CBSE Class 10 Maths Official Sample Paper 2019-20 (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. Statistics · 4 marks

   A cricket academy analyses the runs scored by its batters in a season. For the grouped data, the analyst finds a mean of 32 and a mode of 29. The median class is 30–40, with lower limit 30, the cumulative frequency of the preceding class 30, frequency 20, and total number of innings 64.

   (i) Using the empirical relationship, estimate the median. [1]
   (ii) Which measure of central tendency gives the most frequently occurring score? [1]
   (iii) Find the median using the median formula. [2]

   Worked solution

   (i) Median $={\displaystyle \frac{29+2(32)}{3}}=31$ A1

   (ii) Mode A1

   (iii) $\frac{n}{2}=32$: Median $=30+{\displaystyle \frac{32-30}{20}}\times 10$ M1 $=31$, agreeing with the estimate in (i) A1

2. Probability · 2 marks

   Two dice are thrown simultaneously. Find the probability of getting a doublet (the same number on both dice).

   Worked solution

   Total outcomes 36; doublets (1,1), …, (6,6): 6 M1

   $P=\frac{6}{36}=\frac{1}{6}$ A1

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

   Find $k$ for which the pair $kx-4y=3$, $6x-12y=9$ has infinitely many solutions.

   Worked solution

   ${\displaystyle \frac{k}{6}}={\displaystyle \frac{-4}{-12}}={\displaystyle \frac{3}{9}}$ M1
   $k=2$ A1

4. Arithmetic Progressions · 2 marks

   Find the sum of the first $15$ terms of the AP $6,11,16,\dots$.

   Worked solution

   $S_{15}={\displaystyle \frac{15}{2}}[2(6)+14(5)]$ M1
   $={\displaystyle \frac{15}{2}}\times 82=615$ A1

More on these topics: Statistics · Probability · Pair of Linear Equations in Two Variables · Arithmetic Progressions

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.

• 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
• 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
• 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
• 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

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.

More Class 10 papers

• Board paper 2023
• Board paper 2022
• Sample paper 2021-22
• Sample paper 2020-21
• All 13 Class 10 papers