Nigeria · Grade 12 · Practice Sheet 25

1. 1.

   A force of 22 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   Two masses 6,700 kg and 300 kg are 4 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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3. 3.

   Find the population standard deviation of: 11, 12, 15, 16, 11 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   In a triangle, a = 13, b = 15 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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5. 5.

   ₦1,600 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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6. 6.

   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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7. 7.

   A wave has frequency 345 Hz and wavelength 3.55 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A cone has base radius 6 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   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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10. 10.

    A current of 5.5 A flows through a 5 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the population standard deviation of: 3, 6, 4, 9, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    Find the force needed to accelerate a 4 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the population standard deviation of: 12, 18, 8, 16, 9 (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 5,000 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A 9 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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16. 16.

    A device runs at 44 V drawing 7.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A cone has base radius 6 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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18. 18.

    A force of 30 N moves an object 40 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    In a triangle, a = 8, b = 11 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 body starts at 18 m/s and accelerates at 2.5 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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