Nigeria · Grade 12 · Practice Sheet 41

1. 1.

   A 31 kg object moves at 16 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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3. 3.

   In a triangle, a = 6, b = 8 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   Find the force needed to accelerate a 23 kg mass at 0.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   An object with initial velocity 4 m/s accelerates at 2.3 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   A population of 4,300 grows 10% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   A current of 3.5 A flows through a 29 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A force of 32 N moves an object 34 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the momentum of a 34 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A triangle has sides a = 5 cm and b = 14 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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11. 11.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    A wave has frequency 788 Hz and wavelength 2.33 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the population standard deviation of: 16, 7, 17, 7, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A cone has base radius 12 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    A force of 479 N acts on an area of 8.2 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Find the force needed to accelerate a 41 kg mass at 4.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A force of 29 N moves an object 27 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A body starts at 3 m/s and accelerates at 2.5 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    In a triangle, a = 13, b = 10 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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20. 20.

    A current of 2.8 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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