Nigeria · Grade 12 · Practice Sheet 47

1. 1.

   A wave has frequency 849 Hz and wavelength 3.2 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the population standard deviation of: 8, 3, 17, 20, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   Find the momentum of a 5 kg object moving at 28 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Two masses 3,600 kg and 270 kg are 19 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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5. 5.

   A cone has base radius 12 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   In a triangle, a = 17, b = 13 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   A wave has frequency 133 Hz and wavelength 3.38 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   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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9. 9.

   An object with initial velocity 11 m/s accelerates at 1.4 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    A 36 kg object moves at 6 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    Solve using the quadratic formula: x² + 3x + 0 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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12. 12.

    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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13. 13.

    A wave has frequency 636 Hz and wavelength 0.99 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    ₦1,100 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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15. 15.

    In a triangle, a = 18, b = 16 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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16. 16.

    Find the gravitational potential energy of a 12 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    Find the momentum of a 8 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Find the force needed to accelerate a 41 kg mass at 5.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A 19 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A force of 53 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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