Step-up Maths

𝗚𝗖𝗦𝗘 𝗔𝗹𝗴𝗲𝗯𝗿𝗮 — 𝗨𝗹𝘁𝗶𝗺𝗮𝘁𝗲 𝗖𝗵𝗲𝗰𝗸𝗹𝗶𝘀𝘁 ✅

🟦 𝗖𝗢𝗥𝗘 (Foundation & Higher)
□ Algebraic notation: terms, coefficients, variables; like terms; brackets (…)
□ Substitution: evaluate expressions/formulae correctly (incl. negatives & fractions)
□ Order of operations & calculator fluency (powers, fractions, π, ANS)

🟦 𝗖𝗼𝗹𝗹𝗲𝗰𝘁, 𝗘𝘅𝗽𝗮𝗻𝗱, 𝗙𝗮𝗰𝘁𝗼𝗿𝗶𝘀𝗲
□ Collect like terms (e.g. 3x + 5x = 8x)
□ Expand single brackets: a(b + c) = ab + ac
□ Factor out common factor: ax + ay = a(x + y)
□ Expand double brackets: (x + a)(x + b) = x² + (a + b)x + ab
□ Factorise x² + bx + c into (x + m)(x + n) where mn = c, m + n = b

🟦 𝗜𝗻𝗱𝗶𝗰𝗲𝘀 (𝗣𝗼𝘄𝗲𝗿𝘀)
□ Laws: aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ (a ≠ 0), (aᵐ)ⁿ = aᵐⁿ
□ Special: a⁰ = 1 (a ≠ 0), a⁻ⁿ = 1/aⁿ, a¹⁄ⁿ = √[n]{a}

🟦 𝗔𝗹𝗴𝗲𝗯𝗿𝗮𝗶𝗰 𝗙𝗿𝗮𝗰𝘁𝗶𝗼𝗻𝘀
□ Simplify by cancelling common factors (not terms)
□ Add/subtract with common denominators
□ Multiply/divide algebraic fractions correctly

🟦 𝗘𝗾𝘂𝗮𝘁𝗶𝗼𝗻𝘀 & 𝗙𝗼𝗿𝗺𝘂𝗹𝗮𝗲
□ Solve linear equations (unknown both sides; with brackets/fractions)
□ Form and solve equations from word problems
□ Change the subject of a formula (incl. fractions & powers)

🟦 𝗜𝗻𝗲𝗾𝘂𝗮𝗹𝗶𝘁𝗶𝗲𝘀
□ Solve one-/multi-step; flip sign when × or ÷ by a negative
□ Represent on a number line (open ○ for < or >, filled ● for ≤ or ≥)
□ Solve compound inequalities (e.g. a < x ≤ b); list integer solutions

🟦 𝗦𝗲𝗾𝘂𝗲𝗻𝗰𝗲𝘀 (𝗟𝗶𝗻𝗲𝗮𝗿)
□ Generate terms; recognise constant difference
□ Find the nth term of an arithmetic sequence: aₙ = dn + c
□ Use position-to-term and term-to-term rules

🟦 𝗦𝘁𝗿𝗮𝗶𝗴𝗵𝘁-𝗹𝗶𝗻𝗲 𝗚𝗿𝗮𝗽𝗵𝘀
□ Plot/interpret y = mx + c; identify gradient m and intercept c
□ Intercepts: x = 0 → y-intercept; y = 0 → x-intercept
□ Parallel lines (same m); perpendicular (m₁·m₂ = −1)
□ Solve equations from graphs via intersections

🟦 𝗣𝗿𝗼𝗽𝗼𝗿𝘁𝗶𝗼𝗻
□ Direct: y ∝ x ⇒ y = kx
□ Inverse: y ∝ 1/x ⇒ y = k/x
□ Find/use the constant k in context

🟩 𝗤𝗨𝗔𝗗𝗥𝗔𝗧𝗜𝗖𝗦 (Foundation & Higher)
□ Factorise quadratics where possible
□ Complete the square: x² + bx + c = (x + p)² + q; turning point (−p, q)
□ Solve by factorising / completing the square / quadratic formula
□ Sketch quadratics: shape (∪ if a > 0, ∩ if a < 0), intercepts, axis x = −b/(2a)

🟧 𝗛𝗜𝗚𝗛𝗘𝗥 𝗢𝗡𝗟𝗬 (Grades 7–9)

🟧 𝗔𝗱𝘃𝗮𝗻𝗰𝗲𝗱 𝗙𝗮𝗰𝘁𝗼𝗿𝗶𝘀𝗶𝗻𝗴 & 𝗔𝗹𝗴𝗲𝗯𝗿𝗮𝗶𝗰 𝗙𝗿𝗮𝗰𝘁𝗶𝗼𝗻𝘀
□ Factorise ax² + bx + c (a ≠ 1)
□ Simplify algebraic fractions with quadratic factors; state domain restrictions

🟧 𝗦𝘂𝗿𝗱𝘀 & 𝗣𝗼𝘄𝗲𝗿𝘀
□ Simplify surds (e.g. √ab = √a · √b, a,b ≥ 0); combine/expand
□ Rationalise denominators: a/√b and a/(b + c√d)
□ Apply index laws with fractional/negative powers in algebraic contexts

🟧 𝗤𝘂𝗮𝗱𝗿𝗮𝘁𝗶𝗰 𝗜𝗻𝗲𝗾𝘂𝗮𝗹𝗶𝘁𝗶𝗲𝘀
□ Solve (x − a)(x − b) ≷ 0; show solutions on a number line
(filled endpoints for ≤, ≥; open for )

🟧 𝗦𝗶𝗺𝘂𝗹𝘁𝗮𝗻𝗲𝗼𝘂𝘀 𝗘𝗾𝘂𝗮𝘁𝗶𝗼𝗻𝘀
□ Solve linear–linear (elimination/substitution)
□ Solve linear–quadratic (substitute into quadratic; interpret intersections)

🟧 𝗙𝘂𝗻𝗰𝘁𝗶𝗼𝗻𝘀 & 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗮𝘁𝗶𝗼𝗻𝘀
□ Function notation f(x); evaluate f(a)
□ Composites & inverses: (f∘g)(x), f⁻¹(x) (state domains where needed)
□ Graph transformations: y = f(x) + a, y = f(x + a), y = −f(x), y = f(−x)

🟧 𝗡𝗼𝗻-𝗹𝗶𝗻𝗲𝗮𝗿 𝗚𝗿𝗮𝗽𝗵𝘀
□ Recognise/interpret: y = 1/x, y = x³, y = √x, exponentials y = k·aˣ
□ Use graphs to solve equations and inequalities (regions)

🟧 𝗦𝗲𝗾𝘂𝗲𝗻𝗰𝗲𝘀 𝗕𝗲𝘆𝗼𝗻𝗱 𝗟𝗶𝗻𝗲𝗮𝗿
□ Quadratic sequences (constant 2nd difference); find nth term
□ Geometric sequences: aₙ = a₁·rⁿ⁻¹; growth/decay contexts
□ Iteration: xₙ₊₁ = f(xₙ); efficient calculator use; recognise convergence

🟧 𝗗𝗶𝘀𝗰𝗿𝗶𝗺𝗶𝗻𝗮𝗻𝘁 & 𝗙𝗼𝗿𝗺𝘂𝗹𝗮
□ Discriminant Δ = b² − 4ac (Δ > 0 two roots; Δ = 0 one root; Δ < 0 no real roots)
□ Quadratic formula: x = (−b ± √(b² − 4ac)) / (2a)

🔶 𝗘𝗫𝗔𝗠 𝗦𝗞𝗜𝗟𝗟𝗦 (𝗾𝘂𝗶𝗰𝗸 𝗰𝗵𝗲𝗰𝗸𝘀)
□ Show clear steps (each line can earn marks)
□ Substitute to check solutions (equations & inequalities)
□ State units/rounding; give reasons when asked (“justify”, “show that…”)
□ Time management: ≈ 1½ minutes per mark; move on and return if stuck