PYQ Vault
EbooksTutor

Algebraic Identities 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 (case study, 2 parts)

    This type asked 5 times: CDS 1 2018, CDS 1 2020, CDS 1 2021, CDS 2 2025, CDS 1 2026. This one: CDS 1 2026 See all 5 of this type

    For the next two (02) items that follow : 16(x4+1x4)−257=016\left(x^4 + \frac{1}{x^4}\right) - 257 = 0
    83
    What is (x2+1x2)\left(x^2 + \frac{1}{x^2}\right) equal to ?

    Tap an option to check your answer.

    84
    What is (x3+1x3)\left(x^3 + \frac{1}{x^3}\right) equal to ?

    Tap an option to check your answer.

  2. Question 2

    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?

    Tap an option to check your answer.

  3. Question 3

    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 ?

    Tap an option to check your answer.

  4. Question 4

    This type asked 4 times: CDS 1 2021, CDS 2 2021, CDS 2 2022, CDS 2 2023. This one: CDS 2 2023 See all 4 of this type

    74
    If p=a2(b−a)(c−a)p = \frac{a^2}{(b - a)(c - a)}, q=b2(c−b)(a−b)q = \frac{b^2}{(c - b)(a - b)}, r=c2(a−c)(b−c)r = \frac{c^2}{(a - c)(b - c)}, then what is (p+q+r)2(p + q + r)^2 equal to ?

    Tap an option to check your answer.

  5. Question 5

    Asked 3 times: CDS 2 2017*, CDS 1 2019*, CDS 2 2019 (* = numbers or wording changed that year) See all 3 times it was asked

    46
    What is (x−y)3+(y−z)3+(z−x)33(x−y)(y−z)(z−x)\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{3(x - y)(y - z)(z - x)} equal to ?

    Tap an option to check your answer.

  6. Question 6

    This type asked 3 times: CDS 1 2018, CDS 1 2021, CDS 2 2026. This one: CDS 2 2026 See all 3 of this type

    35
    If x+y+z=0x + y + z = 0, then what is x(y+z)2+y(z+x)2+z(x+y)2x(y + z)^2 + y(z + x)^2 + z(x + y)^2 equal to ?

    Tap an option to check your answer.

  7. Question 7

    This type asked 3 times: CDS 1 2017, CDS 1 2022, CDS 2 2025. This one: CDS 2 2025 See all 3 of this type

    7
    If 1a+1b=56\frac{1}{a}+\frac{1}{b}=\frac{5}{6} and 1a2+1b2=1336\frac{1}{a^2}+\frac{1}{b^2}=\frac{13}{36}, then what is 1a3+1b3\frac{1}{a^3}+\frac{1}{b^3} equal to?

    Tap an option to check your answer.

  8. Question 8

    This type asked 3 times: CDS 2 2019, CDS 1 2024, CDS 2 2024. This one: CDS 2 2024 See all 3 of this type

    33
    What is the minimum value of (a8+a4+1)(b8+b4+1)a4b4\dfrac{(a^8 + a^4 + 1)(b^8 + b^4 + 1)}{a^4 b^4}, where a>0a > 0, b>0b > 0 ?

    Tap an option to check your answer.

  9. Question 9

    This type asked 3 times: CDS 1 2020, CDS 1 2021, CDS 2 2023. This one: CDS 2 2023 See all 3 of this type

    83
    If a,b,c,x,y,za, b, c, x, y, z are real numbers such that (a+b+c)2−3(ab+bc+ca)+3(x2+y2+z2)=0(a + b + c)^2 - 3(ab + bc + ca) + 3(x^2 + y^2 + z^2) = 0, then which one of the following is correct ?

    Tap an option to check your answer.

  10. Question 10

    This type asked 3 times: CDS 1 2021, CDS 1 2022, CDS 2 2022. This one: CDS 2 2022 See all 3 of this type

    12
    What is x6−24x4+144x2(x2+43x+12)(x−23)2\frac{x^6 - 24x^4 + 144x^2}{(x^2 + 4\sqrt{3}x + 12)(x - 2\sqrt{3})^2} equal to ?

    Tap an option to check your answer.