Chapter 5 – Algebra, equations, functions and graphs
Consider the following statements and click to reveal the answer.
1. Simplify the following expressions:
2. Find the general term for each of these sequences:
3. Solve the following pairs of simultaneous equations:
4. Find the gradients and the y-intercepts of the graphs of the following equations:
5. Find the general term for the following sequence:
6. What is a conjecture?
A conjecture is a hypothesis: something that has been surmised or deduced.
7. What different methods can be used to solve simultaneous linear equations?
The methods that can be used to solve simultaneous linear equations are:
- ‘trial and improvement’ (or ‘guess and check’ but not ‘trial and error’ as this implies a mistake);
- eliminating the unknown by multiplying one of the equations to ensure that there is an equal number of a particular unknown in each equation;
- expressing one unknown in terms of another in one of the equations, then substituting the new expression into the other equation, which is then rearranged to find the solution.
8. What is a function?
A function is a rule that changes or maps one number onto another, often represented in primary schools as a ‘function machine’.