Romania · Grade 12 · Practice Sheet 28

1. 1.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 9 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   Solve using the quadratic formula: x² + 0x − 9 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Find the gravitational potential energy of a 25 kg object raised 33 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Two masses 7,200 kg and 640 kg are 2 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.

   A cone has base radius 2 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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6. 6.

   Find the gravitational potential energy of a 3 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A force of 11 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A 39 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    A force of 58 N acts on an area of 2.2 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    Find the force needed to accelerate a 54 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    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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13. 13.

    Two masses 3,600 kg and 160 kg are 2 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.

    Find the sum of the first 8 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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15. 15.

    Find the population standard deviation of: 11, 5, 12, 19, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    lei 3,400 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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17. 17.

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

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A current of 3.4 A flows through a 52 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A force of 20 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the gravitational potential energy of a 10 kg object raised 17 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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