Nepal · Class 10 · Practice Sheet 24

1. 1.

   A triangle has sides a = 12 cm and b = 8 cm with an included angle C = 90°. 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.

   In a triangle, a = 18, b = 8 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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3. 3.

   A force of 116 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A device runs at 159 V drawing 7.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the gravitational potential energy of a 6 kg object raised 33 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   A force of 70 N moves an object 33 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   A triangle has sides a = 18 cm and b = 9 cm with an included angle C = 120°. 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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8. 8.

   Solve for x: 8x + 6 = 38.

   Formula:Solving a Linear Equation

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

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9. 9.

   A cylinder has radius 8 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    Solve for x: 2x + 20 = 30.

    Formula:Solving a Linear Equation

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

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11. 11.

    Solve using the quadratic formula: x² − 4x + 3 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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12. 12.

    A triangle has sides a = 18 cm and b = 8 cm with an included angle C = 90°. 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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13. 13.

    An object with initial velocity 15 m/s accelerates at 3.6 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    A wave has frequency 546 Hz and wavelength 1.12 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A cylinder has radius 10 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    A 4 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    A population of 3,700 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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18. 18.

    Find the gravitational potential energy of a 16 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A force of 28 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    In a triangle, a = 5, b = 9 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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