⚔️ Number Ninja
A rapid chain of arithmetic strikes — addition, subtraction, and multiplication — ten rounds with a 15-second timer each. Faster answers earn more points; a streak of 3+ correct answers fires a bonus multiplier.
How to Play & Why It Works
Press Start, then type your answer and click Strike (or press Enter). Points scale with speed: answer within 5 seconds for 15 points; within 10 seconds for 10 points; any correct answer earns at least 5 points. Building a streak of 3+ correct answers adds a 🔥 bonus on each subsequent answer.
⚡ Times Table Blitz
Choose any times table from 2 to 12 and answer as many questions as possible in 60 seconds. Your best score per table is saved so you can track improvement over time.
Choose a times table:
Why Times Tables Are the Foundation of All Mathematics
Strong multiplication recall underpins fraction simplification, algebraic factorisation, trigonometric ratio recognition, matrix multiplication, and integration by hand. The target is automatic recall — a response time under 2 seconds. The ×7 and ×8 tables are statistically the most commonly missed; focus extra sessions there.
🔷 Shape Quest
Apply real area and perimeter formulas to rectangles, right-angled triangles, circles, and parallelograms — with clearly labelled diagrams generated fresh each round.
Formulas Used in Shape Quest
- Rectangle area: A = length × width
- Rectangle perimeter: P = 2(l + w)
- Right triangle area: A = ½ × base × height
- Circle area: A = πr² (use π ≈ 3.14)
- Circumference: C = 2πr
- Parallelogram area: A = base × perpendicular height
𝑥 Algebra Duel
Solve equations against a 90-second timer across three escalating modes: Linear (10 pts), Quadratic (20 pts), and Simultaneous (25 pts).
Solving Strategies
- Linear (ax + b = c): Subtract b from both sides, then divide by a. Always check by substituting your answer back.
- Quadratic (x² + bx + c = 0): Try factorising first — find two numbers that multiply to c and add to b. If that fails, use x = (−b ± √(b²−4ac)) / 2a.
- Simultaneous: Choose elimination or substitution method.
△ Trig Challenge
Apply sin, cos, and tan to right-angled triangles, and use the Sine Rule and Cosine Rule for general triangles — all with labelled SVG diagrams. Give answers to 2 decimal places.
Press ▶ New Problem to load a triangle.
Essential Trigonometry Rules
- SOH: sin θ = Opposite / Hypotenuse
- CAH: cos θ = Adjacent / Hypotenuse
- TOA: tan θ = Opposite / Adjacent
- Sine Rule: a / sin A = b / sin B = c / sin C
- Cosine Rule: c² = a² + b² − 2ab·cos C
Answers within ±0.05 of the correct value are accepted, matching KCSE marking tolerance.
📉 Graph Decoder
A function is plotted on a coordinate grid. Identify the equation, gradient, y-intercept, roots, or turning point from the graph.
Press ▶ New Graph to load a question.
Graph Reading — Key Techniques
- Gradient (slope): Pick two clear grid points. Gradient = rise ÷ run.
- y-intercept: Where the graph crosses the y-axis — read y when x = 0.
- Roots / x-intercepts: Where the graph crosses the x-axis.
- Parabola vertex: The highest or lowest point — coordinates (h, k) where h = −b/2a.
🧩 Factor Storm
Factorise quadratic expressions — simple trinomials and difference of two squares — before an 8-second storm depletes the bar. Over 200 procedurally generated problems.
Factorisation Methods
- Simple trinomial (x² + bx + c): Find two integers p, q such that p × q = c and p + q = b. Write as (x + p)(x + q).
- Difference of two squares (a² − b²): Always factors as (a + b)(a − b).
- 3-second mental check: After selecting, mentally expand the two brackets to verify.
∂ Calculus Duel
Two modes — Differentiation (power rule, chain rule, product rule, trig, eˣ, ln x) and Integration (indefinite, definite, by parts, substitution). Click Show Working after each question to study the full method.
Core Calculus Rules
- Power Rule (diff): d/dx[xⁿ] = nxⁿ⁻¹
- Chain Rule: d/dx[f(g(x))] = f′(g(x))·g′(x)
- Product Rule: (uv)′ = u′v + uv′
- Power Rule (integ): ∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1)
- Integration by Parts: ∫u dv = uv − ∫v du
⬛ Matrix Cipher
Four operations: Determinants (2×2), Matrix Multiplication (find one element of AB), Inverses (element of A⁻¹), and Eigenvalues (characteristic equation).
Select an operation above to begin.
Key Matrix Formulas
- 2×2 Determinant: det[[a,b],[c,d]] = ad − bc
- 2×2 Inverse: A⁻¹ = (1/det A) × [[d,−b],[−c,a]]
- Matrix Product (AB): Element (i,j) = row i of A · column j of B
- Characteristic Equation: det(A − λI) = 0 gives the eigenvalues λ
∑ Series Verdict
Determine whether an infinite series converges or diverges. Select the optimal convergence test from eight available tests — choosing the best test earns a 10-point bonus on top of the 25-point verdict.
Select the best convergence test to apply:
Convergence Test Selector Guide
- Divergence Test: Always try first. If lim aₙ ≠ 0, the series diverges immediately.
- Geometric (∑arⁿ): Converges iff |r| < 1; sum = a/(1−r).
- p-Series (∑1/nᵖ): Converges iff p > 1.
- Ratio Test: Best for factorials and exponentials. L = lim|aₙ₊₁/aₙ|. Converges if L < 1.
- Alternating Series (Leibniz): Converges if bₙ decreasing and bₙ → 0.
- Integral Test: If f(x) is continuous, positive, and decreasing, ∑aₙ and ∫f(x)dx share fate.
ℂ Complex Arena
Four modes: Arithmetic (add, subtract, multiply complex numbers), Modulus & Argument (with live Argand diagram), De Moivre's Theorem, and Roots of Unity. 30 points per correct answer.
Complex Number Essentials
- Arithmetic: (a+bi)±(c+di) = (a±c)+(b±d)i · Multiply using FOIL and i² = −1
- Modulus: |z| = √(a² + b²)
- Argument: arg(z) = arctan(b/a), adjusted for the correct quadrant (CAST)
- De Moivre: (cos θ + i sin θ)ⁿ = cos(nθ) + i sin(nθ)
- nth Roots of Unity: zₖ = e^(2πik/n) for k = 0, 1, …, n−1