CBSE Class 10 Maths Official Sample Paper 2025-26 (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. Polynomials · 2 marks

   Find a quadratic polynomial whose sum and product of zeroes are $-{\displaystyle \frac{3}{2}}$ and $-1$ respectively.

   Worked solution

   $x^2-(-{\displaystyle \frac{3}{2}})x+(-1)=x^2+{\displaystyle \frac{3}{2}}x-1$ M1
   $={\displaystyle \frac{1}{2}}(2x^2+3x-2)$; required polynomial $2x^2+3x-2$ (or any non-zero multiple) A1

2. Pair of Linear Equations in Two Variables · 2 marks

   Solve by the substitution method: $x+3y=11$, $2x-y=1$.

   Worked solution

   From the second equation $y=2x-1$; substitute: $x+6x-3=11$ M1
   $x=2,y=3$ A1

3. Triangles · 2 marks

   In $\mathrm{△}PQR$, $S$ and $T$ lie on $PQ$ and $PR$ with $ST\parallel QR$. If $PS=4$ cm, $SQ=6$ cm and $PR=15$ cm, find $PT$.

   Worked solution

   ${\displaystyle \frac{PS}{PQ}}={\displaystyle \frac{PT}{PR}}\Rightarrow {\displaystyle \frac{4}{10}}={\displaystyle \frac{PT}{15}}$ M1
   $PT=6$ cm A1

4. Introduction to Trigonometry · 2 marks

   If $12\sin A=5\cos A$, where $A$ is acute, find the value of $\sec A+\mathrm{cosec}A$.

   Worked solution

   $\tan A=\frac{5}{12}$: opposite $=5k$, adjacent $=12k$, hypotenuse $=\sqrt{25k^2+144k^2}=13k$. M1

   $\sec A+\mathrm{cosec}A={\displaystyle \frac{13}{12}}+{\displaystyle \frac{13}{5}}={\displaystyle \frac{65+156}{60}}={\displaystyle \frac{221}{60}}$. A1

More on these topics: Polynomials · Pair of Linear Equations in Two Variables · Triangles · Introduction to Trigonometry

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.

• 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
• Pair of Linear Equations in Two Variables: Comparing only $a$ and $b$ ratios and forgetting $c$ when deciding between parallel and coincident. Also: Sign errors when subtracting equations; check the answer in both original equations. More on one page
• 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
• 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

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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