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📄 HSC Mathematics Extension 1 Past Papers

HSC Paper Functions & Relations (Domain, Range, Even/Odd, Composite) Linear Functions (Gradient, Point-Gradient, Parallel/Perpendicular) Quadratic Functions (Vertex, Inequalities, Discriminant) Cubic Functions The Hyperbola & Variation (Inverse/Direct, Reciprocal) Absolute Value, Piecewise, Circles & Semicircles
2020 Q1: Domain of a square root function [1].
Q10: Stationary points of composite function h(x) = f(g(x)) [2].		 Q11: Modeling water volume with linear equations and labels [3]. Q5: Identifying a parabola graph based on constants [4].
Q30: Intersecting parabolas and finding shaded area [5].		 Q2: Horizontal and vertical translations of y = x³ [1].
Q16: Sketching a cubic with stationary points and inflection [6].		 Q25: Modeling a garden perimeter with a reciprocal relation 72/x [7]. Q7: Integrating a function made of line segments and a semicircle [8].
Q24: Reflection of a circle in the x-axis [9].
2021 Q3: Domain of a logarithmic function f(x) = ln(1-x) [10].
Q9: Tangent to a composite function h(x) = f(g(x)) [11, 12].
Q21: Sketching transformed function y = 4f(2x) [13, 14].		 Q11: Solving a linear algebraic equation [15]. Q31: Finding equations of tangents to a parabola y = x² - 1 passing through a point [16]. Q8: Identifying the equation of a cubic graph from its intercepts [11].
Q16: Finding intervals where f(x) = x² - 2x³ is increasing [17].		 Q19: Sketching hyperbola y = 2 + 1/(x+4) showing asymptotes [18].
Q24: Area bounded by y = 3/(x-1) and a line [19].		 Q12: Finding shaded area involving a right-angled triangle in a semicircle [20].
2022 Q10: Identifying the graph of a composite function g(f(x)) [21]. Q1: Identifying the graph of y = -2x - 2 [22].
Q31: Minimum triangle area from a line through P(1, 2) [23].		 Q4: Determining the range of y = x² - 1 [24].
Q16: Area enclosed by parabola y = x² and a line [25, 26].
Q19: Translations and dilations to transform f(x) = x² [27].		 Q22: Global max/min of a cubic on a closed interval [28]. Q12: Modeling inverse variation (M = k/T) for melting ice [29].
Q28: Intersection of a hyperbola y = a/(b-x) - 1 and a circle [30].		 Q28: Finding area bounded by a hyperbola and the circle x² + y² = 2 [31, 32].
2023 Q3: Domain of f(x) = 3/(1-x) [33].
Q5: Integral properties of an odd function [34].
Q9: Properties of even functions [35].		 Q28: Tangent y = x + 7 parallel to another tangent [36]. Q10: Comparing lengths of intervals where a line meets y = x² [35, 37].
Q19: Solving inequality between absolute value and quadratic [38].		 Q4: Equation of a cubic polynomial from a graph [34].
Q14: Tangent to the cubic curve y = (2x+1)³ [39].
Q28: Gradient function dy/dx = 3x² - 6x - 8 [40].		 Q3: Reciprocal function domain [33]. Q19: Sketching absolute value vs quadratic [38].
Q27: Finding values for f(x) = a|x-b| + c [41].
2024 Q6: Domain of f(x) = 1/√(x²-1) [42].
Q7: Transformations of a function y = f(2x-1) [42, 43].
Q10: Points of inflection for an integral function A(x) [44].		 Q1: Identifying linear equation y = -2x - 3 from a graph [45]. Q4: Reflecting a parabola about the y-axis then x-axis [42].
Q14: Finding intersection and area between y = (x-1)² and y = 5-x² [46].
Q29: Finding a, b, c for a curve with given tangent and normal [47].		 Q19: Sketching y = x⁴ - 2x³ + 2 using stationary points [48]. Q30: Range of limiting sum S involving graph y = -1 - 1/(x-1) [49]. Q31: Perimeter and area of a region QRST in concentric circles [50, 51].
2025 Q6: Transformations and graph of y = -f(-x) [52, 53].
Q10: Stationary points of y = f(e^x) [54, 55].
Q18: Range of composite function g(f(x)) with f(x) = 3/(x-1) [56].		 Q12: Finding tangent to a function at x = 1 [57]. Q11: Turning point and intercepts for h = t² - 8t + 12 [58].
Q24: Tangent to y = ax² + c at point of intersection [59].
Q30: Finding constant k for a translated parabola passing through (6, 11) [60].		 Q4: Identifying graph of y = -5x(x-2)(3-x) [52].
Q12: Tangent to a function with cubic and reciprocal terms [57].		 Q21: Percentiles of a PDF involving 1/x [61, 62]. Q3: Domain of semicircle-related function y = √(6 - x²) [52].
Q28: Dividing a circular paddock into segments with a fence [63, 64].

📄 HSC Mathematics Advanced Past Papers

HELM: Basic Algebra.

HELM: Basic Functions.

HELM: Equations, Inequalities & Partial Fractions.

HELM: Functions and Modelling.

HELM: Exponential & Logarithmic Functions.

HELM: Trigonometry.

HELM: Functions of Several Variables.

HELM: Differentiation.

HELM: Applications of Differentiation.

HELM: Integration.

HELM: Applications of Integration – Part 1.

HELM: Applications of Integration – Part 2.

Addotional materials.

📘 Theory & Complete Notes (Module 7: Nature of Light)

📝 Practice Questions & Worksheets

📄 Past Papers & Trial Exams

📚 Exam Guides & Study Resources

🔗 Additional Supporting Resources

  • science-s6-physics-module-5-advanced-mechanics.docx
  • 12Physics_-module-6-guide.docx
  • Problem set for Year 12 Physics
  • 12Physics_-module-7-guide.docx
  • Mod8
  • science-physics-s6-learning-sequence-diffraction-of-light.docx
    • >