SPM Mathematics 2017, Paper 2 (Questions 9 & 10)


Question 9 (6 marks):
A bag contains five cards, labelled with the letters I, J, K, M and U.
One card is picked at random from the bag and the letter is recorded. Without replacement, another card is picked at random from the bag and the letter is also recorded.
(a) Complete the sample space in the answer space.
(b) By listing all the possible outcomes of the event, find the probability that
(i) the first card picked is labelled with a vowel.
(ii) the first card picked is labelled with a consonant and the second card picked is labelled with a vowel.

Answer:
{(I, J), (I, K), (I, M), (I, U), (J, I), (J, K), (J, M), (J, U), (K, I), (K, J), (   , ), (   , ), ( , ), ( , ), (   , ), (   ,   ), (   , ), (   ,   ), (   , ), (   ,   )}


Solution:
(a)
S = {(I, J), (I, K), (I, M), (I, U), (J, I), (J, K), (J, M), (J, U), (K, I), (K, J), (K, M), (K, U), (M, I), (M, J), (M, K), (M, U), (U, I), (U, J), (U, K), (U, M)}

(b)(i)
{(I, J), (I, K), (I, M), (I, U), (U, I), (U, J), (U, K), (U, M)}
Probability of first card with vowels = 8 20 = 2 5

(b)(ii)
{(J, I), (J, U), (K, I), (K, U), (M, I), (M, U)}
Probability = 6 20 = 3 10


Question 10 (6 marks):
(a) Diagram 5.1 shows a Ferris wheel. The distance between point L and point M is 18 m.

Diagram 5.1

Calculate the minimum number of complete spins required to cover the distance of 600 m in a circular motion.


(b)
 Diagram 5.2 shows one large pizza and two small pizzas. Assume all pizzas are circular with a flat surface.

Diagram 5.2

Using  π= 22 7 , calculate the portion of the large pizza which equals to two small pizzas.


Solution:
(a)

Diameter=18 m Radius=9 m Circumference=2πr                        =2× 22 7 ×9 m                        = 396 7  m 396 7 ×rounds( P )=600 m P=600× 7 396 P= 350 33  rounds P=10 20 33 Thus, the minimum number of complete spins required=10.


(b)
Radius of large pizza=14 cm Area of large pizza  =π r 2 = 22 7 × ( 14 cm ) 2 = 22 7 ×196  cm 2 =616  cm 2 Radius of small pizza=7 cm Area of small pizza =π r 2 = 22 7 × ( 7 cm ) 2 = 22 7 ×49  cm 2 =154  cm 2 Area of 2 small pizza =2×154  cm 2 =308  cm 2 Ratio of area of 1 large pizza : 2 small pizza 616 : 308 616 2  : 308 308 : 308 Thus,  1 2 large pizza=2 small pizza

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