Grade 11 June Mathematics Paper 2 (past paper)

Grade 11 / Mathematics P2 2 JUNE 2024

QUESTION 1

1.1 If sin 28𝑜 = 𝑘, without using a calculator, determine the following ratios in terms of 𝑘.
1.1.1 cos 118𝑜 (2)

1.1.2 tan 62𝑜 (2)

1.1.3 sin 56𝑜 (3)

1.1.4 cos 88𝑜 (3)

1.2 Given: 5 cos 𝛼 + 3 = 0 , 0 < 𝛼 < 180𝑜 . Determine the following ratios.
1.2.1 sin 𝛼 (2)

1.2.2 sin(90 + 𝛼) (2)

tan 𝛼
1.2.3 (2)
cos 𝛼

1.3 Determine the value of the following expression without using a calculator:
sin(−155𝑜 )∙sin(𝑥−180𝑜 )
(6)
tan(180𝑜 −𝑥)∙cos 115𝑜 ∙cos 𝑥

1.4 Simplify the following expression:
sin(−60𝑜 )∙cos2 120𝑜 ∙sin 242𝑜
(6)
sin 298𝑜 ∙tan 405𝑜

1.5 Prove the identity:
tan 𝑥+1
= sin 𝑥 + cos 𝑥 (5)
sin 𝑥∙tan 𝑥+cos 𝑥

1.6 Prove the identity:
2 sin2 𝑥 cos 𝑥
= (6)
2 tan 𝑥−sin 2𝑥 sin 𝑥

1.7 Evaluate the following without using a calculator:

sin 108𝑜 ∙ sin 117𝑜 + sin(−27𝑜 ) ∙ cos 72𝑜 (5)

1.8 Determine the general solution of sin 𝑥 = 2 + cos 2𝑥 (5)

1.9 Solve for 𝑥 where 𝑥 ∈ [0; 180𝑜 ] : sin 2𝑥 − cos(𝑥 + 30) = 0 (6)

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, Grade 11 / Mathematics P2 3 JUNE 2024

QUESTION 2

In the diagram below, the graph of 𝑓(𝑥) = a ∙ sin 𝑏𝑥 and 𝑔(𝑥) = 𝑐 ∙ cos 𝑑𝑥 are drawn for the interval
𝑥 ∈ [−90𝑜 ; 360𝑜 ].




2.1 Determine the values of 𝑎, 𝑏, 𝑐 and 𝑑. (4)

2.2 Write down the period of 𝑓. (1)

2.3 Calculate the amplitude of 𝑔. (1)

2.4 Determine the value(s) of 𝑥 in the interval 𝑥 ∈ [0; 360𝑜 ], for which

2.4.1 𝑓(𝑥) > 𝑔(𝑥) (2)

2.4.2 𝑓(𝑥) ∙ 𝑔(𝑥) ≥ 0 (3)

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