Maths trials papers - Student Name Teacher 2012 T RIAL HSC E XAMINATION Mathematics Examiners Mrs P Biczo Mr S Faulds Ms S Cupac Mr S Gee and Mr J

Maths trials papers - Student Name Teacher 2012 T RIAL HSC...

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2012 TRIAL HSC EXAMINATION Student Name: _______________________ Teacher: _______________________ Mathematics Examiners Mrs P. Biczo, Mr S. Faulds, Ms S. Cupac, Mr S. Gee and Mr J. Dillon General Instructions Reading time - 5 minutes. Working time - 3 hours. Write using black or blue pen. Diagrams may be drawn in pencil. Board-approved calculators and mathematical templates may be used. A table of standard integrals is provided at the back of this paper. Show all necessary working in Questions 11-16. Start each question in a separate answer booklet. Put your student number on each booklet. Total marks - 100 Section I 10 marks Attempt Questions 1-10 Allow about 15 minutes for this section Section II 90 marks Attempt Questions 11-16. Each of these six questions are worth 15 marks Allow about 2 hour 45 minutes for this section
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HAHS Mathematics Trial HSC 2012 2 Section I 10 marks Attempt Questions 1 10 Allow about 15 minutes for this section Use the multiple-choice answer sheet for Questions 1 10 1 Which of the following correctly shows the numeral 0.000 015 in scientific notation: A 5 15 10 B 6 15 10 C 6 1.5 10 D 5 1.5 10 2 When the denominator is rationalised, 1 5 3 A 5 3 2 B 5 3 16 C 5 3 2 D 5 3 3 1 2 x A 2 1 x B 2 x C 1 x D x 4 The solution to 1 3 x is: A 4 2 x   B 2 2 x   C 2 4 x   D 4 x   and 2 x 5 The solutions of 2 7 3 0 x x are A 7 37 2 x   B 7 37 2 x C 7 61 2 x   D 7 61 2 x 6 The solution of 2 5 x is A 3 x   B 3 x   C 3 x D 3 x
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HAHS Mathematics Trial HSC 2012 3 7 The number 0.07086 rounded to 3 significant figures is: A 0.070 B 0.071 C 0.0708 D 0.0709 8 Which of the following parabolas could have the equation ( 5)( 1) y x x ? A B C D 9 The angle of inclination of the line l with the x axis, to the nearest degree, is A 34 B 56 C 124 D 146 10 The solution for x which satisfies the pair of simultaneous equations: 2 3 6 x y x y is: A 3 x   B 1 x   C 5 x D 9 x x y 0 x y 0 x y 0 3 2 x 0 l y y x 0
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HAHS Mathematics Trial HSC 2012 4 Section II 90 marks Attempt Questions 11 16 Allow about 2 hours and 45 minutes for this section Answer each question in a new answer booklet . All necessary working should be shown in every question. Question 11 (15 marks) Start a new answer booklet Marks (a) Solve 2 2 6 0. x x 2 (b) In the diagram A , B and C are the points   1, 3 , 13,7 and 7,9 respectively. The points 3,3 P and 6,2 Q are the midpoints of AC and AB respectively. (i) Find the gradient of PQ . 1 (ii) Prove that ABC is similar to . AQP 3 (iii) Show that the equation of the line PQ is 3 12 0. x y 1 (iv) Find the exact length of PQ . 1 (v) Find the perpendicular distance of the point A to the line PQ . 2 (vi) Hence, find the area of . APQ 1 Question 11 continued over the page 1, 3 A x NOT TO SCALE y O 6,2 Q 3,3 P 13,7 B 7,9 C
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