Analytical Geometry: Midpoints, Gradients and Lines
Master the four core formulas — distance, midpoint, gradient and the line equation — and use gradients to prove shapes and angles.
High School · learning path
Analytical geometry, circles and tangents, Euclidean geometry and proofs, trigonometry — identities, equations, graphs and the sine and area rules — and statistics, from grouped data to regression.
Take them in order, or jump to what you need. Each step is a complete MicroQuest with its own certificate.
Master the four core formulas — distance, midpoint, gradient and the line equation — and use gradients to prove shapes and angles.
Read a circle's centre and radius from its equation, complete the square when it is not in standard form, and find the tangent at any point.
Learn the circle theorems that carry the marks, and write proofs the way they are marked — a statement with a reason on every single line.
Estimate a mean from grouped data, build and read an ogive, and draw a box-and-whisker plot that shows skewness and outliers.
Describe a scatter plot properly, interpret the correlation coefficient, use the least squares line to predict, and know when a prediction is worthless.
Prove triangles similar, use the proportion theorem correctly, and set up ratios that give the right answer every time.
Choose between the sine rule, cosine rule and area rule with confidence, and handle 2D and 3D problems without losing your way.
Solve trig equations with the general solution, and read amplitude, period and shifts off a sine, cosine or tangent graph.
Prove identities with a reliable method, reduce any angle to an acute one, and know which quadrant makes each ratio positive.
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