# Maths HL Paper 1 Ques 1 and 2

**Section 1: Algebra **

**Paper 1, Question 1 and 2**

**Table of Contents:**

**Basic Rules for Manipulation****Fractions below the line****Adding Fractions****Manipulating Equations**

**Simultaneous Equations****Two Variable****Three Variable****Quadratic and a Linear**

**Surds****Underneath the line****Squaring****Modulus**

**Alpha and Beta****Manipulation****Forming a Quadratic****Difference in Roots**

**Roots****Determining the nature of the roots of a Quadratic****How to graph a function**

**Roots and Factors****Explanation of the Factor Theorem****Finding the roots of a cubic****Showing variables equal to other variables**

**Proofs (c-parts)****Terms****Valuable Equations****Solutions**

**Basic Rules for Manipulation:**

To begin it’s important that you are 100% clear on the fundamentals of manipulation. You will have seen these for years but even then you may not have understood them. They will be short and simple but it’s important you are wholly certain of each step. We will cover:

- Fraction below the line
- Adding fractions
- Manipulating Equations

**Example: Fraction below the line**

Simplify:

** {**Take the fraction underneath the line and turn it upside down}

Multiply the new fraction by what was on top of the line. Now you have gotten rid of the fraction below the line

5 x =

**Example: Adding Fractions**

(3)(4) **{**Take what is underneath the lines and multiply them by each other}

**{**Multiply each fraction by (3)(4) }

**WARNING! **Remember that if you multiply on the left you must do the same to the right. So (3)(4) are multiplied by the X as well. Don’t forget. And if there was a fraction on the other side of the equation I would take what is below the line there as well.

** **

4 + 33 = 12x 37 = 12x

**Important Formula: **This Formula works for adding fractions::

**WARNING! **Not in the table book, but you don’t need to learn it really, just know how to apply it.

**Example: Manipulating Equations**

Simplify , express *x* in terms of *y*.

This is a skill which it is vital that you learn. Adjusting the formula/equation to suit your purpose is something...