Tunisia · Grade 12 · Practice Sheet 50

1. 1.

   A cone has base radius 5 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   Find the population standard deviation of: 13, 8, 17, 13, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   An object with initial velocity 6 m/s accelerates at 2.5 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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4. 4.

   Find the force needed to accelerate a 11 kg mass at 5.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A body starts at 10 m/s and accelerates at 1.1 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   A device runs at 72 V drawing 2.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the sum of the first 3 terms of a geometric series with first term a = 4 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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8. 8.

   In a triangle, a = 6, b = 13 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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9. 9.

   A force of 315 N acts on an area of 8.5 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A body starts at 7 m/s and accelerates at 4.8 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    Find the gravitational potential energy of a 27 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Find the force needed to accelerate a 11 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A 11 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    Find the momentum of a 35 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    Find the sum of the first 7 terms of a geometric series with first term a = 8 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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16. 16.

    A body starts at 13 m/s and accelerates at 3.8 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    An object with initial velocity 2 m/s accelerates at 3.6 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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18. 18.

    A device runs at 105 V drawing 1.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A triangle has sides a = 14 cm and b = 18 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 current of 4 A flows through a 54 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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