Belgium · Year 11 · Practice Sheet 43

1. 1.

   Find the sum of the first 3 terms of a geometric series with first term a = 5 and common ratio r = 3.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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2. 2.

   A force of 50 N moves an object 7 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   A device runs at 33 V drawing 3.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the gravitational potential energy of a 43 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   A force of 75 N moves an object 13 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   An object with initial velocity 14 m/s accelerates at 4.8 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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8. 8.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   Find the force needed to accelerate a 48 kg mass at 6.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A cone has base radius 9 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 7 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    A triangle has sides a = 19 cm and b = 15 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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13. 13.

    A right-angled triangle has legs of 12 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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14. 14.

    Find the gravitational potential energy of a 42 kg object raised 21 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    A device runs at 40 V drawing 5.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the momentum of a 32 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A triangle has sides a = 12 cm and b = 20 cm with an included angle C = 45°. 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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18. 18.

    A current of 7.3 A flows through a 32 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A right-angled triangle has legs of 18 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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20. 20.

    A current of 3.9 A flows through a 38 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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