Bocconi admission test course (bachelor’s)

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Kurs içeriği

1. Ünite 1

   Getting started

   How the Online Bocconi Test is built and scored: the four mixed areas, three questions per screen with no return, no calculator, the penalties and the 17-point floor, and what those penalties mean for guessing.

   1. 1.How the Online Bocconi Test works: format, scoring and pacingThe 50 questions, the four areas, three questions per screen with no going back, the scoring rules and the 17-point floor, and a pacing plan.18 dk
   2. 2.Negative marking and guessing: the expected value of an answerWork out exactly what a guess is worth under the −0.2 and −0.33 penalties, how elimination changes it, and how much risk a guess carries.18 dk

2. Ünite 2

   Numbers and sets

   Sets and numbers are both topics on the mathematics syllabus of the Online Bocconi Test. This unit covers set operations, Venn diagrams and counting overlaps; the order properties of the real numbers; and percentages and unit conversions, all worked by hand.

   1. 3.Sets, Venn diagrams and counting overlapsUse set notation for union, intersection, complement and Cartesian product, and count overlapping groups in two and three sets without double counting.22 dk
   2. 4.Order properties of the real numbersKnow which operations keep an inequality and which reverse it, and compare fractions, roots and powers by hand without testing a single convenient number.20 dk
   3. 5.Percentages and unit conversionsHandle percentages as multipliers, reverse a tax or discount, tell percentage points from percent, and convert lengths, areas, volumes and speeds by hand.22 dk

3. Ünite 3

   Algebra

   The algebra the mathematics area of the test relies on, done by hand: powers, radicals and polynomials; first and second degree equations and inequalities; systems with two unknowns; absolute values; and writing one quantity as a function of others.

   1. 6.Algebraic expressions: powers, radicals, polynomials and identitiesUse the rules of powers and radicals, the special products and the remainder theorem to simplify expressions by hand, without a calculator.22 dk
   2. 7.First and second degree equationsSolve linear and quadratic equations by hand, read the discriminant, use the sum and product of roots, and reject values outside the domain.22 dk
   3. 8.First and second degree inequalitiesSolve linear, quadratic and fractional inequalities: when to flip the sign, how to read a parabola, and why you build a sign chart.22 dk
   4. 9.Systems of equations with two unknownsSolve two-unknown systems by substitution or elimination, tell when there is one, no or infinitely many solutions, and intersect a line with a parabola.22 dk
   5. 10.Equations and inequalities with absolute valuesRead absolute value as distance, solve equations and inequalities by splitting into cases, and check the conditions that remove false solutions.22 dk
   6. 11.Expressing one quantity as a function of othersTurn a description into a formula in one variable, eliminate the extra unknowns with the constraints, state the domain, and rearrange formulas.20 dk

4. Ünite 4

   Functions, exponentials and logarithms

   Functions and logarithms with exponentials are both topics on the mathematics syllabus of the Online Bocconi Test. This unit covers notation, domain, composition and inverses; the graphs of powers, exponentials, logarithms and absolute value; the meaning and identities of logarithms; and exponential and logarithmic equations and inequalities, all worked by hand.

   1. 12.Functions: notation, domain, composition and inverseRead function notation precisely, find the domain of any formula from three rules, and compose and invert functions without mixing up the order.22 dk
   2. 13.Graphs of powers, exponentials, logarithms and absolute valueKnow the shape of each elementary graph, move it with shifts and reflections, and count solutions of an equation by counting where two graphs meet.24 dk
   3. 14.Exponentials and logarithms: meaning and identitiesTreat a logarithm as an exponent, use the power and logarithm rules correctly, and compare large powers by hand, without a calculator.22 dk
   4. 15.Exponential and logarithmic equations and inequalitiesSolve exponential and logarithmic equations with a common base, a substitution or a conversion, then check the domain and the direction of any inequality.24 dk

5. Ünite 5

   Geometry and trigonometry

   Bocconi lists plane geometry, analytical geometry and trigonometry among the mathematics topics of its test. This unit covers the area and perimeter formulas for triangles, circles, squares, trapezoids and rhombi; points, distances and lines in the plane; parabolas and circles; the position of a line relative to a circle or parabola; and trigonometry, from right triangles to the main identities. Every figure is described in words, and every value is worked without a calculator.

   1. 16.Plane geometry formulas: triangles, circles and quadrilateralsKnow the area and perimeter formulas for triangles, circles, squares, trapezoids and rhombi, and find the missing length each one needs.20 dk
   2. 17.Points, distances and lines in the planeFind distances, midpoints and slopes, write the equation of a line, and spot parallel and perpendicular lines and where two lines meet.22 dk
   3. 18.Parabolas and circles: equations, centres and verticesRead the centre and radius of a circle and the vertex, axis and direction of a parabola straight from their equations, and build the equations back.22 dk
   4. 19.Lines and conics: secant, tangent or apartDecide whether a line cuts, touches or misses a circle or parabola, find the common points, and choose a parameter that makes the line tangent.22 dk
   5. 20.Trigonometry in right trianglesUse sine, cosine and tangent to find sides and angles of right triangles, with the exact values for 30, 45 and 60 degrees that a no-calculator test needs.20 dk
   6. 21.Trigonometric functions, graphs and identitiesExtend sine, cosine and tangent to any angle on the unit circle, read their graphs and signs, and use the main identities to evaluate and solve.25 dk

6. Ünite 6

   Counting, probability and statistics

   Discrete mathematics, probability and statistics from the Bocconi mathematics syllabus: permutations and combinations with and without repetition, counting with the sum and product rules, equally likely outcomes, unions and intersections of events, conditional probability, total probability and Bayes, and frequencies with measures of centre and spread. Everything is worked by hand, since calculators are not permitted on the test.

   1. 22.Permutations and combinations, with and without repetitionAsk two questions, does order matter and can choices repeat, and pick the right one of four counting formulas without a calculator.22 dk
   2. 23.Counting problems: restrictions, cases and the complementHandle restricted positions, people who must sit together or apart, and "at least one" counts by cases or by the complement, checking one with the other.22 dk
   3. 24.Probability basics: equally likely outcomes and countingBuild the sample space, make sure its outcomes are equally likely, and turn probability questions into two counts done the same way.20 dk
   4. 25.Union, intersection and complement of eventsUse the addition rule, complements and independence to find "or", "and", "neither" and "at least one" probabilities, with a frequency table as a check.22 dk
   5. 26.Conditional probability, total probability and BayesRestrict the sample space to what you know, use trees for total probability, and turn Bayes questions into a frequency table you can trust.25 dk
   6. 27.Frequencies, measures of centre and measures of spreadRead absolute, relative, joint and conditional frequencies, and compute mean, median, mode, range, variance and standard deviation by hand.24 dk

7. Ünite 7

   Reading comprehension

   The standard Online Bocconi Test has 11 reading comprehension questions. Bocconi says the passages involve economic topics such as GDP, the deficit and inflation, may contain numbers and data, and ask about both explicit information and implicit meaning. These lessons teach how to find what a passage states, what it implies, and how to read its figures. Every passage here is original, and the places and firms in it are invented.

   1. 28.Finding explicit information in a passageLocate the sentence a detail question depends on, match its meaning rather than its words, and catch the qualifiers that make an option wrong.18 dk
   2. 29.Reading for implicit meaning: inference, purpose and toneDraw only the inferences a passage supports, explain why an author includes a sentence, and read an author’s attitude without overstating it.20 dk
   3. 30.Economic passages with figuresRead GDP, deficit and inflation figures correctly: rates against levels, deficit against debt, nominal against real, and points against percent.22 dk

8. Ünite 8

   Numerical reasoning

   Six questions of the standard Online Bocconi Test are numerical reasoning. Bocconi says advanced mathematics is not required and the calculations are simple; the difficulty is often reading a chart or table correctly. Calculators are not allowed. These lessons cover reading data, choosing the information a question needs, and calculating quickly by hand. All tables and figures are invented for the course.

   1. 31.Reading charts and tables correctlyRead the frame of a table before its numbers, and keep levels, changes, percentage changes, shares and index points apart.20 dk
   2. 32.Separating relevant from superfluous informationStart from the question, write the formula it needs, and take only those inputs from the data, so extra figures cannot pull you off course.20 dk
   3. 33.Calculating quickly by handPercentages by pieces, fraction equivalents, splitting products, cross-multiplying and estimating: fast, reliable arithmetic without a calculator.20 dk

9. Ünite 9

   Critical thinking

   Nine questions of the standard Online Bocconi Test are critical thinking. Bocconi lists two formats: choosing which statements about given data are true or false, and judging whether an assertion about a short passage is true, false or cannot be deduced. A wrong answer to a three-option critical thinking item costs 0.33 points. These lessons teach strict deduction: what a text guarantees, what it only suggests, and how the logical words work. All passages are invented.

   1. 34.True, false or cannot be deducedJudge an assertion against a short passage with the two-scenario test, and keep "false" apart from "not stated" and "true" apart from "likely".20 dk
   2. 35.Drawing valid conclusions from data and statementsFind the one statement the data guarantees: orderings, overlaps, averages and percentages, each tested for must-be-true rather than could-be-true.22 dk
   3. 36.Excluding unsupported implicationsSpot the plausible leaps a passage does not support (cause from correlation, a rule run backwards, sample to population) and keep the modest truths.20 dk
   4. 37.Quantifiers and conditionalsRead all, some, most, only, if, only if and unless with their strict meanings, negate them correctly, and use the contrapositive.22 dk

10. Ünite 10

    Quick revision

    The whole course condensed into tables, rules and drills for the last weeks before the test: the algebra and function rules, the geometry, counting, probability and statistics formulas, the reading and true / false / cannot be deduced method, the logic of conditionals and arguments, and the numerical reasoning shortcuts. Each sheet ends with fresh check questions, so you can test yourself on the material as well as reread it.

    1. 38.Revision: algebra and functionsIdentities, radicals, Vieta, sign tables, absolute values, systems, domains, inverses, exponentials and logarithms on one sheet, with worked drills.30 dk
    2. 39.Revision: geometry, counting, probability and statisticsLines, circles, parabolas, areas and volumes, the counting matrix, probability rules, averages and compound percentages on one sheet, with drills.30 dk
    3. 40.Revision: reading and true, false or cannot be deducedThe reading protocol, what counts as a valid inference, five distractor types and the three-gate test for true, false or cannot be deduced, on one sheet.28 dk
    4. 41.Revision: logic, deductions and argumentsConditionals, only if and unless, quantifiers, chains, De Morgan, sequencing and paradoxes on one sheet, plus the argument skills that help with reading.30 dk
    5. 42.Revision: numerical reasoningChart and table extraction, shares of shares, index numbers, estimation, reciprocals and percentage changes on one sheet, with the traps that cost marks.28 dk