Review of the Grade 7 algebra course
During the course we learned to build and simplify algebraic expressions, to solve linear equations in one unknown and word problems with them, to work with powers, monomials and polynomials, to factor polynomials, to operate with algebraic fractions and to use elements of combinatorics. The main formulas are (a ± b)² = a² ± 2ab + b², a² - b² = (a - b)(a + b), a³ ± b³ = (a ± b)(a² ∓ ab + b²), aᵐ · aⁿ = aᵐ⁺ⁿ, Pₙ = n!, Cₙᵏ = n!/(k!(n - k)!). To avoid mixing them up, tell apart the left and right sides: (a - b)² is expanded into a polynomial, while a² - b² is turned into a product. Before an exam, solve one typical task from every chapter.
“Exam preparation”: the class splits across 6 stations (expressions, equations, polynomials, factoring, fractions, combinatorics). Each group solves one task at a station and moves on. The group with the most correct answers wins.