Romania · Grade 12 · Practice Sheet 22

1. 1.

   A current of 4 A flows through a 44 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   A force of 71 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 4 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   Two masses 2,500 kg and 490 kg are 4 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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5. 5.

   In a triangle, a = 10, b = 14 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   Find the force needed to accelerate a 58 kg mass at 1.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A 9 kg object moves at 22 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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8. 8.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 4 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   A population of 5,000 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    In a triangle, a = 5, b = 14 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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11. 11.

    Find the population standard deviation of: 20, 19, 18, 5, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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12. 12.

    A force of 103 N moves an object 21 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    Two masses 1,700 kg and 800 kg are 4 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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14. 14.

    A cone has base radius 4 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    lei 2,200 is invested at 4% compound interest per annum for 5 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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16. 16.

    Find the gravitational potential energy of a 18 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A force of 25 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A cone has base radius 6 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    Find the force needed to accelerate a 14 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A cone has base radius 5 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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