Review of the Grade 9 Algebra course
The graph of the quadratic function y = ax² + bx + c is a parabola; its vertex is at x₀ = −b : (2a), and it opens upward if a > 0 and downward if a < 0. A quadratic inequality is solved from the position of the parabola relative to the x-axis or by the interval method. In trigonometry the basic identities are sin²α + cos²α = 1 and tanα = sinα : cosα. For an arithmetic progression a_n = a₁ + (n − 1)d and S_n = (a₁ + a_n) · n : 2; for a geometric progression b_n = b₁q^(n−1), S_n = b₁(q^n − 1) : (q − 1), and if |q| < 1 then S = b₁ : (1 − q). Probability is P(A) = m : n with 0 ≤ P(A) ≤ 1; in statistics we use the mean, mode, median, range, variance D and σ = √D. Before solving a problem, decide which topic it belongs to, choose the right formula and check the answer.
“Review relay”: the class forms teams; team members take turns solving one problem from each chapter (quadratic function, trigonometry, progression, probability) and pass the task on.