EJU Mathematics Course 2 study plan
EJU Mathematics Course 2 · Give each week a clear focus.
8 weeks · About 6 hours per week
Differentiation and Integration (limits, derivatives, tangents, monotonicity, extrema, indefinite and definite integrals, areas) & Numbers and Expressions (real numbers, powers and roots, polynomials, factoring, rational expressions)
Compute limits of polynomial, rational, and irrational functions using algebraic manipulation and the definition of the derivative.
Differentiate polynomial, rational, and composite functions using the power, product, quotient, and chain rules.
Find equations of tangent lines to curves at given points and determine where the tangent is horizontal.
Determine intervals of increase/decrease and classify local extrema using the first derivative test.
Simplify and factor polynomial and rational expressions quickly and accurately as a foundation for calculus.
Your checkpoint
A one-page formula sheet for differentiation rules and a set of 10 solved limit problems, all correct, with each step shown.
Differentiation and Integration (limits, derivatives, tangents, monotonicity, extrema, indefinite and definite integrals, areas) & Quadratic Functions (graphs, maxima/minima, quadratic equations and inequalities, relationship to the number of real roots)
Compute indefinite integrals of basic functions and apply substitution for composite functions.
Evaluate definite integrals using the fundamental theorem of calculus.
Calculate areas between curves and areas bounded by a curve and the x-axis.
Solve quadratic equations and inequalities and relate the discriminant to the number of real roots.
Sketch quadratic functions and identify their vertices, axes of symmetry, and maximum/minimum values.
Your checkpoint
A timed 30-minute quiz with 8 problems (4 on integration and areas, 4 on quadratic functions), scored at least 7/8.
Differentiation and Integration (limits, derivatives, tangents, monotonicity, extrema, indefinite and definite integrals, areas) & Probability (classical probability, independent and dependent events, conditional probability, expected value)
Solve applied optimization problems using derivatives (maxima/minima in context).
Find the area between two curves that intersect multiple times by setting up and evaluating definite integrals.
Compute classical probabilities using permutations and combinations.
Apply the multiplication rule for independent and dependent events and use conditional probability.
Calculate expected values for discrete random variables.
Your checkpoint
A written solution to one full optimization problem and one probability problem involving expected value, each with a clear explanation of the reasoning.
Sets, Logic and Counting (sets, propositions, permutations and combinations, binomial theorem) & Probability (classical probability, independent and dependent events, conditional probability, expected value)
Use set notation and logic (AND, OR, NOT, implication) to translate word problems into mathematical statements.
Solve counting problems using permutations and combinations, including cases with restrictions.
Expand binomial expressions using the binomial theorem and find specific terms.
Solve probability problems involving conditional probability and independence, including tree diagrams.
Compute probabilities using complementary events and the addition rule.
Your checkpoint
A timed 40-minute test with 10 problems covering sets, counting, binomial theorem, and probability, scored at least 80%.
Trigonometry (trigonometric ratios, trigonometric identities, graphs, equations and inequalities) & Plane Geometry (triangles, circles, angles, lengths, areas, similarity, the power of a point, inscribed figures)
Prove and apply trigonometric identities (Pythagorean, sum/difference, double-angle).
Solve trigonometric equations and inequalities within a given interval.
Sketch graphs of sine, cosine, and tangent functions and identify their periods and amplitudes.
Apply the sine rule, cosine rule, and area formula to solve triangles.
Use circle theorems (inscribed angles, tangents, power of a point) to find unknown lengths and angles.
Your checkpoint
A set of 12 solved problems: 6 trigonometry and 6 geometry, each with a clear diagram and all steps.
Number of Integers and Integer Properties (divisibility, Euclidean algorithm, integer solutions, base representation) & Exponential and Logarithmic Functions (exponents, logarithms, exponential/logarithmic equations and inequalities, common and natural logarithms)
Apply the Euclidean algorithm to find the greatest common divisor and solve linear Diophantine equations.
Convert numbers between base representations (binary, decimal, etc.) and perform basic operations in different bases.
Use divisibility rules and modular arithmetic to solve integer problems.
Solve exponential and logarithmic equations and inequalities.
Apply properties of logarithms (product, quotient, power rules) to simplify expressions and solve equations.
Your checkpoint
A one-page summary of number theory and logarithm rules, plus 8 solved problems (4 number theory, 4 logarithms) with correct answers.
Sequences (arithmetic and geometric sequences, sums, recurrence relations, mathematical induction) & Vectors (vector operations, position vectors, inner products, equations of lines and planes, applications to figures)
Find terms and sums of arithmetic and geometric sequences.
Solve recurrence relations and use mathematical induction to prove statements.
Perform vector addition, subtraction, scalar multiplication, and calculate dot products.
Find the equation of a line in vector form and determine intersections and angles between lines.
Apply vectors to geometric problems (e.g., proving points are collinear or finding areas).
Your checkpoint
A set of 10 problems (5 sequences, 5 vectors) solved with complete proofs or calculations, all correct.
Differentiation and Integration (limits, derivatives, tangents, monotonicity, extrema, indefinite and definite integrals, areas) & Probability (classical probability, independent and dependent events, conditional probability, expected value) & Sets, Logic and Counting (sets, propositions, permutations and combinations, binomial theorem)
Review and solve mixed problems from calculus (differentiation, integration, areas) under time pressure.
Review probability and counting problems, focusing on conditional probability and expected value.
Identify and correct common mistakes in previous weeks' work.
Complete two full-length practice sections (calculus and probability/counting) within the official time limits.
Develop a personal checklist of formulas and strategies for exam day.
Your checkpoint
A full-length practice test (all domains) completed in one sitting, scored and reviewed, with a list of errors and corrections.
Milestones
Week 2: Complete a timed 20-minute quiz on differentiation and integration (6 problems) with at least 5 correct.
Week 4: Complete a timed 40-minute test on probability and counting (10 problems) with at least 8 correct.
Week 6: Complete a timed 30-minute quiz on trigonometry and geometry (8 problems) with at least 6 correct.
Week 8: Complete a full-length practice test (all domains) within the official time limit and score at least 70% overall.