Unicus Global Mathematics Olympiad Class 8 Sample Paper

Syllabus:

1. Content Domain: Number System

Rational Numbers

1. Rational numbers and their properties (addition, subtraction, multiplication, and division)
2. Finding rational numbers between two numbers
3. Representation of rational numbers on the number line

Squares and Square Roots

1. Properties of square numbers
2. Some interesting patterns
3. Finding the square and square roots of a number
4. Finding square roots by prime factorisation and long division
5. Square roots of decimals
6. Estimating square root

Cubes and Cube Roots

1. Properties of cube numbers
2. Some interesting patterns of cubes
3. Finding the cube root of a number

Exponents and Power

1. Laws of exponents

2. Content Domain: Comparing Quantities

Comparing Quantities

1. Determine proportions and ratios of quantities
2. Apply or find percentages
3. Convert between percentages and fractions or decimals
4. Profit and loss
5. Discount
6. Simple interest
7. Compound interest

Direct and Indirect Proportion

1. Direct proportion
2. Inverse proportion

3. Content Domain: Algebra

Algebraic Expressions and Identities

1. Algebraic expression and its types
2. Terms, coefficients, and factors
3. Simplify algebraic expressions involving sums, products, and differences
4. Compare expressions to decide if they are equivalent
5. Algebraic identities
6. Write expressions and equations to represent problem situations

Factorisation

1. Factorisation of algebraic expressions
2. Factorising quadratic trinomials

Linear Equations in One Variable; Linear Equations in Two Variables

1. Solve linear equations and simultaneous linear equations in two variables, including validating values as solutions
2. Problems involving framing and solving linear equations in one variable
3. Framing of linear equations in two variables

4. Content Domain: Geometry

Understanding Quadrilaterals

1. Kinds of quadrilaterals and their properties (parallelogram, rhombus, trapezium, etc.)
2. Polygon
3. Sum of the measures of the exterior and interior angles of a polygon

5. Content Domain: Mensuration

Mensuration

1. Perimeter and area of 2-dimensional shapes
2. Use properties of three-dimensional shapes to calculate surface area and volume

6. Content Domain: Statistics

Data Handling

1. Types of graph (frequency distribution tables, bar graphs, double bar graph, line graphs, histograms, and pie charts)
2. Summarise data distributions; calculate, use, or interpret mean, mode, median, and range

Probability

1. For simple and compound events, determine the theoretical probability (based on proportions of favourable outcomes, e.g., rolling a fair die or drawing marbles of a particular colour from a bag)
2. Estimate empirical probability (based on experimental outcomes)