India · Class 10 · Practice Sheet 14

1. 1.

   A triangle has sides a = 14 cm and b = 14 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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2. 2.

   A bag has 29 equally likely marbles, of which 2 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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3. 3.

   A value changes from 35 to 167. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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4. 4.

   A body starts at 17 m/s and accelerates at 2.6 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A wave has frequency 877 Hz and wavelength 0.92 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   Solve for x: 4x + 3 = 23.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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7. 7.

   A body starts at 9 m/s and accelerates at 2.7 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A 2 kg object moves at 19 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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9. 9.

   A wave has frequency 76 Hz and wavelength 0.55 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A current of 7.6 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    A triangle has sides a = 6 cm and b = 20 cm with an included angle C = 30°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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12. 12.

    Find the momentum of a 26 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A force of 75 N moves an object 10 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    ₹2,200 is invested at 3% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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15. 15.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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16. 16.

    Solve for x: 2x + 2 = 22.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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17. 17.

    Find the momentum of a 29 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A 26 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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19. 19.

    A cone has base radius 6 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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20. 20.

    An object with initial velocity 14 m/s accelerates at 4.6 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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