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# ARC 2001S - Mathemat cs Extens on 1 HSC 2001 Mathematics...

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Mathemat cs Extens on 1, HSC - 2001 1 Mathematics Extension I HSC Trial Examination Mapping Grid Question Marks Content Syllabus Outcomes Targeted Performance Bands 1 (a) (i) 2 Inverse Trigonometric Functions HE 4 E2 – E3 1 (a) (ii) 1 Derivatives of a Function P 7 E2 – E3 1 (b) 2 Differentiation from First Principles H 5 P 6 E2 – E3 1 (c) 3 Trigonometric Functions P 4 E2 – E3 1 (d) 2 Permutations and Combinations PE 3 E2 – E3 1 (e) 2 Inequalities PE 3 E2 – E3 2 (a) 3 Integration HE 6 E2 – E3 2 (b) 3 Permutations and Combinations PE 3 E2 – E3 2 (c) 3 Mathematical Induction HE 2 E2 – E3 2 (d) 3 Plane Geometry PE 2 PE 3 E2 – E3 3 (a) 3 Integration; Inverse Trigonometric Functions H 8 HE 4 E2 – E3 3 (b) 3 Binomial Theorem PE 6 HE 7 E2 – E3 3 (c) (i) 2 Quadratic Polynomial and the Parabola PE 3 PE 4 E2 – E3 3 (c) (ii) 4 Quadratic Polynomial and the Parabola PE 3 E3 – E4 4 (a) (i) 4 Trigonometric Functions H 5 E3 – E4 4 (a) (ii) 1 Polynomials PE 3 E2 – E4 4 (a) (iii) 2 Polynomials PE 3 E2 – E4 4 (b) (i) 4 Applications of Calculus to the Physical World HE 3 E2 – E4 4 (b) (ii) 1 Applications of Calculus to the Physical World HE 3 E2 – E3 5 (a) (i) 1 Applications of Calculus to the Physical World HE 3 E2 – E3 5 (a) (ii) 2 Applications of Calculus to the Physical World HE 3 E2 – E3 5 (a) (iii) 1 Applications of Calculus to the Physical World HE 3 E2 – E3 5 (a) (iv) 1 Applications of Calculus to the Physical World HE 3 E2 – E3 5 (b) (i) 1 Exponential Functions P 5 H 3 E2 – E3

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Mathemat cs Extens on 1, HSC - 2001 2 5 (b) (ii) 2 Exponential Functions; Geometric Application of Differentiation H 6 E2 – E3 5 (b) (iii) 3 Exponential Functions; Geometric Application of Differentiation H 6 E2 – E3 5 (b) (iv) 1 Exponential Functions; Geometric Application of Differentiation H 6 E2 – E3 6 (a) (i) 2 Binomial Theorem HE 3 E3 – E4 6 (a) (ii) 4 Binomial Theorem HE 3 E3 – E4 6 (b) (i) 3 Plane Geometry HE 5 P 4 E3 – E4 6 (b) (ii) 3 Plane Geometry PE 2 PE 3 E3 – E4 7 (a) (i) 2 Applications of Calculus to the Physical World PE 2 PE 3 E3 – E4 7 (a) (ii) 1 Applications of Calculus to the Physical World HE 3 E3 – E4 7 (a) (iii) 1 Applications of Calculus to the Physical World HE 3 E2 – E4 7 (b) 2 Binomial Theorem HE 3 E3 – E4 7 (c) (i) 3 Plane Geometry; Applications of Calculus to the Physical World HE 5 P 4 E3 – E4 7 (c) (ii) 3 Applications of Calculus to the Physical World HE 5 E3 – E4
Mathemat cs Extens on 1, HSC - 2001 3 Marking Guidelines 2 Correct expression 1 Error with constant 1 (a) (i) 0 Other errors 1 Correct expression 1 (a) (ii) 0 Any error 1 Correct substitution 1 (b) 1 Correct evaluation and simplification 1 Obtains quadratic equation in θ sin , θ cos 1 Solution of quadratic 1 (c) 1 Correct angles in radians 1 (d) 2 Correct answer 1 Various methods to obtain cubic inequality in x 1 (e) 1 Correct solution from graph on number line 1 Correct substitution 1 Integration 2 (a) 1 Substituting back 1 Formula for r n C 1 Cubic equation in n 2 (b) 1 Solution 1 True for n = 1 and assumption 1 True for n = k + 1 2 (c) 1 Conclusion 1 Exterior angle 1

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ARC 2001S - Mathemat cs Extens on 1 HSC 2001 Mathematics...

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