MYP Math Y9–10 | Advanced Practice Quiz

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Unit 1 · Algebra & Functions

Quadratics · Sequences · Exponents

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Quadratic Formula: x = (−b ± √(b²−4ac)) / 2a

Discriminant Δ = b²−4ac: Δ>0 → 2 roots · Δ=0 → 1 root · Δ<0 → none

Vieta's formulas (ax²+bx+c=0): α+β = −b/a · αβ = c/a

Sum of AP: Sₙ = n/2·(2a + (n−1)d) · nth term: aₙ = a + (n−1)d

GP nth term: aₙ = ar^(n−1) · Sum: Sₙ = a(rⁿ−1)/(r−1)

Laws of Exponents: aᵐ·aⁿ=aᵐ⁺ⁿ · (aᵐ)ⁿ=aᵐⁿ · a^(p/q) = ᵠ√(aᵖ)

Vertex of parabola: x = −b/2a
α² + β² = (α+β)² − 2αβ (key identity)
nth term from Sₙ: aₙ = Sₙ − Sₙ₋₁ (for n ≥ 2)

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Unit 2 · Geometry & Trigonometry

Circles · Similarity · Cosine/Sine Rules

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Sine Rule: a/sinA = b/sinB = c/sinC

Cosine Rule: c² = a² + b² − 2ab·cosC

Area of triangle: ½ab·sinC

Circle: C=2πr · A=πr² · Arc=(θ/360)·2πr · Sector=(θ/360)·πr²

Chord-distance: r² = d² + (chord/2)² [perpendicular from centre bisects chord]

SOHCAHTOA: sinθ=opp/hyp · cosθ=adj/hyp · tanθ=opp/adj
Scale factor k → area ×k² → volume ×k³
Cone total SA = πr(r + l) where l = slant height

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Unit 3 · Linear & Simultaneous Equations

Gradient · Systems · Inequalities

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y = mx + c (slope-intercept) · y−y₁ = m(x−x₁) (point-slope)

Gradient: m = (y₂−y₁)/(x₂−x₁)

Distance: d = √((Δx)² + (Δy)²) · Midpoint: ((x₁+x₂)/2, (y₁+y₂)/2)

Perpendicular lines: m₁ × m₂ = −1
For quadratic inequalities: find roots then test direction (parabola opens up/down)
Substitute to solve non-linear systems

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Unit 4 · Probability & Statistics

Expected Value · Conditional · Variance

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P(A∪B) = P(A) + P(B) − P(A∩B)

Conditional: P(A|B) = P(A∩B) / P(B)

Expected Value: E(X) = Σ x·P(X=x)

Population Variance: σ² = Σ(x−x̄)² / n

IQR = Q3 − Q1 · Outlier if > Q3+1.5·IQR or < Q1−1.5·IQR

Independent: P(A∩B) = P(A)·P(B)
Line of best fit always passes through (x̄, ȳ)

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Unit 5 · Number & Proportion

Surds · Compound Interest · Growth

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Compound interest: A = P(1 + r/n)^(nt)

Surds: √(ab)=√a·√b · (√a+√b)(√a−√b) = a−b (difference of squares)

Rationalise 1/√a: multiply by √a/√a → √a/a

Growth: P·(1+r)ⁿ > target → use logarithms: n > log(target/P)/log(1+r)
Conjugate of (a+√b) is (a−√b)

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Unit 6 · Mensuration & Modelling

Volume · Surface Area · 3D Geometry

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Sphere: V = (4/3)πr³ · SA = 4πr²

Cone: V = (1/3)πr²h · Total SA = πr(r + l), l = slant height

Cylinder: V = πr²h · SA = 2πr(r + h)

Pyramid: V = (1/3) × base area × height