Quick International Maths Olympiad Course 2023

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.

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.

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.