Nigeria · Grade 12 · Practice Sheet 10

1. 1.

   Find the population standard deviation of: 19, 14, 13, 12, 14 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   A population of 5,300 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A device runs at 104 V drawing 7.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   ₦2,600 is invested at 5% 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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5. 5.

   A force of 32 N acts on an area of 6.9 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A device runs at 190 V drawing 5.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A cone has base radius 2 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A force of 15 N moves an object 16 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 force needed to accelerate a 59 kg mass at 4.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A 29 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    An object with initial velocity 12 m/s accelerates at 1.2 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A wave has frequency 720 Hz and wavelength 1.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    A population of 2,200 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 current of 5 A flows through a 30 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the gravitational potential energy of a 29 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A force of 120 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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18. 18.

    A cone has base radius 4 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    A current of 5.8 A flows through a 41 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    Find the gravitational potential energy of a 47 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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