1. State the problem: Create an exam paper based on the listed topics from various math books and chapters. 2. Identify key topics: The topics include Pythagoras' Theorem, Linear Graphs and Simultaneous Equations, Trigonometric Ratios, Financial Transactions, Indices, Surds and Standard Form, Averages of Statistical Data, Factor and Multiples, Integers and Rational Numbers, Basic Algebra, Linear Equations, Functions and Linear Graphs, Percentages, Ratio, Rate and Speed, Basic Geometrical Concepts, Triangles and Polygons, Perimeter and Area, Volume and Surface Area, Statistical Data Handling, Direct and Inverse Proportion, Expansion and Factorisation, Quadratic Equations and Graphs, Algebraic Fractions and Formulae. 3. Formulate questions: Select representative problems from each topic to cover a broad range of skills. 4. Example question 1 (Pythagoras' Theorem): Given a right triangle with sides $a=3$ and $b=4$, find the hypotenuse $c$ using the formula $$c=\sqrt{a^2+b^2}$$. 5. Example question 2 (Linear Graphs): Find the equation of the line passing through points $(1,2)$ and $(3,6)$. 6. Example question 3 (Trigonometric Ratios): Calculate the length of side $a$ opposite to angle $30^\circ$ in a right triangle with hypotenuse $c=10$ using $$a=c\sin 30^\circ$$. 7. Example question 4 (Financial Transactions): Calculate the simple interest on a principal of 1000 at 5% per annum for 3 years using $$I=\frac{P\times R\times T}{100}$$. 8. Example question 5 (Indices and Surds): Simplify $$\sqrt{50} + 3\sqrt{2}$$. 9. Example question 6 (Averages): Find the mean of the data set: 4, 8, 6, 10, 12. 10. Example question 7 (Factor and Multiples): Find the greatest common factor of 24 and 36. 11. Example question 8 (Basic Algebra): Solve for $x$ in the equation $$2x + 5 = 15$$. 12. Example question 9 (Percentages): Find 20% of 150. 13. Example question 10 (Ratio and Speed): If a car travels 150 km in 3 hours, find its speed. 14. Example question 11 (Geometry): Calculate the area of a triangle with base 8 and height 5. 15. Example question 12 (Volume): Find the volume of a cylinder with radius 3 and height 7 using $$V=\pi r^2 h$$. 16. Example question 13 (Direct and Inverse Proportion): If $y$ is directly proportional to $x$ and $y=10$ when $x=2$, find $y$ when $x=5$. 17. Example question 14 (Quadratic Equations): Solve $$x^2 - 5x + 6 = 0$$. 18. Example question 15 (Algebraic Fractions): Simplify $$\frac{x^2 - 9}{x+3}$$. This exam paper covers 15 distinct questions from the provided topics.