@?maths

What is a linear model?? A model which works with a straight line. When creating a linear model, how do you need to change $y = mx + c$?? Instead of using $y$ and $x$ you use variables which reflect the context. What is the general ice cream sales equation?? $\text{ice cream sales} = m \times \text{weather} + c$ What’s a common critique of a linear model?? It predicts impossible negative values. What does the gradient in a linear model reflect?

When working with triangles in a co-ordinate system, the most important step is?? Drawing a sketch. How can you prove that a triangle is right-angled in a co-ordinate system?? Find the gradients of the lines and prove two are perpindicular. How can you prove two lines are perpindicular?? Show their gradients multiply to give $-1$. How can you prove that a triangle is isoceles in a co-ordinate system?? Show two lines have the same length.

What is the formula for the midpoint between two points?? $$ (\frac{(x_2 - x_1)}{2}, \frac{(y_2 - y_1)}{2}) $$ What is the formula for the distance between two points?? $$ \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2} $$ Pythagoras What is the formula for the gradient between two points?? $$ \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{rise}}{\text{run}} $$ What are the two main ways of expressing the quation of a straight line?? $y = mx + c$ $ax + by + c = 0$ When using the $ax+by+c=0$ form of a straight line equation, there is an expectation that…?

Maths Syllabus Link to specification: https://qualifications.pearson.com/content/dam/pdf/A%20Level/Mathematics/2017/specification-and-sample-assesment/a-level-l3-mathematics-specification-issue4.pdf Papers Paper 1 & 2: Pure Mathematics AS-Level [[Maths - Straight Line Graphs]]S [[Maths - Triangles in a Co-ordinate System]]S [[Maths - Linear Models]]S [[Maths - Quadratic and Straight Line Intersections]]S [[Maths - Surds]]S [[Maths - Proof Roots of Primes are Irrational]]S [[Maths - Quadratics Tips and Tricks]]S [[Maths - Sketching Graphs]]S [[Maths - Integration]]S [[Maths - Differentiation]]S [[Maths - Quartics]]S [[Maths - Completing the Square]]S [[Maths - Quadratic Modelling]]?