China · Grade 12 · Practice Sheet 17

1. 1.

   A force of 15 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   Find the sum of the first 8 terms of a geometric series with first term a = 7 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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3. 3.

   Solve using the quadratic formula: x² + 8x + 15 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A force of 15 N moves an object 12 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A population of 7,000 grows 2% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Find the gravitational potential energy of a 3 kg object raised 16 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A device runs at 17 V drawing 7.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A force of 83 N moves an object 30 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the sum of the first 8 terms of an arithmetic series with first term a = 1 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    A current of 6.8 A flows through a 37 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    In a triangle, a = 6, b = 10 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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12. 12.

    Find the sum of the first 19 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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13. 13.

    Find the force needed to accelerate a 28 kg mass at 3.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 7 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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15. 15.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    Two masses 3,500 kg and 890 kg are 17 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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17. 17.

    Find the gravitational potential energy of a 48 kg object raised 29 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Find the population standard deviation of: 5, 14, 11, 6, 17 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A triangle has sides a = 16 cm and b = 11 cm with an included angle C = 90°. 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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20. 20.

    A cone has base radius 4 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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