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Day 20: CDS Maths

5 questions (6 parts). Try each one first, then open its answer.

  1. Question 1

    Surds, Indices and Simplification. This type asked 4 times: CDS 1 2017, CDS 1 2021, CDS 2 2022, CDS 2 2025. This one: CDS 2 2025 See all 4 of this type

    24
    If p+x+p−xp+x−p−x=p\frac{\sqrt{p+x}+\sqrt{p-x}}{\sqrt{p+x}-\sqrt{p-x}}=p, then what is xx equal to?

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  2. Question 2

    Surds, Indices and Simplification. This type asked 4 times: CDS 1 2017, CDS 2 2019, CDS 2 2023, CDS 2 2025. This one: CDS 2 2025 See all 4 of this type

    6
    If (2+3)x+(2−3)x=2(2+\sqrt{3})^x+(2-\sqrt{3})^x=2, then what is (2+3)x−(2−3)x(2+\sqrt{3})^x-(2-\sqrt{3})^x equal to?

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  3. Question 3 (case study, 2 parts)

    Trigonometric Ratios and Identities. This type asked 4 times: CDS 1 2021, CDS 1 2022, CDS 2 2024, CDS 2 2025. This one: CDS 2 2025 See all 4 of this type

    Let 1+sin⁡θcos⁡θ=p+p2+1\dfrac{1 + \sin\theta}{\cos\theta} = p + \sqrt{p^2 + 1}.
    47
    What is sec⁡θ\sec\theta equal to?

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    48
    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 2017, CDS 1 2019, CDS 2 2019, CDS 1 2025. This one: CDS 1 2025 See all 4 of this type

    36
    What is (a−b)2(b−c)(c−a)+(b−c)2(c−a)(a−b)+(c−a)2(a−b)(b−c)−3\frac{(a-b)^2}{(b-c)(c-a)} + \frac{(b-c)^2}{(c-a)(a-b)} + \frac{(c-a)^2}{(a-b)(b-c)} - 3 equal to, where a≠b≠ca \ne b \ne c ?

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  5. Question 5

    Averages. This type asked 4 times: CDS 2 2016, CDS 2 2022, CDS 1 2023, CDS 1 2025. This one: CDS 1 2025 See all 4 of this type

    100
    The arithmetic mean of 100 observations was 50. Later on, it was found that two observations were misread as 82 and 6 instead of 182 and 56. What is the value of the corrected mean ?

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