Denmark · Grade 12 · Practice Sheet 48

1. 1.

   A current of 2.1 A flows through a 13 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   A wave has frequency 663 Hz and wavelength 3.62 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A 9 kg object moves at 2 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   Find the gravitational potential energy of a 44 kg object raised 21 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the momentum of a 24 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the sum of the first 4 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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7. 7.

   A device runs at 133 V drawing 4.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   In a triangle, a = 10, b = 10 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   A cone has base radius 5 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A triangle has sides a = 5 cm and b = 5 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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11. 11.

    A current of 3.9 A flows through a 10 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Find the force needed to accelerate a 56 kg mass at 8.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 5 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    A force of 48 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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17. 17.

    Find the momentum of a 26 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Find the force needed to accelerate a 4 kg mass at 5.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Two masses 1,500 kg and 790 kg are 7 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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20. 20.

    kr 3,600 is invested at 4% compound interest per annum for 3 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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