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Day 18: CDS Maths

5 questions (7 parts). Try each one first, then open its answer.

  1. Question 1 (case study, 2 parts)

    Surds, Indices and Simplification. This type asked 4 times: CDS 1 2018, CDS 1 2023, CDS 2 2025, CDS 1 2026. This one: CDS 1 2026 See all 4 of this type

    For the next two (02) items that follow : Let x=6+56−5x = \frac{\sqrt{6} + \sqrt{5}}{\sqrt{6} - \sqrt{5}} and y=6−56+5y = \frac{\sqrt{6} - \sqrt{5}}{\sqrt{6} + \sqrt{5}}
    85
    What is (x2−y2)\left(x^2 - y^2\right) equal to ?

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    86
    What is (x2−xy+y2)\left(x^2 - xy + y^2\right) equal to ?

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  2. Question 2

    Triangles. This type asked 4 times: CDS 2 2020, CDS 2 2021, CDS 2 2025, CDS 1 2026. This one: CDS 1 2026 See all 4 of this type

    56
    ABC is a triangle right-angled at B. Points M and N trisect BC. If AM=6AM = 6 cm and AN=9AN = 9 cm, then what is AC equal to ?

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  3. Question 3 (case study, 2 parts)

    Trigonometric Ratios and Identities. This type asked 4 times: CDS 1 2017, CDS 1 2021, CDS 2 2021, CDS 1 2026. This one: CDS 1 2026 See all 4 of this type

    For the next two (02) items that follow : p+qcot⁡θ=3cosec⁡θp + q\cot\theta = 3\operatorname{cosec}\theta and q−pcot⁡θ=2cosec⁡θq - p\cot\theta = 2\operatorname{cosec}\theta
    97
    What is p2+q2p^2 + q^2 equal to ?

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    98
    What is tan⁡θ\tan\theta equal to ?

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  4. Question 4

    Algebraic Identities and Simplification. This type asked 4 times: CDS 2 2020, CDS 1 2021, CDS 2 2023, CDS 2 2025. This one: CDS 2 2025 See all 4 of this type

    21
    What is (a+b)2(c−a)(c+a+b)+(a+b)cc2+bc−a2−ab−(a+2b+c)2(c−a)\frac{(a+b)^2}{(c-a)(c+a+b)}+\frac{(a+b)c}{c^2+bc-a^2-ab}-\frac{(a+2b+c)}{2(c-a)}, a≠ba\ne b, b≠cb\ne c, c≠ac\ne a equal to?

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  5. Question 5

    Mensuration 2D. This type asked 4 times: CDS 1 2022, CDS 2 2024, CDS 1 2025, CDS 2 2025. This one: CDS 2 2025 See all 4 of this type

    71
    In a triangle ABCABC, ∠A=30∘\angle A = 30^\circ, AB=7AB = 7 cm and AC=12AC = 12 cm. What is the area of the triangle ABCABC?

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