Yr9 Extension Exam

Willetton Senior High School: Year 9 Mathematics Extension Examination 2022

General Information

  • Exam Duration: 55 minutes

  • Materials Required:

    • To be provided: Question/Answer Booklet, Formula sheet

    • To be brought by students: Pens, pencils, sharpener, eraser, ruler, highlighters, 2 A4 pages of notes.

  • Marking: Show sufficient working for full marks.

Question Breakdown

Question 1: Filling a Tank (4 marks)

  • Graph Analysis: Relationship between time (t) and volume (V) of water in litres.

    • Part a: Quantity of water in tank after 10 minutes: 640 L.

    • Part b: State the constant of proportionality (k) and find the rule:

      • V = 64t; k = 64

    • Part c: Time to fill a 960L tank:

      • Equation: 960 = 64t, therefore t = 15 min.

Question 2: Equation Solving and Simplification (6 marks)

  • Part a: Solve 3(2(2x^4))+12=3(8-x):

    • Solution yields x = 10/7.

  • Part b: Simplify expression 4m^4 = 12mx^7 = 3x^{9}x^2 = 3x^22.

Question 3: Ball Trajectory (7 marks)

  • Height Equation: h = -t^2 + 3t + 4.

  • Part a: Table of values for t and h; find height at various seconds.

  • Part b: Plot the graph based on values.

  • Part c: Maximum height reached: 6.25 m.

  • Part d: Times when ball is at 5.25m: 0.5 sec and 2.5 sec.

Question 4: Factorization (6 marks)

  • a) 12x^2y^3 - 18x^2y^2 = 6x^2y^2(2y - 3).

  • b) x^2 + 11x + 24 = (x + 8)(x + 3).

  • c) 3x^2 + 6x - 9 = 3(x + 3)(x - 1).

Question 5: Area Calculation (4 marks)

  • Triangles: Area of triangle APQ with modified base and height: 9(x^2+x-2) or 9(x+2)(x-1).

Question 6: Cylinder Capacity (3 marks)

  • Height of Cylinder: 12 cm; diagonal straw = 15 cm.

    • Diameter calculated using Pythagorean theorem as 9 cm.

    • Volume: 763 mL.

Question 7: Simple Interest (4 marks)

  • Part a: Amount after 5 years with 4.1% p.a. simple interest: $28,920.

  • Part b: Required rate for 4 years to match this interest: 5.125%.

Question 8: Student Survey (6 marks)

  • Venn Diagram Analysis: Total surveyed students = 60.

    • Students studying only Italian = 24; only Mandarin = 12.

    • Probability of studying at least one language: 50/60.

    • Probability of studying both languages given Mandarin: 7/13.

Question 9: Proving Parallel Lines (5 marks)

  • Proof based on congruency and angle relationships to show DA || CB.

Question 10: Surface Area Calculation (4 marks)

  • Skate Ramp Surface Area: Total area to be painted calculated as approx 269.19 m².

Question 11: Line and Intersection (7 marks)

  • Equation of Line: 3x - 2y = b; value for b determined as 10.

  • Perpendicular Line Gradient: Negative reciprocal, determined as 3/2.

Question 12: Distance and Bearings (7 marks)

  • Diagram required for hiking distances.

  • Shortest distance from Booboo to Yogi calculated as approximately 19.2 km.

  • Bearing to Yogi: calculated as 12.3°T (or N 12.3°E).