Year 9 Mathematics Advanced 2025 Exam Notes

CHERRYBROOK TECHNOLOGY HIGH SCHOOL - YEAR 9 MATHEMATICS ADVANCED 2025 CAT1 Notes

General Instructions

  • Attempt all questions in the spaces provided.

  • Write your name and class on the question paper.

  • Write using black pen.

  • All necessary working should be shown.

  • Calculators approved by NESA may be used.

Outcomes/Questions Marks Breakdown

  • MA5-IND-C-01: Simplifies algebraic fractions with numerical denominators and expands algebraic expressions: Questions 1, 2, 3, 4 (Total: /13 Marks)

  • MA5-IND-P-01: Simplifies algebraic expressions involving positive integers and zero indices, and establishes the meaning of negative indices for numerical bases: Questions 5, 6 (Total: /14 Marks)

  • MA5-MAG-C-01: Applies index laws to operate with algebraic expressions involving negative-integer indices: Question 7 (Total: /4 Marks)

  • Measurement: Solves measurement problems using scientific notation and rounding to a given number of significant figures: Questions 8, 9, 10 (Total: /14 Marks)

  • Total Marks Available: 45

Questions and Answers

Question 1 (2 marks)

  • Task: Expand and simplify: 2x(3x + 4)(x - 4)

  • Steps to solve:

    1. Apply the distributive property.

    2. Combine like terms.

Question 2 (6 marks)

  • Task: Simplify the following expressions:

    • (a) 4x^3 + 3x^2 - 12x + 2

    • (b) 11x^5 imes 15 imes 22x^1

    • (c) 5x^7 rac{10}{1}

    • (d) rac{1}{2}x^2 + rac{1}{4}x^2

  • Steps to solve each part: Same methodology as in Question 1; simplify by combining like terms and applying algebraic rules.

Question 3 (3 marks)

  • Task: Find area and simplify:

    • (a) Area of rectangles provided in a diagram.

    • (b) What binomial product was Sam expanding?

    • (c) Simplify this binomial product.

Question 4 (2 marks)

  • Task: Expand and simplify: (2x + 1)(x - 3).

  • Steps to solve: Distribute each term in the first binomial by each term in the second binomial and simplify.

Question 5 (11 marks)

  • Task: Simplify:

    • (a) 5x^4 x^2

    • (b) 100x^3 rac{1}{10x^2}

    • (c) (x^7 x^3)^2

    • (d) 8x^7 rac{14x^6}{3x^4}

    • (e) 7x^5 imes 14x^7 = 98x^{12}

    • (f) 7x^2 imes (x^5)^{-2} imes 20x^{15}.

Question 6 (3 marks)

  • (a) Show that rac{x^3 y}{y^2} = x^3.

  • (b) Simplify 5x^{12} imes rac{y^5}{y^{-2}}, leaving the answer with a positive index.

Question 7 (4 marks)

  • a) Rewrite (7x^{-3}) with a positive index.

  • b) Simplify (x^{-1})^6, leaving the answer with a negative index.

  • c) Simplify (5x^{3y^3})^2, leaving the answer with a positive index.

Question 8 (4 marks)

  • The mass of an electric Volvo XC40 was given as 2460 kg, correct to the nearest ten kgs. Tasks include:

    • (a) Determine the precision of the device used for measurement.

    • (b) Calculate the absolute error of this measurement.

    • (c) Find the lower and upper limits for the mass of the car.

    • (d) Calculate the percentage error for this measurement (one decimal place).

Question 9 (4 marks)

  • (a) Define a nanometre (1 nm = 0.000000001 m). The width of hair = 100,000 nm. How many would fit in a 3 cm sample?

  • (b) Precision of tools indicates which measurement is more accurate and justify reasoning based on results from four different measurements.

Question 10 (6 marks)

  • (a) Express: mass of small particle = 0.000000000045 g in scientific notation.

  • (b) Speed of light in a vacuum is about 299,792,458 m/s. Convert this to km/s (to four significant figures).

  • (c) Distance from Earth to Nearest Star (Proxima Centauri): 4.24 imes 10^{16} m, calculate time in years to travel this distance at light speed (3.0 imes 10^{8} m/s).

Conclusion

  • The content covered includes algebraic expressions, indices, measurement, scientific notation, and problem-solving skills that will be vital for Year 9 Mathematics Advanced Curriculum. Further practice with each concept via exercises will prepare for assessments.