Study guide: Algebra and Coordinate Geometry

📋 Course Outline

1. Quadratic Factorisation and Indices
2. Algebraic Fractions
3. Coordinates and Straight Lines

📖 1. Quadratic Factorisation and Indices

★ Must-know

• Quadratic expressions are factorised, including difference-of-two-squares expressions and three-term quadratics.

• Index rules cover operations with powers, including negative and fractional indices.

Further detail

• Index equations, such as $2x^4=32$, are solved using index rules.

📖 2. Algebraic Fractions

★ Must-know

• Algebraic fractions are added and subtracted.

• Algebraic fractions are simplified by cancelling common factors in the numerator, the denominator, or both.

• Algebraic fractions are multiplied and divided.

Further detail

• The numerator and denominator of an algebraic fraction may be numeric, linear, or quadratic.

📖 3. Coordinates and Straight Lines

★ Must-know

📐 Formula - For points $(x_1,y_1)$ and $(x_2,y_2)$, the midpoint is $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

📐 Formula - The distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.

📐 Formula - The gradient between points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y_2-y_1}{x_2-x_1}$.

• A straight-line equation can be written in the forms $y=mx+c$ or $ax+by=c$.

Further detail

• The equation of a line can be found from one point and its gradient or from two points.

• Line-equation problems include finding parallel and perpendicular lines and the perpendicular bisector of two points.