Algeria · Grade 12 · Practice Sheet 8

1. 1.

   A 18 kg object moves at 18 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   A triangle has sides a = 6 cm and b = 19 cm with an included angle C = 30°. 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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3. 3.

   Find the population standard deviation of: 4, 3, 8, 9, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A device runs at 211 V drawing 4.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the momentum of a 33 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A population of 7,900 grows 8% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   Find the population standard deviation of: 16, 17, 19, 3, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   A device runs at 14 V drawing 3.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Find the gravitational potential energy of a 13 kg object raised 34 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Find the force needed to accelerate a 29 kg mass at 8.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Find the population standard deviation of: 12, 17, 20, 13, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    A cone has base radius 4 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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13. 13.

    In a triangle, a = 6, b = 12 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    A body starts at 8 m/s and accelerates at 1 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A force of 285 N acts on an area of 5.2 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A body starts at 14 m/s and accelerates at 1.1 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Find the momentum of a 2 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Find the force needed to accelerate a 54 kg mass at 1.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A body starts at 8 m/s and accelerates at 5.5 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A force of 206 N acts on an area of 0.7 m². Find the pressure.

    Formula:Pressure

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

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