Czechia · Grade 12 · Practice Sheet 17

1. 1.

   A 26 kg object moves at 4 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   Find the force needed to accelerate a 13 kg mass at 3.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A triangle has sides a = 16 cm and b = 8 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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4. 4.

   A device runs at 47 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the population standard deviation of: 20, 8, 19, 2, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 5 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   A device runs at 133 V drawing 6.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Two masses 5,400 kg and 880 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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9. 9.

   A force of 16 N moves an object 9 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Find the population standard deviation of: 4, 3, 12, 10, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Find the momentum of a 47 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A force of 143 N acts on an area of 1.1 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A force of 66 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A body starts at 10 m/s and accelerates at 2.3 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Find the sum of the first 7 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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16. 16.

    Two masses 2,300 kg and 360 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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17. 17.

    A cone has base radius 8 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    In a triangle, a = 17, b = 13 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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19. 19.

    Find the momentum of a 52 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A triangle has sides a = 6 cm and b = 14 cm with an included angle C = 120°. 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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