Day 232: CDS Maths

5 questions (8 parts). Try each one first, then open its answer.

Question 1 (case study, 2 parts)
Triangles. Asked once: CDS 2 2026
For the next two (02) items that follow : ABC is an equilateral triangle. BP is perpendicular to AC, PR is perpendicular to AB, and PQ is perpendicular to BC.
87 $AB^2 : BP^2 : PR^2$
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88 $\triangle PRB$
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Question 2
Trigonometric Ratios and Identities. Asked once: CDS 2 2026
37 $\frac{1 - \tan x}{1 + \tan x} = 1 - \frac{2\tan x}{1 + \tan^2 x}$
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Question 3
Algebraic Identities and Simplification. Asked once: CDS 1 2026
4 $\frac{1}{x} = \frac{1}{p} + \frac{1}{q}$
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Question 4
Averages. Asked once: CDS 2 2024
77 $31^\circ$
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Question 5 (case study, 3 parts)
Circles. Asked once: CDS 2 2024
Let $MN$ be a chord of length 16 cm of a circle with centre at $O$ and radius 10 cm. The tangents at $M$ and $N$ intersect at a point $P$ . Further, $OP$ intersects $MN$ perpendicularly at $Q$ .
58 $OQ$
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59 $PM$
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60 $OMN$
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Question 1 (case study, 2 parts)