Gr 12 Mathematics P1 (Afrikaans) Question Paper

Exam Information

  • Type: WISKUNDE (Mathematics) Exam 2023

  • Subject Code: 10611

  • Duration: 3 hours

  • Total Marks: 150

  • Pages: 10 + 1 Information Sheet

Instructions and Information (Page 2)

  1. This exam consists of 12 questions.

  2. Answer ALL questions.

  3. Clearly indicate ALL calculations, diagrams, graphs, etc., used to derive answers.

  4. Full marks will not necessarily be awarded for answers alone.

  5. Allowed: an approved non-programmable and non-graphical scientific calculator (unless stated otherwise).

  6. If necessary, round answers to TWO decimal places, unless otherwise stated.

  7. An INFORMATION SHEET with formulas is included at the end of the exam.

  8. Number the answers correctly according to the numbering system used in this exam.

  9. Write neatly and legibly.

Questions Overview

Question 1 (Page 3)

  • 1.1 Solve for x:

    • 1.1.1: Solve the equation (4 - 2x + 0 = 2) (3 marks)

    • 1.1.2: Solve (24 - 11 = 12 - x) (Correct to TWO decimal places) (3 marks)

    • 1.1.3: Solve the inequality (2 - 15x < 9x) (4 marks)

    • 1.1.4: Solve (2x - 2 - 7 - 2x = 1) (5 marks)

  • 1.2 Simultaneous Equations:

    • Solve (a + b = 2, ab = 2) and (log_3(5) = 8) (5 marks)

  • 1.3: Determine values of x for which (16 - 2x^2 + 2 = p) is real. (4 marks)

Question 2 (Page 3-4)

  • 2.1 Arithmetic Sequence:

    • 2.1.1: Calculate the value of p (2 marks)

    • 2.1.2: State the first term and the constant difference (1 mark each)

    • 2.1.3: Explain why none of the numbers are perfect squares (2 marks)

  • 2.2 Quadratic Sequence:

    • Determine expression for the general term of the first differences. (3 marks)

    • Calculate the first difference between the 35th and 36th terms (1 mark)

    • Determine expression for the nth term of the quadratic sequence. (4 marks)

    • Prove that the sequence never has positive terms. (2 marks)

Question 3 (Page 4)

  • 3.1 Given: (S_n = 4n^2 + 1). Find (T_6) (3 marks)

  • 3.2: Values of x for which the series converges. (4 marks)

  • 3.3: Calculate (\sum_{k=1}^{k=2} (k-3)) (2 marks)

Question 4 (Page 4-5)

  • An examination of the functions (g(x) = \frac{3x^2 - 3}{6}) and (h(x) = \frac{x^2 + 6}{3}).

    • Write the definition domain and range of g. (1 mark each)

    • Shift g to overlap h, determining horizontal and vertical shifts. (1 mark each)

    • State equations of asymptotes for g. (2 marks)

    • Calculate x-intercept of g. (1 mark)

    • Sketch g indicating all asymptotes and intercepts. (3 marks)

    • Determine k such that h is a symmetry axis. (2 marks)

    • Find values of x when (x - k > -3 + x + 2 + 6). (1 mark)

    • Reflect g across x-axis, write the new equation. (1 mark)

Question 5 (Page 5)

  • Functions of f and g are involved.

    • 5.1: State coordinates of the turning point E of f. (1 mark)

    • 5.2: Calculate the average gradient of f from (x=1) to (x=5). (4 marks)

    • 5.3: Determine value of a at point D. (3 marks)

    • 5.4: Determine ST in terms of x. (2 marks)

    • 5.5: Calculate the maximum length of ST. (3 marks)

Other Questions (Page 6 to Page 10)

  • Subsequent questions include topics such as recursive sequences, series summation, calculus derivatives, probability, and any necessary application of mathematical principles as implied in the preceding questions mentioned.

Information Sheet (Page 11)

  • Formulas for various mathematical concepts including series, derivatives, and probability.

  • Key equations provided for reference during calculations and problem-solving.

Total Marks

  • Total for the exam: 150 marks.