Grade 9 maths: roots, quadratic functions and trigonometry

Grade 9 connects several strands: roots solve the quadratic equation, the parabola becomes a function type of its own, and sine, cosine and tangent let you calculate in any triangle for the first time.

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.

A quadratic equation has zero, one or two solutions. Check on the graph how many make sense and discard results that are impossible in context. When using a calculator, verify it is set to degrees or radians.

1. Powers and roots

Powers with integer exponents can be written with negative exponents using reciprocals. Taking a root reverses squaring. You may not take roots of sums term by term.

2. Quadratic equations and functions

Solve by factorising, completing the square or the quadratic formula. The vertex lies on the axis of symmetry; the discriminant tells you how many solutions exist. The zeros of a function are the solutions of the matching equation.

3. Trigonometry and solids

Sine, cosine and tangent start in right-angled triangles. For spheres, cylinders, cones and pyramids, calculate surface area and volume separately. Do not mix up area and volume.

4. Counting methods

When drawing without replacement, the number of options decreases at each step; with replacement it does not. Use the complementary event when direct counting becomes too laborious.