Algeria · Grade 12 · Practice Sheet 49

1. 1.

   Find the force needed to accelerate a 13 kg mass at 1.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A current of 4.4 A flows through a 35 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   Find the force needed to accelerate a 60 kg mass at 1.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   In a triangle, a = 7, b = 5 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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6. 6.

   A 27 kg object moves at 19 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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7. 7.

   Find the population standard deviation of: 2, 12, 18, 16, 11 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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9. 9.

   A body starts at 18 m/s and accelerates at 5.4 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    An object with initial velocity 12 m/s accelerates at 2.1 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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11. 11.

    A body starts at 18 m/s and accelerates at 2 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A wave has frequency 469 Hz and wavelength 2.14 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the population standard deviation of: 7, 5, 17, 3, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A population of 3,000 grows 10% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A cone has base radius 3 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A force of 92 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A force of 24 N acts on an area of 5 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A body starts at 10 m/s and accelerates at 3.7 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A device runs at 142 V drawing 2.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A 31 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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