Quick International Maths Olympiad Course 2023

Explore how ratios express relationships, while fractions show parts of a total, with boys and girls examples; learn why you cannot add ratios directly.

Divide a total value into shares using ratios, such as 24,000 dollars into A, B, and C (6,000, 8,000, 10,000), and learn to combine ratios by equalizing values.

Explore proportion as a relation of ratios with examples like 50 cents yielding 10 chocolates and 70 cents yielding 14, and apply product of extremes equals product of means.

Explore the four types of proportion, including main (mean), third, and fourth proportion, and distinguish direct and inverse proportion with examples like speed versus distance and heat versus water level.

Learn how percentages express a score as a portion of a total, computed as obtained value divided by total value multiplied by 100, and use it to compare performances.

Compute percentage change using (new minus old) over old times 100, shown with 350 to 450 marks, and convert percentages to fractions by dividing by 100.

Practice practical percent calculations with step-by-step examples, such as 20 percent of 600, 40 percent of 350, and 250 percent of 300, to build quick mental math skills.

Master calculating percent off, percent of a number, and multi-step percent changes using practical examples, including discounts on 4000, shirt, and television prices.

Master percentage change by applying increases and decreases to a base value using the change over initial value formula, with mobile price and population examples.

Compute profit and loss by linking cost price, selling price, and mark price. Apply formulas for profit percentage, loss percentage, and discount percentage using the relevant denominators.

Graphically analyze a pricing problem with a 20 percent discount and 20 percent profit, relating cost price, selling price, and market price to determine cost price from 600 Mark Price.

Learn how to compute profit or loss percentage from cost price and selling price, using examples with mobile purchases and equal selling prices to determine overall outcomes.

Learn to find the original car price from successive discounts of 30% and 40% when the final price is $1,026,000, using a base price method and algebra.

Compare simple and compound interest, detailing how principal, time, and rate determine the amount and illustrate interest on interest with a 5000 rupee, 20 percent, three-year example.

Learn how to compute averages for linear data using the first and last numbers, with examples like 1–5 and the first 100 even numbers. Compare linear and nonlinear data.

Explains nonlinear data with no order, introduces simple average as sum divided by observations, and demonstrates weighted average with a class example of boys, girls, and teachers.

Learn to solve average problems in a cricket team context. Calculate the sixth player's score from the first six average 50, last six average 35, eleven players, and average 40.

Explains mixtures with an example of combining two mixtures in ratios 2:3 and 3:4, using a common multiple to standardize quantities, and finding final composition as 29 to 41 parts.

Apply common multiples to reconcile a two-to-one volume ratio between resin vessels. Determine the final mixture's volumes and ratio, illustrated by the condensed milk-water-salt example.

Determine how to convert a 4:1 milk-to-water mixture to a 1:4 ratio by adding 240 liters of water, starting from 64 liters milk and 16 liters water.

Explore speed, average speed, and relative speed with distance and time. Apply the formulas: speed = distance/time, average speed = distance/total time, and relative speed = difference.

Two trains start from stations A and B toward each other at 60 and 80 mph, with a 1010-mile gap. They meet after 5.5 hours, 440 miles from station B.

Compute the average speed for a three-segment trip with speeds 40, 50, and 60 mph over 600 miles per leg, totaling 1800 miles in 37 hours, i.e., 1800/37 mph.

Explore a rate-time problem using speeds of 20 m/s and 30 m/s, where six seconds late and four seconds early determine the distance between house and office and normal time.

Compute the profit from a performance with $120 revenue, where 43% covers costs; with eight attendees, the profit is about $68.4.

Compute earth's average orbital speed by dividing the distance of about 580,000 thousand miles by the yearly hours (365×24), yielding roughly 66,210 mph and the closest option.

Explore lines and angles in geometry, including lines, rays, line segments, parallel and perpendicular lines, supplementary and complementary angles, vertical opposite angles, and proportional line division.

Study triangle basics, including angle side relationships, the 180-degree interior angle sum, the triangle inequality, and exterior angles equal to the sum of opposite angles.

Master triangle formulae by applying the area rule 1/2 base times height, explore incircle area via radius and semiperimeter, and derive equilateral triangle height and area with Pythagoras.

Explore the Pythagorean theorem, hypotenuse relations, and how 3-4-5 triplets and their multiples illustrate similar and congruent triangles through ratios and proportions.

Classifies triangles by sides and angles—scalene, isosceles, equilateral; right, acute, and obtuse angles—and covers centers such as incenter, circumcenter, excenter, centroid, and orthocenter, plus midpoint theorem and one-fourth area.

Explore special triangles, including 30-60-90 and 45-45-90, from equilateral triangle altitudes. Apply Pythagoras to derive side ratios: 1:√3:2 and 1:1:√2.

Explores quadrilaterals and their types—square, rectangle, rhombus, parallelogram, and trapezium—highlighting angle sums, opposite sides and angles, diagonals, and area and perimeter relationships.

Master polygon concepts from quadrilaterals to hexagons, learning how interior angle sums follow n-2 times 180 and exterior angles total 360 degrees, plus diagonals and regular polygon basics.

Explore circle basics—radius, diameter, center, chord, tangent, arc, and sector, plus major and minor arcs and segments, circumference, arc length, and sector area formulas.

Learn circle properties, proving that angles in a semicircle are right angles and that any inscribed triangle is right; explore radii, equal angles in the same segment, and tangent–radius perpendicularity.

Explore three-dimensional geometry with cuboids and cubes, and introduce cylinders, cones, spheres, and hemispheres while computing lateral and total surface areas, volumes, and the longest line inside a figure.

Explore cylinders, cones, spheres, hemispheres, prisms, and pyramids, and learn to calculate lateral and total surface areas, volumes, and key dimensions like radius, height, and slant height.

Master coordinate geometry by locating points in four quadrants, computing distances and slopes, and finding midpoints. Derive line equations with x- and y-intercepts, slope-intercept, two-point, and intercept forms.

Introduce algebra, including algebraic expressions with variables X and Y and operations; classify terms as binomials and trinomials and explore equations like three squared plus two plus three equals zero.

Teach factorization and the quadratic formula to solve x^2+x-6=0, yielding roots 2 and -3, and discuss discriminant, real and distinct roots, and sum and product of roots.

Explore exponent basics and power rules, including zero exponents, and master binomial expansions such as (x+y)^2 and (x+y)^3.

Master functions and algebraic expressions in one variable, including special function concepts, and solve simple equations using coefficient elimination, exploring zero, unique, and infinite solutions for lines.

Explore inequalities with linear expressions, solving for x using examples like 3x+4 ≥ x+7 and 3x+4 ≤ 2x+7, and learn how negatives flip the inequality on the number line.

Explore how absolute values turn negatives into positives and yield ranges like X <= -5 or X >= 5, and |X-3| <= 2 gives X between 1 and 5.

Solve a quadratic inequality by factoring x^2-4x+3 into (x-3)(x-1) and use zero-product and sign analysis to find intervals where the expression is ≥0 or ≤0, with endpoints included or excluded.

Factor the quadratic f(x) = x^2 - 4x + 3 as (x-1)(x-3). The solution lies between 1 and 3, with roots at 1 and 3 and the graph positive outside.

Explore how algebra uses letters to represent numbers and unknowns, enables operations on variables, and shows that a variable can take different values in algebraic expressions.

Compute the total apples by multiplying 30 apples per box by the number of boxes, showing the expression for total apples as 30 × number of boxes.

Develop problem-solving skills by solving age relations, equilateral triangle perimeter, cube edge totals, circle diameter in terms of radius, and forming algebraic expressions.

Classify expressions into monomials, binomials, and trinomials; determine coefficients and identify like and unlike terms using examples with x, y, and other variables.

Identify the terms in each expression and find their factors, illustrating with examples like x, minus five, minus xy, 2y^2, and minus three x^2.

Identify and classify algebraic expressions by the number of terms, distinguishing monomials, binomials, and trinomials, and determine like versus unlike terms through practice problems.

Learn to add and subtract algebraic expressions by combining like terms, such as 7xy, 4xy, and 2xy to 13xy, and 9n from 15n to 6n.

collect like terms and simplify algebraic expressions, combining m^2 and m terms and constants to yield 14 m^2 - 11 m + 16.

Practice subtracting and simplifying algebraic expressions, combining like terms, and evaluating polynomials across multiple variables such as x, y, m, n, p, and q.

Master the value of algebraic expressions by substituting known variable values, checking whether values satisfy equations, and applying geometry formulas like the area of a square with side 5 cm.

Discover how to multiply algebraic expressions by combining monomials, such as 3x and 4y into 12xy, then multiply the result with a third monomial; extendable to any number.

Multiply monomials and polynomials by applying the distributive law and exponent rules, as shown in exercise five and its monomial, binomial, and polynomial products.

Demonstrates multiplication of algebraic expressions using the distributive law, expanding and simplifying polynomials such as 3x+9 with 2x−5 and other polynomial products.

Explore standard algebraic identities, such as a plus b squared, a minus b squared, and (a plus b)(a minus b), and apply them to exercise seven.

Explore the difference between permutations and combinations, learn when order matters, and apply concepts through practical examples like prize rankings and team selection.

Explore how to count permutations and combinations when selecting three people from ten, showing 10P3 equals 720 and 10C3 equals 120, and relate to the formula nPr.

Identify the target and whether order matters, draw slots, and apply permutation or combination rules to solve problems; illustrated with 30 students, resulting in 435 ways.

Explore conditional slots in a combinatorics problem on an octagon by selecting two vertices to form diagonals and solving with a selection approach using 8C1 and 5C2.

Use a slot method to pick three boys from five and two girls from six, yielding 150 ways, and count rectangles and squares on a five by five board.

Define probability as the ratio of favorable outcomes to total outcomes, with values between zero and one, and apply the complement rule for at least one rain day.

Identify independent events where outcomes do not affect each other; multiply probabilities with replacement. Explain dependent events where outcomes influence subsequent results; apply union and intersection rules, including without replacement.

Explore types of probability questions by counting outcomes in coin tosses and dice throws, using powers of two and six to determine sample spaces and denominators.

Explore progressions, including arithmetic, geometric, and harmonic progressions, with key sum formulas for natural numbers, squares, and cubes. Learn to identify sequences and apply sums and ratios in each type.

Differentiate sets from lists, noting no repetition and order independence, and use Venn diagrams to analyze unions, intersections, not in A, only in B, universe, and subsets.

Apply the union and intersection principles with a Venn diagram to solve two-set problems, using |A∪B| = |A|+|B|−|A∩B|, illustrated by a class of forty students.

Learn to represent three sets with a Venn diagram and apply the inclusion–exclusion formula to calculate the total of students, including none, with an example totaling 66.

Build a group grade to classify students into boys, girls, vegetarian, non-vegetarian, and total, then solve the 500-student problem using the given ratios.