Grade 13 maths: analytical geometry and stochastics
Grade 13 focuses on the two major final-exam areas: analytical geometry with vectors and stochastics with random variables and the key distributions.
Reference: existing NRW curriculum mapping in Germany. Topics and sequence may vary by federal state, school type and classroom. This selection is not a complete curriculum.
For positions of lines and planes, check first whether the direction vectors are parallel; only then decide between intersecting or skew. In stochastics, define the random variable with its meaning and unit before calculating.
1. Lines and planes in space
Describe a line with a point and a direction vector, a plane with a point and two spanning vectors or a coordinate equation. For intersections, set the representations equal and solve the resulting system.
2. Random variables and the binomial distribution
The expected value describes the long-run mean, the standard deviation the typical spread. The binomial distribution requires a constant probability and independent trials. Sigma rules give ranges around the expected value.
3. The normal distribution
The normal distribution is symmetric about the expected value and determined by mean and standard deviation. Read probabilities using the standardised value z. For large samples, the binomial distribution can be approximated by the normal distribution.
Two questions to get started
A line has position vector (1; 2; 3) and direction vector (2; 0; −1). Where is the point for t = 2?
Answer and worked solution
(5; 2; 1)
p + 2 · u = (1; 2; 3) + (4; 0; −2) = (5; 2; 1).
A die shows its score. What is the expected value?
Answer and worked solution
3.5
Every score has probability 1/6. (1+2+3+4+5+6) ÷ 6 = 21 ÷ 6 = 3.5.
Continue with MatheJump
Sign in to use MatheJump’s learning resources and personal practice paths.
Sign in