SPM Mathematics 2019, Paper 2 (Question 6)


Question 6:
(a) State whether the following sentence is a statement or not a statement. [1 mark]

  2 x 2 +3y  

(b) Write down two implications based on the following statement: [2 marks]

  Matrix ( a    b c    d ) does not have the inverse if and only if ad−bc=0.  

(c) Make a general conclusion by induction for the sequence of the numbers 3, 38, 133, 318 which follows the following pattern: [2 marks]

    3 = 5(1) – 2
  38 = 5(8) – 2
133 = 5(27) – 2
318 = 5(64) – 2
            .
            .
            .


Solution:
(a)
Not a statement

(b)(i)
If ( a    b c    d ) does not have the inverse, then ad−bc=0.

(b)(ii)
If ad−bc=0, then ( a    b c    d ) does not have the inverse.

(c)
      3 = 5(1) – 2 = 5 (1)3 – 2
    38 = 5(8) – 2 = 5 (2)3 – 2 
133 = 5(27) – 2 = 5 (3)3 – 2 
318 = 5(64) – 2 = 5 (4)3 – 2
                          = 5n3 – 2, n = 1, 2, 3, …..

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