CBSE Guess Paper
Mathematics
Class - X
1. Draw the graph of the system of equations x + y = 5 & 2x – y = 2. Shade the region bounded by these lines & the x – axis. Find the area of the shaded region.
2. On dividing P(x) = 3x3 − 2x2 + 5x − 5 by a polynomial g(x), we get quotient and remainder as x2 − x + 2 and ‐7 respectively. Find g(x).
3. Prove that: {(sinA + cosA)/(sinA-cosA)} + {(sinA - cosA)/(sinA + cosA)} = 2/(2sin2A – 1)
4. Prove that in a triangle the line drawn parallel to one side, divides the other two sides proportionally.
5. Prove that the area of the equilateral Δ described on the side of a square is half the area of equilateral Δ described on its diagonals.
6. Daily pocket expenses of (in Rs) of 80 students of a school are given in the table below:
| Expenses | 0-5 | 5-10 | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 |
| No. of students. | 5 | 15 | 20 | 10 | 10 | 15 | 5 |
Change the data into a’ more than type table’ and hence draw ‘more than type’ give.
7. Prove that: {(1 + sinθ – cosθ)/(sinθ – 1 + cosθ)} = {cosθ / (1 - sinθ)}.
8. If sin 3θ = cos (θ - 60) where 3θ and (θ – 60) are acute angles, find θ.
9. On dividing x3- 3x2 + x +2 by a polynomial g(x), the quotient and remainder were x-2 and -2x + 4 respectively. Find g (x).
10. A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age graphically, if policies are given only to persons having age 18 years onwards but less than 60 year.
11. The monthly incomes of A and B are in the ratio of 9:7 and their monthly expenditures are in the ratio of 4:3. If each saves Rs 1600per month, find the monthly incomes of each.
12. Solve the following pair of equations graphically: 2x+3y=8, x +4y=9. Also find the points where the lines meet the x-axis.
13. A takes 16 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 6 days, find the time taken by B to finish the work.