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Chapter 8 Practice Paper: Matrices — question paper

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QQ/S3EM/CH8

Secondary 3 · Elementary Mathematics (G2 / G3)

Chapter 8 Practice Paper

Matrices

Duration: 40 minutes
Total: 30 marks
Name:
Class:
Register No.:
Date:

READ THESE INSTRUCTIONS FIRST

  • Write your name, class and register number in the spaces at the top of this page.
  • Answer all questions.
  • Show all necessary working. Omission of essential working will result in loss of marks.
  • Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
  • Geometrical instruments and an approved calculator may be used.
  • The number of marks is given in brackets [ ] at the end of each question or part question.
  • The total number of marks for each paper is shown on its cover.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapter 8 (N9 Matrices: order and elements, sums and scalar multiples, products where defined, data interpretation).

For Examiner’s Use
Section A/ 30
Total/ 30

Section A: Structured questions[30 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks.

  1. 1

    The matrix M = [[6, 1, 4], [2, 0, 7]] records deliveries, where rows are two drivers and columns are three routes.

    1. (a)

      State the order of M.

      [1]
    2. (b)

      Write down the value of m₂₃.

      [1]
    3. (c)

      Interpret the entry 6 in context.

      [1]
  2. 2

    Given A = [[3, −2], [1, 5]] and B = [[0, 4], [−1, 2]], find (a) A + B and (b) 2A − B.

    1. (a)

      Find A + B.

      [2]
    2. (b)

      Find 2A − B.

      [2]
  3. 3

    Matrix P has order 3 × 2 and matrix Q has order 2 × 5.

    1. (a)

      Determine whether PQ is defined, and state its order if it is.

      [2]
    2. (b)

      Determine whether QP is defined, giving a reason.

      [1]
  4. 4

    Find (a) [[2, 1], [3, 4]] × [[1, 5], [2, 1]] and (b) [[1, 5], [2, 1]] × [[2, 1], [3, 4]].

    1. (a)

      First product.

      [3]
    2. (b)

      Second product.

      [2]
  5. 5

    A café sells two set meals. Weekday sales are W = [[25, 18], [31, 9]] (rows = two outlets; columns = meal A, meal B). Meal A costs $6 and meal B costs $8.

    1. (a)

      Write down the price column matrix.

      [1]
    2. (b)

      Find WP.

      [2]
    3. (c)

      Interpret the two entries of WP.

      [2]
  6. 6

    A bookshop’s stock is S = [[12, 6, 3], [5, 10, 8]] (rows = two branches; columns = fiction, science, history) and a restock adds R = [[4, 1, 2], [2, 3, 6]].

    1. (a)

      Find S + R.

      [2]
    2. (b)

      The books cost $9 (fiction), $12 (science) and $7 (history). Use a matrix product to find the value of stock at each branch after the restock.

      [2]
    3. (c)

      State which branch holds the more valuable stock.

      [1]
  7. 7

    A = [[1, 3], [2, x]] and B = [[4, 1], [2, 5]].

    1. (a)

      Show that AB = [[10, 16], [8 + 2x, 2 + 5x]].

      [3]
    2. (b)

      Given that AB = [[10, 16], [14, 17]], find x and verify it with the bottom-right entry.

      [2]

— End of paper —