National 5 Mathematics Pythagoras Theorem Powerpoint
Covers finding missing sides, perimeters of composite shapes, circles and Pythagoras, 3D Pythagoras, Pythagoras involving surds, and Pythagoras with quadratics.
36 slides.
Hyperlinked contents page
Find a numerical output
Finding an output in terms of a variable(s)
Find an input given an output
Functions and Surds
Intersection of functions
24 slides.
Full, animated workings.
Animated workings that come up line by line.
Hyperlinked contents page
40 slides
Simplifying, adding, subtracting, multiplying, dividing, rationalising denominator, expanding brackets, geometry contexts, conjugates, surds with Pythagoras/SOH CAH TOA.
National 5 Mathematics Algebraic Fractions Powerpoint
44 slides
Hyperlinked contents page:
Simplifying Algebraic Fractions
Adding and Subtracting Algebraic Fractions
Multiplying and Dividing Algebraic Fractions
Solving Equations with Algebraic Fractions
Algebraic Fractions and Distance, Speed and Time
Full workings for each question. Workings are animated.
National 5 Mathematics Volumes of Standard and Composite Solids Powerpoint
100 slides
Annotated diagrams and animated workings throughout
Shapes include cubes, cuboids, prisms with L-shaped/semi-circle/sectors/sector + triangle/trapezoidal/pentagonal/hexagonal cross-sections, pyramids, solid and hollow spheres, hemispheres, cylinders, cones, combos of various shapes with problem-solving.
Many questions are multi-topic including:
3D coordinates
Area of a triangle with trig
Circle theorems
Cosine rule
Exact values
Factorising
Mathematical Similarity
Pythagoras (2D and 3D)
Ratios
Sector area
SOH CAH TOA
Straight Lines
Surds
Unit conversion
All essays are around 1000 words.
1) Reflective essay on mountaineering/phobia of heights. .
2) Creative essay about a conflict between two sisters. .
3) Discursive essay about Formula 1 racing safety. Fully referenced.
4) Creative essay (1300 words), about the ethics of drug use.
5) Creative essay re. reflections on the banking crisis.
6) Reflective essay about gymnastics.
7) Discursive Essay Rehabilitation vs Retribution.
8) Discursive Essay: women serving on the front lines.
9) Creative essay (1300 words) inspired by 'The Great Gatsby'.
10) Creative essay. Short story called 'SPQR' set in ancient Rome.
11) Discursive essay: academic pressures on students.
12) Discursive essay on extreme sports. Full references included.
13) Reflective essay: peer pressure and consumerism at Christmas.
14) Personal reflective essay: the impact of divorce.
15) Personal reflective essay: the film 'Mississippi Burning'.
16) Persuasive essay: swearing.
17) Persuasive essay: bullying.
18) Persuasive essay: making Music studies a compulsory subject in schools.
19) Persuasive essay: Moon landing conspiracy theories.
20) Persuasive essay on the topic of food waste.
21) Persuasive essay on head coverings worn in public
22) Persuasive essay which argues against undertaking cosmetic surgery.
23) Persuasive essay arguing against animal testing.
24) Persuasive essay on comparing the merits of fiction with journalism.
25) Discursive essay: LGBTQ issues.
26) Reflective essay on depression and grief.
27) Reflective essay on growing up in Mauritius.
28) Reflective essay: ambitions.
29) Discursive wild animals as pets.
30) Reflective essay: sibling rivalry.
31) Reflective essay: alcohol.
32) Persuasive essay: banning zoos.
33) Discursive essay: genetic engineering.
34) Discursive: Welfare State / Benefits.
35) Discursive: Population Control and One Child Policy.
36) Discursive: Intervention in Syria (Obama Administration).
37) Persuasive: Intervention in Syria (Trump Administration).
38) Reflective essay - Spanish holiday .
39) Creative essay re. a lost dog.
40) Persuasive essay on the fashion industry and fat shaming.
1) Higher English sample persuasive essay on the subject of swearing. Approx. 1000 words.
2) Higher English sample persuasive essay on the subject of bullying. Approx. 1000 words.
3) Higher English sample persuasive essay on making Music studies a compulsory subject in schools.
Approx 1300 words.
4) Higher English sample persuasive essay on Moon landing conspiracy theories
Approx 1300 words.
5) Higher English sample persuasive essay (approx. 1000 words) on the topic of food waste.
6) Higher English sample persuasive essay on head coverings worn in public (1300 words).
7) Higher English sample persuasive essay which argues against undertaking cosmetic surgery. Approx. 1000 words. Discusses the subject in the context of the way that young girls may be influenced by the physical appearances of Disney princesses / characters etc during their formative years and how this kind of media pressure can promote an unrealistic perspective about their looks. The essay discusses the issue of diversity and the Disney portrayal of the links between 'virtue' and beauty. Full list of references included.
8) The essay argues against animal testing. Approx. 1000 words. Full list of references included.
9) The essay argues for the merits of fiction in comparison to journalism. Approx. 1300 words.
10) A Grade Higher English Discursive / Persuasive Essay: Population Control and the One Child Policy. The essay is around 1000 words and includes in-text references and a bibliography.
These essays may be used as class preparation for the Higher English portfolio.
English Vocabulary and Grammar Resources (particularly suited to P6-S3 level classes depending on ability)
1) 1 page Word document vocabulary assessment with the following directions: Circle one of the three words (choices) that most nearly expresses the meaning of the italicized word in the phrases that are in the left-hand column.
2) 1 page close reading exercises asking students to correct spelling and grammar mistakes in the passage.
3) 2 page 25 most common spelling mistakes. Students have to choose the correct spelling for each word.
4) Worksheet in the form of a letter which includes lots of spelling and grammar mistakes for students to correct.
5) 7 slide Powerpoint presentation on the use of colons.
6) 35 slide Powerpoint presentation on clause analysis.
7) One page Word document with sentences which need to have full stops and capital letters added by students.
8) 93 slide Powerpoint with advice on vocabulary, structure and punctuation usage.
9) 40 page Word document revision booklet for EFL / ESL / Primary English students. This includes notes and exercises on questions, conditionals, prepositions, vocabulary, clichés, and imagery etc.
Advanced Higher Maths 135 slide Powerpoint Proofs
Hyperlinked contents page
Full workings come up line by line on click.
Topics:
Notation and number sets
Direct Proof
Divisibility
Geometry
Inequalities
Odd and even numbers
Rational numbers
Series
Trigonometry
Proof by Counterexample
Absolute values
Divisibility
Exponentials
Inequalities
Integrals
Linear Equations
Prime Numbers
Radicals
Recurrence Relations
Trigonometry
Proof by Contrapositive
Inequalities
Odd and Even numbers
Rational Numbers
Indirect Proof / Proof by Contradiction
Geometry
Inequalities
Odd and even numbers
Prime Numbers
Rational Numbers
Proof by Induction
Exponentials
Factorials
Fibonacci
Inequalities
Matrices
Recurrence relations
Series and Sigma Notation
De Moivre’s Theorem
Advanced Higher Maths Number Theory 75 slide Powerpoint
Hyperlinked contents page
Notes and fully worked solutions that come up line by line.
Topics:
Number Bases
Euclidian Division and the Euclidian algorithm
Proof of the Euclidian algorithm
The extended Euclidian algorithm
Expressing an integer multiple of d as a linear combination of a and b
Diophantine Equations
The fundamental theorem of arithmetic
Essay one discusses the importance of the Plaza scene as a key turning point in the plot of the novel and its importance in an analysis of the American Dream. Approx. 3400 words.
Essay two explores Gatsby's flawed character and how this results in his tragic end. This essay is approx. 1000 words.
Essay three (approx. 1700 words) focuses on the ways in which the setting in time and place is particularly significant to the novel as a whole.
Essay four examines the use of symbolism. This essay is approx. 1000 words.
Essay five is around 1200 words and argues that Gatsby is an admirable character.
6 page test booklet
1 page of personal research questions on the novel
1 page of suggested essay questions
150 slide PowerPoint Higher Maths Differentiation
Hyperlinked Contents Page
Examples with fully worked, animated workings for questions that come up line by line.
Diagrams throughout.
Contents
Differentiating algebraic expressions
Differentiating trigonometric functions
Chain rule for Differentiation
Differentiation and Motion
Equation of a tangent
Increasing and decreasing functions
Stationary Points and Curve sketching
Differentiation on Closed Intervals
Sketching Derived Functions
150 slide Advanced Higher Maths PowerPoint Differentiation
Fully worked solutions with animated workings that appear line by line.
Hyperlinked contents page.
Topics:
Trigonometry Summary
Differentiation from First Principles
Differentiating using the chain rule
Differentiating exponential and logarithmic functions
Product Rule
Quotient Rule
Differentiating Inverse Trigonometric Functions
Higher Derivatives
Related Rates
Differentiating implicitly defined functions
Differentiating functions defined parametrically
Applications
130 slide Powerpoint Advanced Higher Mathematics Matrices
Hyperlinked contents page, notes, full and animated examples with full workings that appear line by line on the following:
Matrix Addition and Subtraction
Matrix Multiplication
Determinants
Cramer’s Rule
Inverse Matrices
Self-inverse Matrices
Minors, Cofactors and the Adjoint of a 3 x 3 Matrix
Identity Matrix
Transpose Matrices
Orthogonal Matrices
Symmetric and skew-symmetric matrices
Transformation matrices
Dilatation
Reflection
Rotation
Invariant Points
Transformation of Loci
Matrices and complex numbers
Lower and Upper Triangular Matrices
Gaussian Elimination
Using an inverse to solve a system of equations
Ill-conditioned matrices
Matrices and Redundancy
Matrices and inconsistency
Matrices and Proofs
Proof by Induction
Cassini’s Identity
Applications
Advanced Higher Mathematics 110 slide Powerpoint Ordinary Differential Equations (ODEs)
Fully worked examples with animated workings that come up line by line.
Hyperlinked contents page.
Separation of Variables
First Order with Integrating Factor
Second Order Homogenous
Second Order Nonhomogeneous
Applications
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