CBSE Class 10 Maths Official Sample Paper 2022-23 (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. Introduction to Trigonometry · 2 marks

   Prove that ${\displaystyle \frac{\tan \theta }{\sec \theta -1}}\cdot {\displaystyle \frac{\tan \theta }{\sec \theta +1}}=1$, for $0^{\circ }<\theta <{90}^{\circ }$.

   Worked solution

   LHS $={\displaystyle \frac{{\tan }^2\theta }{{\sec }^2\theta -1}}$ M1

   $={\displaystyle \frac{{\tan }^2\theta }{{\tan }^2\theta }}=1=$ RHS (using ${\sec }^2\theta -1={\tan }^2\theta$) A1

2. Some Applications of Trigonometry · 2 marks

   From the top of a 60 m high lighthouse, the angle of depression of a fishing boat is ${30}^{\circ }$. How far is the boat from the foot of the lighthouse?

   Worked solution

   $\tan {30}^{\circ }={\displaystyle \frac{60}{d}}$ M1

   $d=60\sqrt{3}$ m A1

3. Surface Areas and Volumes · 2 marks

   A solid consists of a cylinder of radius 5 cm and height 10 cm with a cone of the same radius and height 12 cm on one end. Find the total surface area of the solid. $(\pi =3.14)$

   Worked solution

   $l=\sqrt{144+25}=13$ cm; exposed surfaces: base $\pi r^2$, curved cylinder $2\pi rh$, curved cone $\pi rl$ M1

   $=25\pi +100\pi +65\pi =190\pi =596.6{\text{cm}}^2$ A1

4. Probability · 2 marks

   A bag contains 40 balls, red and blue in the ratio $3:5$. Find the number of red balls, and the probability that a ball drawn at random is blue.

   Worked solution

   Red $=\frac{3}{8}\times 40=15$, blue $=25$ A1

   $P(\text{blue})=\frac{25}{40}=\frac{5}{8}$ A1

More on these topics: Introduction to Trigonometry · Some Applications of Trigonometry · Surface Areas and Volumes · Probability

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.

• 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
• Some Applications of Trigonometry: Measuring the angle of depression from the vertical instead of the horizontal. Also: Forgetting the observer's eye height when a person's height is given. 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
• Probability: Treating "HT" and "TH" as one outcome, or listing (2,3) but not (3,2) for two dice. Also: Forgetting that 1 is neither prime nor composite. 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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