Mathematics Exam Preparation
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Sample questions with model answers
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The longest side of a triangle is twice the shortest side and the third side is 2 cm longer than the shortest side. If the perimeter of the triangle is more than 166 cm then find the minimum length of the shortest side.
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x = 41
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Prove that: $\tan 4x = \frac{4 \tan x (1-\tan^2 x)}{1-6 \tan^2 x + \tan^4 x}$.
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Proved using trigonometric identities.
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If $A = \{3, 5, 7, 9, 11\}$, $B = \{7, 9, 11, 13\}$, $C = \{11, 13, 15\}$ and $D = \{15, 17\}$; find (i) $A \cap (B \cup C)$ (ii) $A \cap D$ (iii) $A \cap (B \cup D)$ (iv) $(A \cap B) \cap (B \cup C)$ (v) $(A \cup D) \cap (B \cup C)$ and draw the venn diagram for each operation.
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Results obtained and Venn diagrams drawn.
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Find the modulus of $(1 + \frac{2+i}{3+i})$.
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1
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