National 5 and Higher Maths Course Online (Scotland)
The two Scottish maths courses most learners need, taught in order: National 5 for the algebra, geometry and trigonometry, then Higher for functions, vectors and calculus.
Syllabus updated October 2026
Questions? WhatsApp +91 91233 66161 or email connect@modernagecoders.com
Recordings are free with a Google sign-in. These recordings show how we teach, not the exact syllabus of this course.
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Book a Priority DemoHow long this course takes
This course runs About 6 months per level: National 5, then Higher (12 months for both) at 2 live classes/week + 3-4 hours of practice, rising to full papers before the exams. The range allows for background and pace: a complete beginner uses the full span, and a student with prior knowledge finishes sooner. The syllabus below is planned to the shorter end, with margin kept for revision.
For personalised duration planning, call +91 91233 66161 and we'll map a schedule to your goals.
At a glance
- Who it is for
- S3 to S6 learners and adults in Scotland taking National 5 or Higher Mathematics.
- Prerequisites
- For National 5: the fourth curriculum level or National 4 Mathematics, as the course specification recommends. For Higher: National 5 Mathematics or equivalent. A diagnostic in the first week places every learner
- Format
- Live, interactive classes with a real teacher, never pre-recorded videos. Live classes run about one hour.
- Language
- English or Hindi, depending on the batch.
- Duration
- About 6 months per level: National 5, then Higher (12 months for both)
- Weekly commitment
- 2 live classes/week + 3-4 hours of practice, rising to full papers before the exams
- Class size
- Group batches of 15 to 20 students, mini batches of up to 6, or 1-on-1.
- Certificate
- Course-completion certificate from Modern Age Coders
- Watch first
- Free recordings of real classes for ages 13 and up, free with a Google sign-in. These recordings show how we teach, not the exact syllabus of this course.
- Live demo
- Optional. Enrol directly on this page, or book a Priority Demo: a full live class of about 45 to 60 minutes with a mentor reserved for you.
- Questions
- WhatsApp +91 91233 66161 or email connect@modernagecoders.com.
How we teach
Deep understanding. Real projects. Expert guidance.
Learn coding, AI and maths through careful explanations, practical demonstrations, and hands-on problem-solving. Our instructors guide you from the foundations to advanced ideas, helping you understand what happens, why it happens, and how to build it yourself.
You will explore concepts step by step, write and improve code, investigate mistakes, ask questions, and apply your knowledge to meaningful projects. Lessons are designed around active participation, thoughtful feedback, and growing independence.
Expert-led live teaching, with practical participation built into every lesson.
- Students explain their thinking.
- Instructors demonstrate, then guide practice.
- Learners code, solve, or build during lessons.
- Questions and misconceptions get attention.
- Assignments receive useful feedback.
- Progress is checked before advancing.
How to join National 5 and Higher Maths Course Online (Scotland)
Four steps from this page to the first class. See a full class first with a Priority Demo, or choose a plan and enrol today.
Rated 4.9 across 547 Google reviews. Monthly billing, cancel any time.
How enrolment works
See a full class first (optional)
Book a Priority Demo: a live class of about 45 to 60 minutes with a mentor reserved for you, today or tomorrow. After the class the mentor sends a written skill report and a personal learning roadmap on WhatsApp. If you enrol, the demo fee is adjusted against your first month's fee. Share your demo Order ID with us on WhatsApp and we take it off.
Book a Priority DemoDemo fee ₹499Choose a plan
Group batch (15 to 20 students), mini batch (up to 6 students, India only) or 1-on-1 with your own mentor. Every plan is live online, and each class runs about one hour. The cards below show classes per week and the monthly fee in your currency.
Enrol and pay the first month
Press Enrol Now on your plan, fill in the student's name, email and phone, and pay through secure Razorpay checkout: UPI, cards or net banking in India, and debit or credit card from any other country.
Fix your class timings
After payment, message us on WhatsApp or call +91 91233 66161 with the student's name, the course and your preferred time slot. We confirm the batch, send the class link and schedule the first class at your chosen time.
Billing is monthly and you can cancel any time.
International Students (Outside India)
Billed monthly in US dollars, the same price in every country. Contact us with any questions.
Questions before you enrol? Talk to our team.
Ask about class timings, the right level for your child, what they need to know already, or payment. Parents and adult learners can reach us on WhatsApp, by email or by phone.
Program Overview
National 5 Mathematics (course code C847 75) and Higher Mathematics (C847 76) are the Scottish courses that open the door to most further study. Their course specifications, published by Qualifications Scotland on sqa.org.uk, give each a notional 160 hours of learning and two question papers. National 5 has a 40-mark non-calculator paper of 1 hour and a 50-mark paper of 1 hour 30 minutes. Higher has a 55-mark non-calculator paper of 1 hour 15 minutes and a 65-mark paper of 1 hour 30 minutes. Both courses are graded A to D on the total mark.
This course teaches them in sequence. The National 5 half covers the numerical, algebraic, geometric, trigonometric and statistical skills the specification lists, from surds and indices to the sine and cosine rules. The Higher half builds the algebraic and trigonometric, geometric and calculus skills Higher adds: polynomials, logarithms and exponentials, the wave function, the straight line and the circle, vectors, recurrence relations, differentiation and integration. Learners who already hold National 5 start at the Higher half after a diagnostic.
Each level ends with a month of full papers under real timing, marked against published marking instructions. Reasoning is taught throughout, because both specifications expect learners to interpret a situation and explain a solution, not just calculate. Classes are live and small, and they run at times that suit Scottish school days and exam leave.
What Makes This Program Different
- Built from the National 5 and Higher Mathematics course specifications, version 3.0, valid from session 2023 to 24
- Non-calculator Paper 1 skills practised every week at both levels
- Reasoning taught explicitly: interpreting a situation and explaining a solution
- National 5 then Higher in one sequence, or Higher alone after a diagnostic
- A month of full papers per level, marked against published marking instructions
- Scottish terms and structure throughout: S3 to S6, prelims and the national exam diet
Your Learning Journey
Career Progression
Detailed Course Curriculum
Explore the complete week-by-week breakdown of what you'll learn in this comprehensive program.
Topics Covered
- A diagnostic paper to place each learner
- Simplifying surds and rationalising denominators
- Indices, including negative and fractional indices
- Scientific notation
- Rounding to significant figures
- Setting out non-calculator working clearly
Projects You Build
- Skills checklist started: every National 5 skill coloured by confidence
Practice & Assignments
15 non-calculator number questions a week
Topics Covered
- Reverse percentages
- Appreciation and depreciation, including compound interest
- Operations and combinations of operations on fractions
- Mixed numbers without a calculator
- Choosing a calculator method for repeated percentage change
- Reasoning: explaining whether an offer is worth it
Projects You Build
- Money file: interest and depreciation problems solved and explained
Practice & Assignments
12 percentage and fraction problems a week
Assessment
Month 1 check: a 30-minute non-calculator paper
Topics Covered
- Expanding brackets, including ax(bx + c) and products of binomials
- Factorising: common factors, difference of two squares, trinomials
- Completing the square
- Algebraic fractions: simplifying and the four operations
- Changing the subject of a formula
- Checking by substitution
Projects You Build
- Algebra method sheet: one worked example of every technique
Practice & Assignments
20 algebra questions a week
Topics Covered
- Gradient from two points and from a graph
- The equation of a straight line in different forms
- Linear equations and inequations
- Simultaneous equations by graph and by algebra
- Constructing equations from text
- Reasoning: interpreting the solution in context
Projects You Build
- Equation bank: simultaneous equation problems built from real contexts
Practice & Assignments
15 equation problems a week
Assessment
Month 2 check: a 40-minute algebra paper
Topics Covered
- Quadratic functions and their graphs
- Turning points and axes of symmetry
- Solving quadratic equations by factorising and by formula
- The discriminant and the nature of the roots
- Sketching a parabola from its equation
- Problems that lead to a quadratic
Projects You Build
- Parabola file: six quadratics sketched with roots and turning points
Practice & Assignments
15 quadratic problems a week
Topics Covered
- Functional notation, f(x)
- Finding a quadratic function from its graph
- Reading information from graphs
- Mixed algebra questions from past papers
- Non-calculator algebra under time
- Error log review
Projects You Build
- Skills checklist updated after the first three months
Practice & Assignments
Two 25-minute mixed algebra sets a week
Assessment
Month 3 check: a 45-minute mixed paper
Topics Covered
- Arc length and sector area
- Volumes of prisms, cylinders, cones, pyramids and spheres
- Pythagoras' theorem in complex situations, including 3D
- Properties of quadrilaterals, triangles, polygons and circles
- Similarity and scale factors for area and volume
- Rounding volume and area answers sensibly
Projects You Build
- Geometry sheet: every formula and property with a worked example
Practice & Assignments
15 geometry problems a week
Topics Covered
- Two-dimensional vectors: adding, subtracting and multiplying by a scalar
- Vector pathways in shapes
- Three-dimensional coordinates from a diagram
- Magnitude of a vector
- Reasoning: explaining a geometric result
- Past paper geometry questions
Projects You Build
- Vector diagram set: five shapes with pathways labelled
Practice & Assignments
12 vector and coordinate problems a week
Assessment
Month 4 check: a 45-minute geometry paper
Topics Covered
- Area of a triangle using trigonometry
- The sine rule and the cosine rule
- Bearings in problems
- Graphs of trigonometric functions and their translations
- Solving trigonometric equations
- Trigonometric identities used at National 5
Projects You Build
- Triangle casebook: when to use each rule, with a solved example
Practice & Assignments
15 trigonometry problems a week
Topics Covered
- Comparing data sets using statistics
- Standard deviation and the semi-interquartile range
- Scatter graphs and the line of fit
- Writing a comparison in context
- Mixed questions across all National 5 skills
- Planning the papers month
Projects You Build
- Skills checklist completed for National 5
Practice & Assignments
12 statistics questions a week plus a mixed set
Assessment
Month 5 check: a full mixed paper at National 5
Topics Covered
- A full Paper 1 and Paper 2 under timing
- Marking against published marking instructions
- Sorting lost marks by skill and by habit
- Re-teaching the weakest skills
- Pacing Paper 1 without a calculator
- Showing working that earns process marks
Projects You Build
- Paper tracker started for National 5
Practice & Assignments
One full paper pair a week
Topics Covered
- A final paper pair under timing
- Review of every lost mark
- Exam-day routine and equipment
- Bridging tasks for Higher: functions and further algebra
- Planning Higher for those continuing
- Revision plan up to the exam
Projects You Build
- Completed National 5 paper tracker and error log
Practice & Assignments
Targeted sets from the error log
Assessment
National 5 paper review, one to one
Topics Covered
- A diagnostic for learners joining at Higher
- Factorising cubics and quartics with the factor theorem
- Solving polynomial equations
- Quadratic inequalities and the discriminant
- Tangency and intersection of lines and curves
- Completing the square at Higher depth
Projects You Build
- Higher skills checklist started
Practice & Assignments
15 polynomial and quadratic problems a week
Topics Covered
- Composite and inverse functions
- Domain and range
- Related graphs and transformations
- Exponential and logarithmic functions
- Laws of logarithms and solving equations
- Sketching the inverse of a logarithmic or exponential function
Projects You Build
- Graph file: transformations and log graphs annotated
Practice & Assignments
15 function and logarithm problems a week
Assessment
Month 7 check: a 45-minute Higher algebra paper
Topics Covered
- Radians and exact values
- Addition formulae and double-angle formulae
- Trigonometric identities
- Solving trigonometric equations in degrees and radians
- Graphs of trigonometric functions
- Non-calculator trigonometry
Projects You Build
- Trigonometry sheet: exact values, formulae and identities
Practice & Assignments
15 trigonometry problems a week
Topics Covered
- Converting a cos x + b sin x to k cos(x - a) and related forms
- Maximum and minimum values
- Solving equations using the wave function
- Sketching the resulting graph
- Applications in context
- Past paper wave function questions
Projects You Build
- Wave function casebook: four forms with a worked example each
Practice & Assignments
10 wave function problems a week
Assessment
Month 8 check: a 45-minute trigonometry paper
Topics Covered
- Gradients, perpendicular lines and collinearity
- Medians, altitudes and perpendicular bisectors
- Equations of a circle
- Intersection of a line and a circle, and tangency
- Intersection of two circles, and tangency problems
- Coordinate geometry reasoning
Projects You Build
- Coordinate geometry sheet with a solved past-paper style problem
Practice & Assignments
15 straight line and circle problems a week
Topics Covered
- Vectors in three dimensions
- The scalar product and the angle between vectors
- Collinearity and dividing a line in a ratio
- Recurrence relations and their limits
- Modelling a situation with a recurrence relation
- Interpreting a limit in context
Projects You Build
- Recurrence model: a real situation modelled and its limit explained
Practice & Assignments
12 vector and recurrence problems a week
Assessment
Month 9 check: a 45-minute geometry paper
Topics Covered
- Differentiating algebraic functions
- Differentiating k sin x and k cos x
- The chain rule
- Equations of tangents
- Increasing and decreasing functions
- Stationary points and their nature
Projects You Build
- Calculus method sheet: one worked example per rule
Practice & Assignments
20 differentiation problems a week
Topics Covered
- Sketching curves from stationary points
- Greatest and least values on an interval
- Optimisation problems in context
- Rates of change
- Reasoning: justifying a maximum or minimum
- Past paper optimisation questions
Projects You Build
- Optimisation file: three context problems solved and explained
Practice & Assignments
12 applied differentiation problems a week
Assessment
Month 10 check: a 45-minute calculus paper
Topics Covered
- Integrating algebraic functions
- Integrating sine and cosine
- Integrating with the chain rule in reverse for linear inner functions
- Definite integrals
- Solving simple differential equations
- Checking an integral by differentiating
Projects You Build
- Calculus method sheet extended with integration
Practice & Assignments
20 integration problems a week
Topics Covered
- Area under a curve
- Area between two curves
- Mixed calculus questions
- Mixed Higher questions across all skills
- Non-calculator calculus under time
- Planning the papers month
Projects You Build
- Higher skills checklist completed
Practice & Assignments
Two 30-minute mixed sets a week
Assessment
Month 11 check: a full mixed paper at Higher
Topics Covered
- A full Paper 1 and Paper 2 under timing
- Marking against published marking instructions
- Sorting lost marks by skill and by habit
- Re-teaching the weakest skills
- Pacing the non-calculator paper
- Process marks and clear communication
Projects You Build
- Paper tracker started for Higher
Practice & Assignments
One full paper pair a week
Topics Covered
- A final paper pair under timing
- Review of every lost mark
- Exam-day routine and equipment
- A calm plan for exam leave
- Looking ahead to Advanced Higher for those continuing
- Revision plan up to the exam
Projects You Build
- Completed Higher paper tracker and error log
Practice & Assignments
Targeted sets from the error log
Assessment
Higher paper review, one to one
Projects You'll Build
Build a professional portfolio with A complete revision kit for National 5 and Higher: checklists, method sheets, casebooks and marked paper trackers real-world projects.
Weekly Learning Structure
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Straight answers about National 5 and Higher Maths Course Online (Scotland)
- Who should take this course?
- S3 to S6 learners and adults in Scotland taking National 5 or Higher Mathematics. It suits s3 and s4 learners working towards national 5 mathematics; s5 and s6 learners taking higher mathematics; learners whose school class moves faster than they can follow and who want steady teaching alongside it.
- What will they learn and build?
- National 5 Mathematics (course code C847 75) and Higher Mathematics (C847 76) are the Scottish courses that open the door to most further study. Their course specifications, published by Qualifications Scotland on sqa.org.uk, give each a notional 160 hours of learning and two question papers. National 5 has a 40-mark non-calculator paper of 1 hour and a 50-mark paper of 1 hour 30 minutes.
- How deeply are topics covered?
- The course runs About 6 months per level: National 5, then Higher (12 months for both) at 2 live classes/week + 3-4 hours of practice, rising to full papers before the exams, across 4 phases listed week by week in the syllabus below. A structured plan built from the National 5 and Higher course specifications.
- Who teaches it?
- Modern Age Coders mentors, who teach the live classes themselves. You can watch them at work in the free class recordings before you decide.
- How do practice, feedback and assessment work?
- Monthly checks and a full papers month at each level, marked against published marking instructions. Doubt support between classes over WhatsApp. A course-completion certificate and a revision kit the learner keeps.
- What does it cost?
- Three monthly plans: a group batch, a mini batch and 1-on-1. Prices are shown in your currency in the plans section. Monthly billing, cancel any time.
- When can classes take place?
- Live classes are scheduled around your week. Group batches meet at a fixed weekly slot; 1-on-1 students choose their own. International students are scheduled in their own timezone. Ask on WhatsApp for the current slots.
- Can I watch the teaching before deciding?
- Yes. Full recordings of real 13 and up classes are free to watch, free with a Google sign-in. These recordings show how we teach, not the exact syllabus of this course. Some classes are in English and some in Hindi; everyone follows at their own pace. Watch a class end to end, like you are in it. Sessions are interactive and each moment builds on the last.
- Can I enroll without a live demo?
- Yes. Choose a plan on this page and enrol directly; a demo is not required. If you would like to see a full class with a mentor first, book a Priority Demo.
- How do I reach you with a question?
- WhatsApp +91 91233 66161, email connect@modernagecoders.com, or call +91 91233 66161. Tell us the student's age and what they have learned so far, and we will point you to the right plan and batch.
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Read ArticleReady to start National 5 and Higher Maths Course Online (Scotland)?
Book a Priority Demo to see a full live class with a mentor reserved for you, today or tomorrow. Or choose a plan and enrol now.
Questions? WhatsApp +91 91233 66161 or email connect@modernagecoders.com