TOLC-I engineering admission test course

Mapa myśli testu

Cały test na jednej stronie: otwórz część, aby zobaczyć jej lekcje, i przejdź prosto do jednej z nich.

Spis treści kursu

1. Dział 1

   Getting started

   Plan your sitting and interpret the four main section scores.

   1. 1.How the TOLC-I worksPlan around four section clocks, calculate your score by hand and check the admission rules for the engineering programme you want to enter.18 min

2. Dział 2

   Mathematics

   Work by hand with numbers, equations, geometry, functions, trigonometry and probability. The section allows 50 minutes for 20 questions.

   1. 2.Real numbers, powers and radicalsCompare exact real numbers, simplify powers and roots, and estimate sizes by hand using normalised scientific notation.18 min
   2. 3.Ratios, percentage changes and divisibilityChoose a percentage base, scale a ratio, and use integer factors and remainders to solve grouping and scheduling problems by hand.18 min
   3. 4.Polynomial division and factorisationUse the remainder theorem and Ruffini’s rule to divide by a linear factor, then factor higher-degree expressions and simplify fractions.18 min
   4. 5.Quadratic equations and inequalitiesUse factors, the discriminant and the direction of a parabola to locate every real solution of a quadratic equation or inequality.18 min
   5. 6.Rational inequalities and systemsBuild a sign chart for an algebraic fraction, handle holes and repeated factors, and intersect the answers to simultaneous inequalities.18 min
   6. 7.Radical and absolute-value inequalitiesUse domain and sign conditions before squaring a radical inequality, and translate absolute-value bounds into distances on the real line.18 min
   7. 8.Exponential and logarithmic equations and inequalitiesRewrite powers with a common base, use a positive substitution, and solve logarithmic comparisons while preserving the original domain.18 min
   8. 9.Plane geometry with triangles and circlesMatch similar triangles, use projections in a right triangle, and connect chords, tangents and angles to the arc they intercept.18 min
   9. 10.Solid geometry and changes of scaleChoose a base and perpendicular height, separate exposed area from volume and recover a length scale from an area or volume ratio.20 min
   10. 11.Coordinates, lines and distancesBuild a line through a given point, find the shortest distance to it and use coordinate differences to measure lengths and areas.20 min
   11. 12.Circles, parabolas, ellipses and hyperbolasRead a conic from its equation, recover its centre or vertex and decide whether a line cuts, touches or misses a circle.20 min
   12. 13.Function domains, inverses and graph transformationsTrack allowed inputs through a composition, decide when a function can be reversed and follow points through shifts and reflections.20 min
   13. 14.Exponential and logarithmic graphsSketch inverse graphs from exact points, use logarithm laws with their domains and compare logarithms in increasing or decreasing bases.20 min
   14. 15.The unit circle and trigonometric equationsRead signs and exact values from the unit circle, use double-angle identities and find every angle in a specified interval.20 min
   15. 16.The sine and cosine rules for trianglesMatch sides to opposite angles, choose a triangle rule from the known measurements and find an area without calculating a height.20 min
   16. 17.Weighted means, medians and probabilityCombine group means using group sizes, find a median from frequencies and distinguish overlapping, independent and mutually exclusive events.20 min

3. Dział 3

   Logic

   Use diagrams, counterexamples and small tables to test what follows from a rule.

   1. 18.Implications and necessary conditionsTranslate if, only if and unless into one-way rules, chain deductions and test a proposed conclusion with a counterexample.18 min
   2. 19.Quantifiers, negation and Venn diagramsTrack what all, some and none commit you to, negate claims exactly and test syllogisms by placing individual objects in sets.18 min
   3. 20.Constraints, guarantees and flowsOrganise scheduling clues, find the smallest guaranteed count and combine compatible work rates using a common unit.18 min
   4. 21.Sequences and patternsTest additive, multiplicative and interleaved rules, track positions carefully and explain which continuation follows a specified pattern.18 min

4. Dział 4

   Sciences

   Follow forces, energy and electric charge through physical systems. Then use particle counts, mole ratios and concentrations to explain chemical changes.

   1. 22.Vectors, motion and inclined planesRead motion graphs and resolve forces along a slope to find a moving object's acceleration, including the effects of tension and friction.20 min
   2. 23.Energy, fluids and ideal gasesTrack energy transfers, compare pressures at depth, calculate buoyancy and use absolute temperature to predict changes in an ideal gas.20 min
   3. 24.Charges, circuits and opticsCompare electric forces, trace current and voltage in resistor networks, and use the normal to predict reflection and refraction by hand.20 min
   4. 25.Atoms, bonds and reacting amountsUse particle counts to identify atoms and ions, predict simple bonding patterns, and find how much product a limited supply of reactant can make.20 min
   5. 26.Solutions, equilibrium and pHCalculate molarity after dilution, predict how a disturbed equilibrium responds, and read hydrogen-ion concentrations from a logarithmic pH scale.20 min

5. Dział 5

   Verbal comprehension

   Trace a passage’s argument, locate stated details and test a word against its context.

   1. 27.Cohesion and inferenceUse connective words, pronoun references and a passage’s structure to identify the conclusion its evidence supports.18 min
   2. 28.Stated information and meaning in contextMatch a paraphrase to a precise detail and use the surrounding sentences to choose the intended meaning of a word or phrase.18 min