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Mathematics Advanced

Academic track (grades 8–10) with a look ahead to upper secondary.

Tip: The videos also have an English audio track. On YouTube, open ⚙ Settings → Audio track.

14:30

Episode 2

Percentage Change – Advanced

What you will learn

  • base value, rate and percentage – one formula for all three
  • the growth factor: +20 % means × 1.2, −20 % means × 0.8
  • several changes: multiply the factors, don’t add the percentages
  • working backwards: price before the discount, net price without VAT
  • percent or percentage points? What the news often gets wrong
  • the four traps that cost marks in exams
Watch on YouTube
13:49

Episode 3

Special Products & Factoring – Advanced

What you will learn

  • expanding double brackets – every term with every term
  • perfect squares (a ± b)² and the difference of two squares
  • 21², 19 × 21 and 99² in your head
  • factoring: common factors and special products backwards
  • simplifying algebraic fractions – and why x ≠ 3 matters
  • five exam traps
Watch on YouTube
13:08

Episode 4

Rational Equations & Special Cases – Advanced

What you will learn

  • variables on both sides
  • clearing fractions with the lowest common denominator
  • rational equations: write down the excluded values first
  • spotting extraneous solutions
  • no solution or infinitely many
  • rearranging formulas: °F to °C, v = s / t
  • four exam traps
Watch on YouTube
11:44

Episode 5

Slope & Intersection – Advanced

What you will learn

  • reading f(x) and slope as a rate of change
  • slope from two points – rise over run
  • finding the equation of a line
  • zeros (x-intercepts)
  • intersection points
  • parallel and perpendicular lines: m₁ · m₂ = −1
  • gradients in percent
  • four exam traps
Watch on YouTube
15:33

Episode 6

Systems of Linear Equations – Advanced

What you will learn

  • substitution, equating and elimination – and when to use which
  • multiplying equations before you add them
  • the solution as the intersection of two lines
  • special cases: no solution or infinitely many (0 = 2, 0 = 0)
  • three unknowns with row echelon form
  • modelling: currents, mixtures, tickets
  • the four most common exam traps
Watch on YouTube
13:24

Episode 7

Exponent Rules & Exponential Growth – Advanced

What you will learn

  • exponent rules: add, subtract, multiply exponents
  • why a⁰ = 1 and 2⁻² = ¼
  • exponent ½ = square root
  • scientific notation from bacteria to terabytes
  • linear or exponential – one cent that keeps doubling
  • compound interest on savings – and on debt
  • exponential decay and half-life
  • exponential equations like 2ˣ = 32
Watch on YouTube
11:44

Episode 8

Cylinders, Cones & Spheres – Advanced

What you will learn

  • sectors and arcs: the fraction α/360°
  • cylinders: volume and surface area from the net
  • cones and pyramids: the pouring experiment and the one third
  • spheres: V = 4/3 · π · r³ and A = 4 · π · r²
  • scaling: area · k², volume · k³
  • the four most common exam traps
Watch on YouTube
11:11

Episode 9

3D Pythagoras & Similarity – Advanced

What you will learn

  • proving the Pythagorean theorem
  • the space diagonal: d² = a² + b² + c²
  • the distance formula
  • the height of an equilateral triangle
  • similar figures and the scale factor k
  • intercept theorems: measuring heights by their shadows
  • scale for lengths and areas
Watch on YouTube
14:25

Episode 10

Quadratic Formula & Vertex – Advanced

What you will learn

  • standard form: ax² + bx + c = 0
  • factoring and Vieta’s formulas
  • completing the square – with a picture
  • the quadratic formula and the pq formula
  • the discriminant: two, one or no solutions
  • vertex form a(x − d)² + e
  • a thrown ball: highest point and landing time
  • the largest area with 100 m of fence
Watch on YouTube
12:58

Episode 11

Unit Circle & Sine Waves – Advanced

What you will learn

  • cos α and sin α as coordinates on the unit circle
  • angles above 90° and sin²α + cos²α = 1
  • law of cosines: Pythagoras with a correction term
  • law of sines – and when there are two solutions
  • radians: 360° = 2π
  • the sine curve: amplitude, period, midline
  • Ferris wheel: h(t) = 22 − 20 · cos(π/5 · t)
Watch on YouTube
11:39

Episode 12

Binomial Distribution – Advanced

What you will learn

  • tree diagrams: multiply along a path, add paths
  • “at least one” via the complementary event
  • combinatorics: 10⁴, 5! and “5 choose 2”
  • n choose k as the number of paths
  • the binomial distribution: P(X = k)
  • expected value n · p
  • spam filter and two-way table: P(spam | flagged)
Watch on YouTube
11:32

Episode 13

Limits & Derivatives – Advanced

What you will learn

  • lim, convergent and divergent
  • the highest-power trick
  • geometric series: a / (1 − q)
  • horizontal asymptotes
  • hole or pole: cancel first, then substitute
  • compound interest and the number e ≈ 2.718
  • secant → tangent: the idea of the derivative
Watch on YouTube
13:18

Episode 14

Optimizing a Skatepark with Math – Advanced

What you will learn

  • maximum area with a 100 m fence: A(x) = x(50 − x) → 625 m²
  • price increase: €72,000 · 1.03² = €76,384.80
  • company A or B? Break-even at 40 hours
  • digging out the bowl: 18π ≈ 56.5 m³
  • the slanted corner with the law of cosines: ≈ 26.1 m
  • visitor forecast 2,000 · 1.1ⁿ – when does it double?
  • rain risk 48.8 % and the expected value
  • slope of the quarter pipe: 2, so ≈ 63.4°
Watch on YouTube