Nigeria · Grade 12 · Practice Sheet 4

1. 1.

   An object with initial velocity 7 m/s accelerates at 3.3 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   A wave has frequency 358 Hz and wavelength 0.56 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   Solve using the quadratic formula: x² + 9x + 18 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A device runs at 116 V drawing 3.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Two masses 5,000 kg and 660 kg are 16 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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6. 6.

   A device runs at 110 V drawing 0.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Two masses 6,700 kg and 170 kg are 7 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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8. 8.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 2 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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9. 9.

   A force of 73 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A current of 2.9 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the force needed to accelerate a 4 kg mass at 0.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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13. 13.

    Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

    A force of 70 N acts on an area of 1.9 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Find the population standard deviation of: 7, 18, 17, 17, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    Find the sum of the first 5 terms of a geometric series with first term a = 6 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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17. 17.

    Find the momentum of a 59 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    In a triangle, a = 13, b = 9 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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19. 19.

    An object with initial velocity 10 m/s accelerates at 1.9 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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20. 20.

    Find the population standard deviation of: 6, 15, 2, 17, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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