Screening Paper II · 1 General Mental and Psychological Abilities · APPSC Group 1
1.2.2 Algebra: equations, identities and progressions notes
6 notes, in reading order.
- 1.2.2.1Linear equations in one and two variables: word problems
Name the unknown, write one equation for each fact given, and solve; most word problems in aptitude papers are one or two linear equations in disguise.
Advanced · 8 min · Full course - 1.2.2.2Quadratic equations: roots, nature of roots and comparing two quantities
A quadratic ax² + bx + c = 0 has two roots whose sum is −b/a and product is c/a; the discriminant b² − 4ac tells you what kind of roots they are before you solve.
Advanced · 7 min · Full course - 1.2.2.3Algebraic identities and factorisation for fast simplification
A handful of identities turn long arithmetic into one-line answers: spot the pattern (a ± b)², a² − b², a³ ± b³ or x + 1/x, and the calculation collapses.
Advanced · 6 min · Full course - 1.2.2.4Logarithms: laws, change of base and simplification
A logarithm is just an exponent: log_a N = x means aˣ = N, so the laws of logs are the laws of indices written the other way round.
Advanced · 5 min · Full course - 1.2.2.5Arithmetic and geometric progressions: nth term and sums
An AP adds the same number each step and a GP multiplies by the same number; two formulas each (nth term and sum) answer almost every progression question.
Advanced · 6 min · Full course - 1.2.2.6Inequalities and modulus: solving and comparing expressions
Solve an inequality like an equation, with one extra rule: multiplying or dividing by a negative number flips the sign; a modulus |x − a| is simply the distance from x to a.
Advanced · 6 min · Full course
Practise Algebra: equations, identities and progressions. Questions with answers explained, from the same topics.
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