Israel · Grade 12 · Practice Sheet 33

1. 1.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   In a triangle, a = 10, b = 5 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   Find the momentum of a 41 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A force of 109 N acts on an area of 7.9 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A 31 kg object moves at 6 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   An object with initial velocity 12 m/s accelerates at 1.6 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   Find the force needed to accelerate a 6 kg mass at 3.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A body starts at 10 m/s and accelerates at 3.8 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   An object with initial velocity 5 m/s accelerates at 3.1 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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10. 10.

    Find the force needed to accelerate a 38 kg mass at 5.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    ₪1,700 is invested at 6% compound interest per annum for 3 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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12. 12.

    A force of 44 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    An object with initial velocity 2 m/s accelerates at 3.5 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    A force of 97 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    Two masses 4,000 kg and 700 kg are 19 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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16. 16.

    Find the population standard deviation of: 10, 14, 7, 7, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    A force of 21 N acts on an area of 1.7 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A device runs at 15 V drawing 7.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Two masses 7,900 kg and 660 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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20. 20.

    A current of 1.1 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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