Nigeria · Grade 12 · Practice Sheet 50

1. 1.

   A cone has base radius 3 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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2. 2.

   A device runs at 14 V drawing 4.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   Find the momentum of a 55 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A force of 470 N acts on an area of 3.5 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A force of 70 N moves an object 30 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A device runs at 95 V drawing 5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A population of 5,100 grows 10% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   Find the momentum of a 3 kg object moving at 22 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   Find the force needed to accelerate a 39 kg mass at 1.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Two masses 2,900 kg and 680 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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11. 11.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    A population of 3,400 grows 10% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the gravitational potential energy of a 30 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the force needed to accelerate a 22 kg mass at 6.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A device runs at 231 V drawing 1.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    In a triangle, a = 8, b = 12 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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18. 18.

    A wave has frequency 448 Hz and wavelength 3.42 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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19. 19.

    Two masses 6,000 kg and 220 kg are 14 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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20. 20.

    ₦3,500 is invested at 4% 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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