PYQ Vault
EbooksTutor

Surds, Indices and Simplification

CDS Maths. Try each one first, then open its answer.

Top 10 CDS PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 6 times: CDS 2 2016, CDS 1 2019, CDS 1 2021, CDS 2 2021, CDS 1 2023, CDS 1 2025. This one: CDS 1 2025 See all 6 of this type

    41
    What is 17−415+8−215\sqrt{17 - 4\sqrt{15}} + \sqrt{8 - 2\sqrt{15}} equal to ?

    Tap an option to check your answer.

  2. Question 2

    This type asked 4 times: CDS 1 2019, CDS 1 2022, CDS 2 2023, CDS 2 2026. This one: CDS 2 2026 See all 4 of this type

    10
    If x=11+230x = 11 + 2\sqrt{30}, then what is the value of x1/2+x−1/2x^{1/2} + x^{-1/2} ?

    Tap an option to check your answer.

  3. Question 3 (case study, 2 parts)

    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 ?

    Tap an option to check your answer.

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

    Tap an option to check your answer.

  4. Question 4

    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?

    Tap an option to check your answer.

  5. Question 5

    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?

    Tap an option to check your answer.

  6. Question 6

    This type asked 4 times: CDS 2 2017, CDS 2 2019, CDS 1 2020, CDS 1 2025. This one: CDS 1 2025 See all 4 of this type

    77
    If p=0.09‾p = 0.0\overline{9}, then what is the value of 70p2+43p−570p^2 + 43p - 5 ?

    Tap an option to check your answer.

  7. Question 7

    This type asked 4 times: CDS 1 2019, CDS 2 2019, CDS 1 2022, CDS 1 2024. This one: CDS 1 2024 See all 4 of this type

    36
    If 1a+1b+1c+1d+1e=421972\cfrac{1}{a + \cfrac{1}{b + \cfrac{1}{c + \cfrac{1}{d + \cfrac{1}{e}}}}} = \frac{421}{972}, then what is the value of a×b×c×d×ea \times b \times c \times d \times e ?

    Tap an option to check your answer.

  8. Question 8

    This type asked 4 times: CDS 2 2017, CDS 2 2019, CDS 2 2022, CDS 1 2023. This one: CDS 1 2023 See all 4 of this type

    25
    If x=4444…x = \sqrt{4\sqrt{4\sqrt{4\sqrt{4 \ldots}}}}, then what is the value of x?

    Tap an option to check your answer.

  9. Question 9

    Asked 3 times: CDS 1 2017*, CDS 2 2018*, CDS 2 2026 (* = numbers or wording changed that year) See all 3 times it was asked

    30
    If x=3−31/3−32/3x = 3 - 3^{1/3} - 3^{2/3}, then what is x(x−3)(x−6)x(x - 3)(x - 6) equal to ?

    Tap an option to check your answer.

  10. Question 10

    Asked 3 times: CDS 2 2020*, CDS 1 2022*, CDS 2 2024 (* = numbers or wording changed that year) See all 3 times it was asked

    8
    What is 110+9+111+10+112+11+…+1196+195\frac{1}{\sqrt{10} + \sqrt{9}} + \frac{1}{\sqrt{11} + \sqrt{10}} + \frac{1}{\sqrt{12} + \sqrt{11}} + \ldots + \frac{1}{\sqrt{196} + \sqrt{195}} equal to ?

    Tap an option to check your answer.