CBSE Class 10 Maths Board Paper 2024 (Basic and Standard)

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. Triangles · 2 marks

   $D$ and $E$ are points on sides $AB$ and $AC$ of $\mathrm{△}ABC$ with $AD=6$ cm, $DB=9$ cm, $AE=8$ cm and $EC=12$ cm. Is $DE\parallel BC$? Justify.

   Worked solution

   ${\displaystyle \frac{AD}{DB}}={\displaystyle \frac{6}{9}}={\displaystyle \frac{2}{3}}$, ${\displaystyle \frac{AE}{EC}}={\displaystyle \frac{8}{12}}={\displaystyle \frac{2}{3}}$ M1
   Ratios are equal, so $DE\parallel BC$ by the converse of BPT. A1

2. Coordinate Geometry · 2 marks

   Find the values of $x$ for which the distance between $(x,-1)$ and $(3,2)$ is $5$ units.

   Worked solution

   $(x-3{)}^2+9=25\Rightarrow (x-3{)}^2=16$ M1
   $x=7$ or $x=-1$ A1

3. Circles · 2 marks

   The tangent from an external point $P$ to a circle of radius $r$ has length equal to $r$. Find $OP$ in terms of $r$, and the angle between the two tangents drawn from $P$.

   Worked solution

   $\mathrm{\angle }OAP={90}^{\circ }$: $OP=\sqrt{r^2+r^2}=r\sqrt{2}$ M1

   $\mathrm{△}OAP$ is isosceles right-angled, so $\mathrm{\angle }APO={45}^{\circ }$; the angle between the tangents is $2\times {45}^{\circ }={90}^{\circ }$ A1

4. Surface Areas and Volumes · 2 marks

   A solid is a cylinder of radius 3.5 cm and height 6 cm with a hemisphere of the same radius fixed on top. Find its volume. $(\pi =\frac{22}{7})$

   Worked solution

   $\pi r^{2}h+\frac{2}{3}\pi r^3={\displaystyle \frac{22}{7}}\times 12.25\times 6+{\displaystyle \frac{2}{3}}\times {\displaystyle \frac{22}{7}}\times 42.875=231+89.83$ M1

   $\approx 320.83{\text{cm}}^3$ A1

More on these topics: Triangles · Coordinate Geometry · Circles · Surface Areas and Volumes

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.

• Triangles: Writing ${\displaystyle \frac{AD}{DB}}={\displaystyle \frac{DE}{BC}}$ — wrong; use ${\displaystyle \frac{AD}{AB}}={\displaystyle \frac{DE}{BC}}$. Also: Matching vertices in the wrong order, leading to wrong side ratios. More on one page
• 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
• Circles: Using $O{P}^2=P{A}^2-r^2$: $OP$ is the hypotenuse, not a leg. Also: Claiming $\mathrm{\angle }APB=\mathrm{\angle }AOB$. They are supplementary, not equal. More on one page
• 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

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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