# Chapter 5 – Algebra, equations, functions and graphs

Consider the following statements and click to reveal the answer.

1. Simplify the following expressions:

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2. Find the general term for each of these sequences:

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3. Solve the following pairs of simultaneous equations:

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4. Find the gradients and the y-intercepts of the graphs of the following equations:

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5. Find the general term for the following sequence:

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**Answer:**

*A conjecture is a hypothesis: something that has been surmised or deduced.*

7. What different methods can be used to solve simultaneous linear equations?

**Answer:**

*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. *

**Answer:**

*A function is a rule that changes or maps one number onto another, often represented in primary schools as a ‘function machine’.*