Algeria · Grade 12 · Practice Sheet 41

1. 1.

   Find the momentum of a 39 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Find the force needed to accelerate a 25 kg mass at 6.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A force of 427 N acts on an area of 4.4 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   Find the population standard deviation of: 8, 17, 13, 5, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   A device runs at 122 V drawing 8.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the sum of the first 6 terms of a geometric series with first term a = 6 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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7. 7.

   A device runs at 141 V drawing 1.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

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

   Formula:Sum of a Geometric Series

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

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9. 9.

   DA 3,600 is invested at 4% compound interest per annum for 2 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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10. 10.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    A body starts at 20 m/s and accelerates at 1.5 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A population of 4,100 grows 2% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A force of 366 N acts on an area of 4.8 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    An object with initial velocity 13 m/s accelerates at 1.8 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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15. 15.

    Two masses 7,700 kg and 260 kg are 18 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 momentum of a 30 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    In a triangle, a = 8, b = 16 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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18. 18.

    A force of 71 N moves an object 15 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    A current of 0.8 A flows through a 35 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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