CBSE Class 10 Maths Official Sample Paper 2023-24 (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. Coordinate Geometry · 2 marks

   In what ratio does the point $P(2,3)$ divide the segment joining $A(-2,5)$ and $B(8,0)$?

   Worked solution

   Let the ratio be $k:1$: ${\displaystyle \frac{8k-2}{k+1}}=2\Rightarrow 6k=4$ M1
   $k={\displaystyle \frac{2}{3}}$: ratio $2:3$ (check: $y={\displaystyle \frac{0+15}{5}}=3$ ✓) A1

2. Introduction to Trigonometry · 2 marks

   If $\sin (2A-B)=1$ and $\tan (A+B)=\sqrt{3}$, where $2A-B$ and $A+B$ are acute or right angles and $A,B>0^{\circ }$, find $A$ and $B$.

   Worked solution

   $2A-B={90}^{\circ }$ and $A+B={60}^{\circ }$. M1

   Adding: $3A={150}^{\circ }\Rightarrow A={50}^{\circ },B={10}^{\circ }$. A1

3. Areas Related to Circles · 2 marks

   Find the length of the arc of a circle of radius 4.2 cm that subtends an angle of ${150}^{\circ }$ at the centre. $(\pi =\frac{22}{7})$

   Worked solution

   $l={\displaystyle \frac{150}{360}}\times 2\times {\displaystyle \frac{22}{7}}\times 4.2$ M1

   $=11$ cm A1

4. Statistics · 2 marks

   For a moderately skewed distribution, the mean is 27 and the median is 26. Find the mode.

   Worked solution

   Mode $=3\text{Median}-2\text{Mean}$ M1

   $=78-54=24$ A1

More on these topics: Coordinate Geometry · Introduction to Trigonometry · Areas Related to Circles · Statistics

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.

• Coordinate Geometry: Swapping $m_1$ and $m_2$ in the section formula — $m_1$ multiplies the coordinates of the second point. Also: Forgetting the square root, or squaring a negative difference incorrectly. More on one page
• Introduction to Trigonometry: Writing $\sin A$ as $\sin \times A$, or ${\sin }^{2}A$ as $\sin A^2$. Also: Assuming $\sin (A+B)=\sin A+\sin B$ — check with $A=B={30}^{\circ }$: $\sin {60}^{\circ }\ne 1$. More on one page
• Areas Related to Circles: Adding the triangle to the sector instead of subtracting it to get the minor segment. Also: Using the diameter in place of the radius. 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

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.

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