CBSE Class 10 Maths Board Paper 2025 (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. Quadratic Equations · 2 marks

   Find the discriminant of $2x^2-6x+5=0$ and hence state the nature of its roots.

   Worked solution

   $D=36-40=-4$ A1
   $D<0$: no real roots. A1

2. Arithmetic Progressions · 2 marks

   The sum of the $5$th and $9$th terms of an AP is $58$. Find its $7$th term.

   Worked solution

   $a_5+a_9=(a+4d)+(a+8d)=2(a+6d)=58$ M1
   $a_7=a+6d=29$ A1

3. Introduction to Trigonometry · 2 marks

   Evaluate ${\displaystyle \frac{4{\cot }^2{60}^{\circ }+{\sec }^2{30}^{\circ }-2{\sin }^2{45}^{\circ }}{{\cos }^2{45}^{\circ }+{\tan }^2{60}^{\circ }}}$.

   Worked solution

   $={\displaystyle \frac{4\cdot \frac{1}{3}+\frac{4}{3}-2\cdot \frac{1}{2}}{\frac{1}{2}+3}}$ M1

   $={\displaystyle \frac{\frac{5}{3}}{\frac{7}{2}}}={\displaystyle \frac{10}{21}}$ A1

4. Circles · 2 marks

   $PA$ and $PB$ are tangents from an external point $P$ to a circle with centre $O$. If $\mathrm{\angle }PAB={55}^{\circ }$, find $\mathrm{\angle }APB$ and $\mathrm{\angle }AOB$.

   Worked solution

   $PA=PB$ (tangents from $P$), so $\mathrm{\angle }PBA={55}^{\circ }$ and $\mathrm{\angle }APB={180}^{\circ }-{110}^{\circ }={70}^{\circ }$ M1

   $\mathrm{\angle }AOB={180}^{\circ }-{70}^{\circ }={110}^{\circ }$ A1

More on these topics: Quadratic Equations · Arithmetic Progressions · Introduction to Trigonometry · Circles

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.

• 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
• Arithmetic Progressions: Using $a+nd$ instead of $a+(n-1)d$. Also: Finding the number of terms as ${\displaystyle \frac{l-a}{d}}$ and forgetting the “$+1$”. 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
• 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

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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