CBSE Class 10 Maths Official Sample Paper 2020-21 (Standard and Basic)

4 Class 10 questions like these, with worked solutions

Written and checked by us, not taken from the CBSE paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Surface Areas and Volumes · 2 marks

   A cylindrical hole of radius 1 cm is drilled right through a solid cube of edge 6 cm, perpendicular to a pair of opposite faces. Find the volume of the remaining solid. $(\pi =3.14)$

   Worked solution

   Volume $=6^3-\pi (1{)}^2(6)$ M1

   $=216-18.84=197.16{\text{cm}}^3$ A1

2. Statistics · 2 marks

   For a grouped distribution of the heights (in cm) of students, $a=150$, $h=5$, $\sum f_i{u}_i=12$ and $\sum f_i=40$. Find the mean height.

   Worked solution

   $\overline{x}=150+5\times {\displaystyle \frac{12}{40}}$ M1

   $=150+1.5=151.5$ cm A1

3. Polynomials · 2 marks

   If $\alpha$ and $\beta$ are the zeroes of $2x^2-5x+3$, find the value of ${\alpha }^2+{\beta }^2$.

   Worked solution

   $\alpha +\beta ={\displaystyle \frac{5}{2}},\alpha \beta ={\displaystyle \frac{3}{2}}$ B1
   ${\alpha }^2+{\beta }^2={\displaystyle \frac{25}{4}}-3={\displaystyle \frac{13}{4}}$ A1

4. Quadratic Equations · 2 marks

   Solve by factorisation: $\sqrt{5}{x}^2+9x+4\sqrt{5}=0$.

   Worked solution

   $\sqrt{5}{x}^2+5x+4x+4\sqrt{5}=\sqrt{5}x(x+\sqrt{5})+4(x+\sqrt{5})=(\sqrt{5}x+4)(x+\sqrt{5})$ M1
   $x=-\sqrt{5}$ or $x=-{\displaystyle \frac{4}{\sqrt{5}}}=-{\displaystyle \frac{4\sqrt{5}}{5}}$ A1

More on these topics: Surface Areas and Volumes · Statistics · Polynomials · Quadratic Equations

Marks often lost in these chapters

Check your answers to the questions above, and this paper's questions on the same chapters, for these slips.

• Surface Areas and Volumes: Adding the total surface areas of the parts and so counting the hidden joined faces. Also: Using the vertical height $h$ in $\pi rl$ instead of the slant height. More on one page
• Statistics: Using the cf of the median class itself instead of the class before it. Also: Taking $f_0,f_2$ from the wrong classes, or using the class with the largest cf as the modal class. More on one page
• Polynomials: Sign slip: the sum of zeroes is $-b/a$, not $b/a$. Also: Writing $x^2+Sx+P$ instead of $x^2-Sx+P$. More on one page
• Quadratic Equations: Dividing both sides by $x$ and losing the root $x=0$. Also: Using $b$ instead of $-b$ in the formula, or dividing only the root term by $2a$. More on one page

What the paper covers

The unit weightage, with each unit's chapters, is on the Class 10 Maths papers page. We haven't mapped this paper question by question yet.

Formula booklet

CBSE Mathematics (Class 10 and Class 12) · CBSE · No official formula booklet

CBSE does not publish a formula booklet and none is given in the exam: formulas must be learnt. Use our one-page sheets to revise them.

More Class 10 papers

• Board paper 2023
• Board paper 2022
• Sample paper 2021-22
• Sample paper 2019-20
• All 13 Class 10 papers