit – with decimals |
Video 27 |
|
|
2∙2 |
Silver Outcome 2 |
Calculating the limit – with fractions |
Video 28 |
|
|
2∙2 |
Gold Outcome 3 |
Finding a or b when given the limit |
Video 29 |
|
|
2∙3 |
Outcome 1 |
Finding the values of a and b |
Video 30 |
|
|
2∙4 |
Outcome 1 |
Recurrence relations in context |
Video 31 |
|
|
Topic 3 – Functions |
||||
|
3∙1 |
Bronze Outcome 1 |
Composite functions – ‘f(g(number))’ |
Video 32 |
|
|
3∙1 |
Silver Outcome 2 |
Composite functions – ‘f(g(x))’ |
Video 33 |
|
|
3∙1 |
Gold Outcome 3 |
Composite functions – working backwards |
Video 34 |
|
|
3∙2 |
Bronze Outcome 1 |
Restrictions on the domain – for fractions |
Video 35 |
|
|
3∙2 |
Silver Outcome 2 |
Restrictions on the domain – for square roots |
Video 36 |
|
|
3∙2 |
Gold Outcome 3 |
Domain and range |
Video 37 |
|
|
3∙3 |
Outcome 1 |
Calculating inverse functions |
Video 38 |
|
|
Topic 4 – Graphs of Related Functions |
||||
|
4∙1 |
Bronze Outcome 1 |
Graphs of functions – changing the y coords |
Video 39 |
|
|
4∙1 |
Silver Outcome 2 |
Graphs of functions – changing the x coords |
Video 40 |
|
|
4∙1 |
Gold Outcome 3 |
Graphs of functions – changing both of them |
Video 41 |
|
|
4∙2 |
Bronze Outcome 1 |
Graphs of exponential functions |
Video 40 |
|
|
4∙2 |
Silver Outcome 2 |
Graphs of logarithmic functions |
Video 41 |
|
|
4∙2 |
Gold Outcome 3 |
Inverse graphs of exp & log functions |
Video 42 |
|
|
Topic 5 – Graphs of trigonometric functions |
||||
|
5∙1 |
Bronze Outcome 1 |
Changing radians into degrees |
Video 43 |
|
|
5∙1 |
Silver Outcome 2 |
Changing degrees into radians |
Video 44 |
|
|
5∙1 |
Gold Outcome 3 |
Exact values |
Video 45 |
|
|
5∙2 |
Bronze Outcome 1 |
Trig graphs - finding the values of a & b |
Video 46 |
|
|
5∙2 |
Silver Outcome 2 |
Trig graphs - Finding the values of a, b & c |
Video 47 |
|
|
5∙2 |
Gold Outcome 3 |
Sketching graphs of trickier trig functions |
Video 48 |
|
|
Topic 6 – Differentiation |
||||
|
6∙1 |
Bronze Outcome 1 |
Basic differentiation |
Video 49 |
|
|
6∙1 |
Silver Outcome 2 |
Differentiation – with fractions and indices |
Video 50 |
|
|
6∙1 |
Gold Outcome 3 |
Harder differentiation |
Video 51 |
|
|
6∙2 |
Bronze Outcome 1 |
Finding the derivative at a particular point |
Video 52 |
https://youtu.be/0X5LvncW8j4
|
|
6∙2 |
Silver Outcome 2 |
Harder substitution |
Video 53 |
https://youtu.be/yS1LLreS-28
|
|
6∙2 |
Gold Outcome 3 |
Rates of change |
Video 54 |
https://youtu.be/3Af4PhDs-8Y
|
|
6∙3 |
Bronze Outcome 1 |
The gradient of a tangent to curve |
Video 55 |
https://youtu.be/6vGRc8OCHqc
|
|
6∙3 |
Silver Outcome 2 |
The equation of a tangent to curve |
Video 56 |
|
|
6∙3 |
Gold Outcome 3 |
Finding a point when given the gradient |
Video 57 |
|
|
6∙4 |
Bronze Outcome 1 |
Increasing/decreasing functions |
Video 58 |
|
|
6∙4 |
Silver Outcome 2 |
Stationary functions |
Video 59 |
|
|
6∙4 |
Gold Outcome 3 |
The graph of the derived function |
Video 60 |
|
|
6∙5 |
Bronze Outcome 1 |
The coordinates of stationary points |
Video 61 |
|
|
6∙5 |
Silver Outcome 2 |
Determining the nature of stationary points |
Video 62 |
|
|
6∙5 |
Gold Outcome 3 |
Curve sketching |
Video 63 |
|
|
6∙6 |
Outcome 1 |
Max & min values within a closed interval |
Video 64 |
|
|
6∙7 |
Outcome 1 |
Optimisation |
Video 65 |
|
|
Topic 7 – Polynomials |
||||
|
7∙1 |
Bronze Outcome 1 |
Factorising cubic polynomials when given factor |
Video 66 |
|
|
7∙1 |
Silver Outcome 2 |
Factorising cubic polynomials when not given a factor and missing terms |
Video 67 |
|
|
7∙1 |
Gold Outcome 3 |
Factorising polynomials of degree 4 |
Video 68 |
|
|
7∙2 |
Bronze Outcome 1 |
Finding ‘k’ in simple expressions |
Video 69 |
|
|
7∙2 |
Silver Outcome 2 |
Finding ‘c’ in trickier expressions |
Video 70 |
|
|
7∙2 |
Gold Outcome 3 |
Finding the values of ‘a’ and ‘b’ in polynomials |
Video 71 |
|
|
7∙3 |
Bronze Outcome 1 |
Points of intersection with curve & x-axis |
Video 72 |
|
|
7∙3 |
Silver Outcome 2 |
Intersection between curve & straight line |
Video 73 |
|
|
7∙3 |
Gold Outcome 3 |
Points of intersection with cubic & quadratic |
Video 74 |
|
|
Topic 8 – Quadratics |
||||
|
8∙1 |
Bronze Outcome 1 |
Writing the equation of a quadratic function with a common factor |
Video 75 |
|
|
8∙1 |
Silver Outcome 2 |
Writing the equation of a quadratic function in trinomial form |
Video 76 |
|
|
8∙1 |
Gold Outcome 3 |
Writing the equation of a cubic function |
Video 77 |
|
|
8∙2 |
Bronze Outcome 1 |
Completing the square ( non-unitary x²) |
Video 78 |
|
|
8∙2 |
Silver Outcome 2 |
Completing the square ( negative non-unitary x²) |
Video 79 |
|
|
8∙2 |
Gold Outcome 3 |
Maximum and minimum values |
Video 80 |
|
|
8∙3 |
Bronze Outcome 1 |
Solving quadratic inequalities - common factor |
Video 81 |
|
|
8∙3 |
Silver Outcome 2 |
Quadratic inequalities - unitary x² trinomials |
Video 82 |
|
|
8∙3 |
Gold Outcome 3 |
Quadratic inequalities - non-unitary x² trinomials |
Video 83 |
|
|
8∙4 |
Bronze Outcome 1 |
The discriminant - solving for equal roots |
Video 84 |
|
|
8∙4 |
Silver Outcome 2 |
Solving for real or no real roots |
Video 85 |
|
|
8∙4 |
Gold Outcome 3 |
Solving for equal, real or no real roots |
Video 86 |
|
|
8∙5 |
Bronze Outcome 1 |
Intersection of line & curve – 2 points of contact |
Video 87 |
|
|
8∙5 |
Silver Outcome 2 |
Intersection of line & curve – 1 point of contact |
Video 88 |
|
|
8∙5 |
Gold Outcome 3 |
Intersection of line & curve – no points of contact |
Video 89 |
|
|
Topic 9 – Integration |
||||
|
9∙1 |
Bronze Outcome 1 |
Indefinite integrals – for basic integration |
Video 90 |
|
|
9∙1 |
Silver Outcome 2 |
Indefinite integrals - fractions & indices |
Video 91 |
|
|
9∙1 |
Gold Outcome 3 |
Indefinite integrals - harder integration! |
Video 92 |
|
|
9∙2 |
Bronze Outcome 1 |
Indefinite integrals - basic integration |
Video 93 |
|
|
9∙2 |
Silver Outcome 2 |
Indefinite integrals - standard integration |
Video 94 |
|
|
9∙2 |
Gold Outcome 3 |
Indefinite integrals - working backwards |
Video 95 |
|
|
9∙3 |
Outcome 1 |
Differential equations |
Video 96 |
|
|
9∙4 |
Bronze Outcome 1 |
The area between a curve and the x-axis |
Video 97 |
|
|
9∙4 |
Silver Outcome 2 |
The area between a curve and a line |
Video 98 |
|
|
9∙4 |
Gold Outcome 3 |
The area between two curves |
Video 99 |
|
|
Topic 10 – Trigonometry |
||||
|
10∙1 |
Bronze Outcome 1 |
Double angle formula – sin2x |
Video 100 |
|
|
10∙1 |
Silver Outcome 2 |
Double angle formula – cos2x |
Video 101 |
|
|
10∙1 |
Gold Outcome 3 |
Addition formulae – for sine and cosine |
Video 102 |
|
|
10∙2 |
Bronze Outcome 1 |
Solving “type 1” trig equations |
Video 103 |
|
|
10∙2 |
Silver Outcome 2 |
Solving “type 2” trig equations |
Video 104 |
|
|
10∙2 |
Gold Outcome 3 |
Solving “type 3” trig equations |
Video 105 |
|
|
10∙3 |
Bronze Outcome 1 |
Trig identities with sin2x |
Video 106 |
|
|
10∙3 |
Silver Outcome 2 |
Trig identities with cos2x |
Video 107 |
|
|
10∙3 |
Gold Outcome 3 |
Trig identities with more than 1 identity |
Video 108 |
|
|
Topic 11 – Circles |
||||
|
11∙1 |
Bronze Outcome 1 |
The equation (x - a)²+ (y – b)² = r² |
Video 109 |
|
|
11∙1 |
Silver Outcome 2 |
The equation x²+ y² - 2gx – 2fy + c = 0 |
Video 110 |
|
|
11∙1 |
Gold Outcome 3 |
Equation when given two end-points of a diameter |
Video 111 |
|
|
11∙2 |
Bronze Outcome 1 |
The gradient of a tangent to the circle |
Video 112 |
|
|
11∙2 |
Silver Outcome 2 |
The equation of a tangent to the circle |
Video 113 |
|
|
11∙2 |
Gold Outcome 3 |
Equation when given the other end point |
Video 114 |
|
|
11∙3 |
Bronze Outcome 1 |
Intersection of line & circle – 2 points of contact |
Video 115 |
|
|
11∙3 |
Silver Outcome 2 |
Intersection of line & circle – 1 point of contact |
Video 116 |
|
|
11∙3 |
Gold Outcome 3 |
Intersection of line & circle – 0 points of contact |
Video 117 |
|
|
11∙4 |
Bronze Outcome 1 |
Intersecting circles – 2 points of contact |
Video 118 |
|
|
11∙4 |
Silver Outcome 2 |
Intersecting circles – 1 point of contact |
Video 119 |
|
|
11∙4 |
Gold Outcome 3 |
Intersecting circles – no points of contact |
Video 120 |
|
|
Topic 12 – Vectors |
||||
|
12∙1 |
Bronze Outcome 1 |
Using vector components |
Video 121 |
|
|
12∙1 |
Silver Outcome 2 |
The magnitude of a vector |
Video 122 |
|
|
12∙1 |
Gold Outcome 3 |
Unit vectors |
Video 123 |
|
|
12∙2 |
Bronze Outcome 1 |
Describing vector journeys |
Video 124 |
|
|
12∙2 |
Silver Outcome 2 |
Vector journeys – using previous answer |
Video 125 |
|
|
12∙2 |
Gold Outcome 3 |
Calculating components of a vector journey |
Video 126 |
|
|
12∙3 |
Bronze Outcome 1 |
2D Collinearity |
Video 127 |
|
|
12∙3 |
Silver Outcome 2 |
3D Collinearity |
Video 128 |
|
|
12∙3 |
Gold Outcome 3 |
Finding a point when given the ratio |
Video 129 |
|
|
12∙4 |
Bronze Outcome 1 |
Scalar product |
Video 130 |
|
|
12∙4 |
Silver Outcome 2 |
Perpendicular vectors |
Video 131 |
|
|
12∙4 |
Gold Outcome 3 |
Hard a∙b stuff |
Video 132 |
|
|
12∙5 |
Outcome 1 |
The angle between 2 vectors |
Video 133 |
|
|
Topic 13 – Further Calculus |
||||
|
13∙1 |
Bronze Outcome 1 |
Further differentiation - with brackets |
Video 134 |
|
|
13∙1 |
Silver Outcome 2 |
Further differentiation - with trigonometry |
Video 135 |
|
|
13∙1 |
Gold Outcome 3 |
Further differentiation - with brackets & trig |
Video 136 |
|
|
13∙2 |
Bronze Outcome 1 |
Further integration - with brackets |
Video 137 |
|
|
13∙2 |
Silver Outcome 2 |
Further integration - with trigonometry |
Video 138 |
|
|
13∙2 |
Gold Outcome 3 |
Definite integrals with radian limits |
Video 139 |
https://youtu.be/zmmdYJShMZM |
|
Topic 14 – Logs and Exponentials |
||||
|
14∙1 |
Bronze Outcome 1 |
Evaluating logarithmic expressions |
Video 140 |
|
|
14∙1 |
Silver Outcome 2 |
Logarithmic expressions – combining logs |
Video 141 |
|
|
14∙1 |
Gold Outcome 3 |
Logarithmic expressions – moving stuff ‘up/down’ |
Video 142 |
|
|
14∙2 |
Bronze Outcome 1 |
Solving simple logarithmic equations |
Video 143 |
|
|
14∙2 |
Silver Outcome 2 |
Solving logarithmic equations |
Video 144 |
|
|
14∙2 |
Gold Outcome 3 |
Solving logarithmic equations with brackets |
Video 145 |
https://youtu.be/HqaMrqNoBzA |
|
14∙3 |
Bronze Outcome 1 |
Solving exponential equations |
Video 146 |
|
|
14∙3 |
Silver Outcome 2 |
Evaluating exponential equations |
Video 147 |
|
|
14∙3 |
Gold Outcome 3 |
Finding the ‘half-life’ |
Video 148 |
|
|
14∙4 |
Bronze Outcome 1 |
Experimental data - of the form y = ax |
Video 149 |
|
|
14∙4 |
Silver Outcome 2 |
Experimental data - of the form y = kax |
Video 150 |
|
|
14∙4 |
Gold Outcome 3 |
Experimental data - of the form y = kxn |
Video 151 |
|
|
Topic 15 – The Wave Function |
||||
|
15∙1 |
Bronze Outcome 1 |
The wave function - 1st quadrant angles |
Video 152 |
|
|
15∙1 |
Silver Outcome 2 |
2nd, 3rd & 4th quadrant angles |
Video 153 |
|
|
15∙1 |
Gold Outcome 3 |
The wave function - angles in radians |
Video 154 |
|
|
15∙2 |
Bronze Outcome 1 |
Part (b) - Solving ‘type 1’ trig equations |
Video 155 |
|
|
15∙2 |
Silver Outcome 2 |
Part (b) - Maximum and minimum values |
Video 156 |
|
|
15∙2 |
Gold Outcome 3 |
Part (b) - Sketching trig graphs |
Video 157 |
|
Calling all Parents & Students!
Click here for more information regarding access to our online learning portals to aid home revision.
Print 