Curriculum ChecklistOfficial IBDP Syllabus • First Assessment 2021

IB Syllabus Master Checklist

Track topic mastery across the official IBDP curriculum. Every syllabus point includes examiner trap notes and direct links to practice free exam-style questions on Revision Village.

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Topic 1

Number and Algebra

Practice All Topic 1 on Revision Village ↗
[1.1]Scientific Notation, Arithmetic Operations & RoundingSL/HL
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Express numbers in form a×10ka \times 10^k where $1 \le a < 10, k \in \mathbb{Z}$. Watch significant figures.
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[1.2]Arithmetic Sequences and Series (General term, Finite sum)SL/HL
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General term: un=u1+(n−1)du_n = u_1 + (n-1)d; Sum: Sn=n2(2u1+(n−1)d)=n2(u1+un)S_n = \frac{n}{2}(2u_1 + (n-1)d) = \frac{n}{2}(u_1 + u_n).
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[1.3]Geometric Sequences and Series (Finite & Infinite Convergent Sum)SL/HL
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General term: un=u1rn−1u_n = u_1 r^{n-1}; Sum: Sn=u1(1−rn)1−rS_n = \frac{u_1(1-r^n)}{1-r}; Convergent sum: S∞=u11−rS_\infty = \frac{u_1}{1-r} iff ∣r∣<1|r| < 1.
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[1.4]Financial Mathematics: Compound Interest, Depreciation, InflationSL/HL
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Compound interest: FV=PV(1+r100k)knFV = PV\left(1 + \frac{r}{100k}\right)^{kn} for kk compounding periods per year.
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[1.5]Laws of Exponents & Logarithms (Log identities & Change of Base)SL/HL
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log⁡a(xy)=log⁡ax+log⁡ay\log_a(xy) = \log_a x + \log_a y; log⁡a(x/y)=log⁡ax−log⁡ay\log_a(x/y) = \log_a x - \log_a y; Change of base: log⁡ab=ln⁡bln⁡a\log_a b = \frac{\ln b}{\ln a}.
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[1.6]Binomial Theorem for Positive Integer Exponents nSL/HL
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(a+b)n=∑r=0n(nr)an−rbr(a+b)^n = \sum_{r=0}^n \binom{n}{r} a^{n-r} b^r where (nr)=n!r!(n−r)!\binom{n}{r} = \frac{n!}{r!(n-r)!}. Pascal’s triangle symmetry.
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[1.7]Permutations, Combinations & Counting PrinciplesHL
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Arrangements: nPr=n!(n−r)!^n P_r = \frac{n!}{(n-r)!}; Selections: nCr=(nr)^n C_r = \binom{n}{r}. Watch restrictions and circular arrangements.
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[1.8]Partial Fractions: Linear Factors & Irreducible DenominatorsHL
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Decomposition: px+q(ax+b)(cx+d)=Aax+b+Bcx+d\frac{px+q}{(ax+b)(cx+d)} = \frac{A}{ax+b} + \frac{B}{cx+d}; and repeated factors B(ax+b)2\frac{B}{(ax+b)^2}.
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[1.9]Complex Numbers: Cartesian Form, Conjugate, Mod-Arg & Euler FormHL
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z=a+biz = a + bi; Modulus ∣z∣=a2+b2|z| = \sqrt{a^2+b^2}; Argument arg⁡(z)=θ\arg(z) = \theta; Polar/Euler: z=r(cos⁡θ+isin⁡θ)=reiθz = r(\cos\theta + i\sin\theta) = r e^{i\theta}.
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[1.10]Powers & Roots of Complex Numbers: De Moivre’s Theorem & Roots of UnityHL
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De Moivre: [r(cos⁡θ+isin⁡θ)]n=rn(cos⁡nθ+isin⁡nθ)=rneinθ[r(\cos\theta + i\sin\theta)]^n = r^n(\cos n\theta + i\sin n\theta) = r^n e^{in\theta}. nn-th roots of unity zn=1z^n = 1.
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[1.11]Proof by Mathematical Induction, Contradiction & CounterexampleHL
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Induction 3-step proof: Base step n=1n=1, inductive hypothesis assume n=kn=k, prove n=k+1n=k+1, conclude formally.
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[1.12]Extended Binomial Theorem for Any Rational Exponent r (Maclaurin)HL
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(1+x)r=1+rx+r(r−1)2!x2+…(1+x)^r = 1 + rx + \frac{r(r-1)}{2!}x^2 + \dots valid strictly when ∣x∣<1|x| < 1.
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[1.13]Systems of 3 Linear Equations: Augmented Matrices & Geometric PlanesHL
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Row reduction (Gaussian elimination). Geometric meaning: unique intersection point, line of intersection, or inconsistent.
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Topic 2

Functions

Practice All Topic 2 on Revision Village ↗
[2.1]Concept of Function, Domain, Range & Vertical Line TestSL/HL
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Function mapping: each element of domain maps to at most one element of range. Vertical line test.
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[2.2]Linear Functions: Gradient, Intercepts, Parallel & Perpendicular LinesSL/HL
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Gradient m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2-x_1}; Parallel: m1=m2m_1 = m_2; Perpendicular lines: m1m2=−1m_1 m_2 = -1.
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[2.3]Quadratic Functions: Vertex Form, Axis of Symmetry, DiscriminantSL/HL
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Vertex x=−b2ax = -\frac{b}{2a}; Discriminant Δ=b2−4ac\Delta = b^2 - 4ac: Δ>0\Delta > 0 (2 distinct real), Δ=0\Delta = 0 (equal), Δ<0\Delta < 0 (none).
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[2.4]Composite & Inverse Functions (Bijective Condition, Symmetry across y=x)SL/HL
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(f∘g)(x)=f(g(x))(f \circ g)(x) = f(g(x)); Inverse f−1(x)f^{-1}(x) exists iff f(x)f(x) is one-to-one (passes horizontal line test).
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[2.5]Rational Functions & Asymptotes (Horizontal, Vertical, Oblique)SL/HL
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f(x)=ax+bcx+df(x) = \frac{ax+b}{cx+d}: Vertical asymptote at x=−dcx = -\frac{d}{c}, horizontal asymptote at y=acy = \frac{a}{c}.
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[2.6]Exponential & Logarithmic Functions (Growth, Decay, Base e)SL/HL
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f(x)=axf(x) = a^x and g(x)=log⁡axg(x) = \log_a x are mutual inverses. Horizontal asymptote y=0y=0 for axa^x; vertical x=0x=0 for ln⁡x\ln x.
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[2.7]Function Transformations: Translations, Stretches, ReflectionsSL/HL
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y=a f(b(x−c))+dy = a\,f(b(x-c)) + d: stretch vertical aa, horizontal 1/b1/b, shift right cc, shift up dd.
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[2.8]Polynomial Remainder & Factor TheoremsHL
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Remainder theorem: P(c)=RP(c) = R; Factor theorem: (x−c)(x-c) is a factor of P(x)P(x) iff P(c)=0P(c) = 0.
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[2.9]Vieta’s Formulas Relating Roots and CoefficientsHL
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For ax2+bx+c=0ax^2+bx+c=0: x1+x2=−bax_1+x_2 = -\frac{b}{a}, x1x2=cax_1 x_2 = \frac{c}{a}. Cubic: ∑α=−ba\sum \alpha = -\frac{b}{a}, ∑αβ=ca\sum \alpha\beta = \frac{c}{a}, αβγ=−da\alpha\beta\gamma = -\frac{d}{a}.
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[2.10]Modulus Functions: Graphing y = |f(x)| and y = f(|x|)HL
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y=∣f(x)∣y = |f(x)| reflects sections below xx-axis upwards; y=f(∣x∣)y = f(|x|) deletes left of yy-axis and mirrors right.
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[2.11]Odd, Even & Periodic Functions (Symmetries & Periodicity)HL
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Even: f(−x)=f(x)f(-x) = f(x) (yy-axis reflection); Odd: f(−x)=−f(x)f(-x) = -f(x) (180∘180^\circ rotational symmetry about origin).
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[2.12]Solving Polynomial and Rational Inequalities AnalyticallyHL
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Sign tables / test intervals around critical values (roots and denominator zeroes). Never multiply across by unknown sign.
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Topic 3

Geometry and Trigonometry

Practice All Topic 3 on Revision Village ↗
[3.1]3D Geometry: Coordinate Distance, Midpoint, Surface Area & VolumeSL/HL
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Distance: d=(x2−x1)2+(y2−y1)2+(z2−z1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}. Cylinder V=πr2hV = \pi r^2 h, Sphere V=43πr3V = \frac{4}{3}\pi r^3.
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[3.2]Radian Measure, Arc Length, Sector Area & Segment AreaSL/HL
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Arc length: s=rθs = r\theta; Sector area: A=12r2θA = \frac{1}{2}r^2\theta; Segment area: A=12r2(θ−sin⁡θ)A = \frac{1}{2}r^2(\theta - \sin\theta) (radians).
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[3.3]Sine & Cosine Rules, Triangle Area & The Ambiguous Case (SSA)SL/HL
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asin⁡A=bsin⁡B\frac{a}{\sin A} = \frac{b}{\sin B}; c2=a2+b2−2abcos⁡Cc^2 = a^2+b^2-2ab\cos C; Area =12absin⁡C= \frac{1}{2}ab\sin C. Ambiguous case occurs when bsin⁡A<a<bb\sin A < a < b.
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[3.4]Unit Circle, Exact Trig Values & Basic Pythagorean IdentitySL/HL
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sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1; tan⁡θ=sin⁡θcos⁡θ\tan\theta = \frac{\sin\theta}{\cos\theta}. Exact values for $0, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}$.
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[3.5]Double Angle & Compound Angle IdentitiesSL/HL
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sin⁡(2θ)=2sin⁡θcos⁡θ\sin(2\theta) = 2\sin\theta\cos\theta; cos⁡(2θ)=cos⁡2θ−sin⁡2θ=2cos⁡2θ−1=1−2sin⁡2θ\cos(2\theta) = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta; tan⁡(2θ)=2tan⁡θ1−tan⁡2θ\tan(2\theta) = \frac{2\tan\theta}{1-\tan^2\theta}.
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[3.6]Trigonometric Functions: Graphs, Amplitude, Period & Phase ShiftSL/HL
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f(x)=Asin⁡(B(x−C))+Df(x) = A\sin(B(x-C)) + D: Amplitude ∣A∣|A|, period 2πB\frac{2\pi}{B}, phase shift CC, vertical shift DD.
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[3.7]Reciprocal Trig Functions: Secant, Cosecant, Cotangent & IdentitiesHL
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sec⁡θ=1cos⁡θ\sec\theta = \frac{1}{\cos\theta}, csc⁡θ=1sin⁡θ\csc\theta = \frac{1}{\sin\theta}, cot⁡θ=1tan⁡θ\cot\theta = \frac{1}{\tan\theta}; 1+tan⁡2θ=sec⁡2θ1+\tan^2\theta = \sec^2\theta, 1+cot⁡2θ=csc⁡2θ1+\cot^2\theta = \csc^2\theta.
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[3.8]Inverse Trigonometric Functions: Arcsin, Arccos, Arctan & DomainsHL
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arcsin⁡x∈[−π2,π2]\arcsin x \in [-\frac{\pi}{2}, \frac{\pi}{2}]; arccos⁡x∈[0,π]\arccos x \in [0, \pi]; arctan⁡x∈(−π2,π2)\arctan x \in (-\frac{\pi}{2}, \frac{\pi}{2}).
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[3.9]2D & 3D Vectors: Magnitude, Unit Vectors, Dot Product & AnglesHL
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Magnitude ∣v∣=v12+v22+v32|\mathbf{v}| = \sqrt{v_1^2+v_2^2+v_3^2}; Dot product: v⋅w=∣v∣∣w∣cos⁡θ\mathbf{v} \cdot \mathbf{w} = |\mathbf{v}||\mathbf{w}|\cos\theta; Perpendicular iff v⋅w=0\mathbf{v} \cdot \mathbf{w} = 0.
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[3.10]Vector Cross Product: Normal Vectors, Parallelogram & Triangle AreasHL
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Cross product v×w\mathbf{v} \times \mathbf{w} is perpendicular to both. Area of parallelogram =∣v×w∣= |\mathbf{v} \times \mathbf{w}|; Triangle =12∣v×w∣= \frac{1}{2}|\mathbf{v} \times \mathbf{w}|.
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[3.11]3D Lines: Vector & Parametric Equations, Intersecting/Parallel/Skew LinesHL
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Line: r=a+λb\mathbf{r} = \mathbf{a} + \lambda\mathbf{b}. Test if parallel (collinear directions), intersecting (single point), or skew (non-coplanar).
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[3.12]3D Planes: Vector, Scalar Product & Cartesian Equations, IntersectionsHL
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Plane: r⋅n=a⋅n  ⟹  ax+by+cz=d\mathbf{r} \cdot \mathbf{n} = \mathbf{a} \cdot \mathbf{n} \implies ax + by + cz = d. Normal vector n=(abc)\mathbf{n} = \begin{pmatrix} a \\ b \\ c \end{pmatrix}. Line-plane angle: sin⁡θ=∣b⋅n∣∣b∣∣n∣\sin\theta = \frac{|\mathbf{b}\cdot\mathbf{n}|}{|\mathbf{b}||\mathbf{n}|}.
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Topic 4

Statistics and Probability

Practice All Topic 4 on Revision Village ↗
[4.1]Data Presentation: Frequency, Histograms, Box-and-Whisker PlotsSL/HL
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Quartiles Q1,Q2(median),Q3Q_1, Q_2 (\text{median}), Q_3; Outliers fence: strictly outside [Q1−1.5×IQR,Q3+1.5×IQR][Q_1 - 1.5\times\text{IQR}, Q_3 + 1.5\times\text{IQR}].
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[4.2]Measures of Central Tendency & Dispersion (Mean, Variance, Std Dev)SL/HL
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Mean xˉ=∑xn\bar{x} = \frac{\sum x}{n}; Standard deviation σ=∑(x−xˉ)2n\sigma = \sqrt{\frac{\sum(x-\bar{x})^2}{n}}. Effect of linear transformations ax+bax+b.
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[4.3]Bivariate Correlation & Linear Regression (Pearson’s r, Best-Fit Line)SL/HL
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Pearson’s r∈[−1,1]r \in [-1, 1]. Line of best fit y−yˉ=m(x−xˉ)y - \bar{y} = m(x - \bar{x}) passes through centroid (xˉ,yˉ)(\bar{x}, \bar{y}). Interpolation vs extrapolation.
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[4.4]Probability Rules: Independent, Mutually Exclusive, Conditional P(A|B)SL/HL
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P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B); Conditional: P(A∣B)=P(A∩B)P(B)P(A|B) = \frac{P(A \cap B)}{P(B)}; Independent iff P(A∩B)=P(A)P(B)P(A \cap B) = P(A)P(B).
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[4.5]Discrete Random Variables: Expected Value E(X) & Variance Var(X)SL/HL
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∑P(X=x)=1\sum P(X=x) = 1; Expectation: E(X)=∑xP(X=x)E(X) = \sum x P(X=x); Variance: Var(X)=E(X2)−[E(X)]2\text{Var}(X) = E(X^2) - [E(X)]^2.
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[4.6]Binomial Distribution X ~ B(n, p): Probabilities, Mean & VarianceSL/HL
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P(X=r)=(nr)pr(1−p)n−rP(X=r) = \binom{n}{r} p^r (1-p)^{n-r}; Mean E(X)=npE(X) = np; Variance Var(X)=np(1−p)\text{Var}(X) = np(1-p). GDC binompdf / binomcdf.
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[4.7]Normal Distribution X ~ N(mu, sigma^2): Z-Scores & Inverse NormalSL/HL
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Bell curve symmetry about μ\mu; Standard normal: Z=X−μσ∼N(0,1)Z = \frac{X-\mu}{\sigma} \sim N(0, 1). GDC normcdf / invNorm.
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[4.8]Bayes’ Theorem for Conditional Probabilities with PartitionsHL
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Posterior probability: P(Bi∣A)=P(Bi)P(A∣Bi)∑jP(Bj)P(A∣Bj)P(B_i|A) = \frac{P(B_i)P(A|B_i)}{\sum_{j} P(B_j)P(A|B_j)}. Solved with comprehensive probability trees.
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[4.9]Continuous Random Variables: Probability Density Function (PDF) & CDFHL
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∫−∞∞f(x)dx=1\int_{-\infty}^\infty f(x) dx = 1; P(a≤X≤b)=∫abf(x)dxP(a \le X \le b) = \int_a^b f(x) dx; Expectation: E(X)=∫−∞∞xf(x)dxE(X) = \int_{-\infty}^\infty x f(x) dx.
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Topic 5

Calculus

Practice All Topic 5 on Revision Village ↗
[5.1]Derivative from First Principles & Basic Differentiation RulesSL/HL
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First principles: f′(x)=lim⁡h→0f(x+h)−f(x)hf'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}. Power rule: ddx[xn]=nxn−1\frac{d}{dx}[x^n] = n x^{n-1}.
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[5.2]Chain Rule, Product Rule, Quotient Rule & Tangents/NormalsSL/HL
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Chain: dydx=dydududx\frac{dy}{dx} = \frac{dy}{du}\frac{du}{dx}; Product: (uv)′=u′v+uv′(uv)' = u'v + uv'; Normal gradient: mnormal=−1mtangentm_{\text{normal}} = -\frac{1}{m_{\text{tangent}}}.
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[5.3]Second Derivatives, Concavity, Inflection Points & OptimizationSL/HL
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f′′(x)>0f''(x) > 0 concave up (min); f′′(x)<0f''(x) < 0 concave down (max). Inflection requires f′′=0f''=0 with concavity sign change.
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[5.4]Indefinite & Definite Integrals, Fundamental Theorem of CalculusSL/HL
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∫xndx=xn+1n+1+C\int x^n dx = \frac{x^{n+1}}{n+1} + C; Area between curves: A=∫ab∣f(x)−g(x)∣dxA = \int_a^b |f(x) - g(x)| dx. Fundamental theorem: ∫abf(x)dx=F(b)−F(a)\int_a^b f(x) dx = F(b) - F(a).
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[5.5]Kinematics: Displacement s(t), Velocity v(t), Acceleration a(t)SL/HL
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v(t)=s′(t)v(t) = s'(t), a(t)=v′(t)=s′′(t)a(t) = v'(t) = s''(t); Displacement =∫v(t)dt= \int v(t) dt; Total distance =∫∣v(t)∣dt= \int |v(t)| dt.
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[5.6]Derivatives of Reciprocal & Inverse Trig FunctionsHL
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ddx[arcsin⁡x]=11−x2\frac{d}{dx}[\arcsin x] = \frac{1}{\sqrt{1-x^2}}; ddx[arccos⁡x]=−11−x2\frac{d}{dx}[\arccos x] = -\frac{1}{\sqrt{1-x^2}}; ddx[arctan⁡x]=11+x2\frac{d}{dx}[\arctan x] = \frac{1}{1+x^2}.
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[5.7]Implicit Differentiation & Related Rates of ChangeHL
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Implicit: differentiate F(x,y)=cF(x, y) = c with respect to xx using chain rule ddx[yn]=nyn−1dydx\frac{d}{dx}[y^n] = n y^{n-1}\frac{dy}{dx}. Related rates: link dVdt,drdt\frac{dV}{dt}, \frac{dr}{dt}.
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[5.8]L’Hôpital’s Rule for Indeterminate Limits (0/0 and inf/inf)HL
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lim⁡x→af(x)g(x)=lim⁡x→af′(x)g′(x)\lim_{x \to a} \frac{f(x)}{g(x)} = \lim_{x \to a} \frac{f'(x)}{g'(x)} iff direct substitution yields 00\frac{0}{0} or ±∞±∞\frac{\pm\infty}{\pm\infty}.
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[5.9]Integration by Substitution & Integration by PartsHL
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Parts: ∫udvdxdx=uv−∫vdudxdx\int u \frac{dv}{dx} dx = uv - \int v \frac{du}{dx} dx. LIATE rule (Log, Inverse trig, Algebraic, Trig, Exponential).
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[5.10]Volumes of Revolution About x-Axis and y-AxisHL
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Rotation about xx-axis: V=π∫ab[f(x)]2dxV = \pi \int_a^b [f(x)]^2 dx; Rotation about yy-axis: V=π∫cd[g(y)]2dyV = \pi \int_c^d [g(y)]^2 dy.
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[5.11]Differential Equations: Separation of Variables & Integrating FactorHL
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Separation: ∫1h(y)dy=∫g(x)dx\int \frac{1}{h(y)} dy = \int g(x) dx; Integrating factor for dydx+P(x)y=Q(x)\frac{dy}{dx} + P(x)y = Q(x) is I(x)=e∫P(x)dxI(x) = e^{\int P(x) dx}.
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[5.12]Maclaurin and Taylor Series ExpansionsHL
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Maclaurin: f(x)=∑n=0∞f(n)(0)n!xnf(x) = \sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!} x^n; Booklet series for ex,sin⁡x,cos⁡x,ln⁡(1+x),(1+x)pe^x, \sin x, \cos x, \ln(1+x), (1+x)^p.
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