Tunisia · Grade 10 · Practice Sheet 38

1. 1.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 5 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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2. 2.

   A current of 2.4 A flows through a 23 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A force of 269 N acts on an area of 6.9 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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4. 4.

   A current of 7.3 A flows through a 14 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A 13 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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6. 6.

   Find the force needed to accelerate a 42 kg mass at 4.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 12 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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8. 8.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A body starts at 8 m/s and accelerates at 4.7 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    Solve using the quadratic formula: x² − 5x − 6 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A triangle has sides a = 16 cm and b = 5 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.

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

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    Find the force needed to accelerate a 14 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A triangle has sides a = 17 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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15. 15.

    A body starts at 18 m/s and accelerates at 4 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    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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17. 17.

    Find the force needed to accelerate a 30 kg mass at 2.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    Find the momentum of a 58 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A wave has frequency 441 Hz and wavelength 0.95 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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