Nigeria · Grade 12 · Practice Sheet 30

1. 1.

   An object with initial velocity 12 m/s accelerates at 4.9 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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2. 2.

   Two masses 8,700 kg and 720 kg are 9 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.

   A device runs at 118 V drawing 2.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   In a triangle, a = 14, b = 14 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   An object with initial velocity 14 m/s accelerates at 3.7 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   Find the force needed to accelerate a 17 kg mass at 3.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 4 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   Find the sum of the first 4 terms of a geometric series with first term a = 3 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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10. 10.

    A current of 3.9 A flows through a 24 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    A body starts at 14 m/s and accelerates at 2.4 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the force needed to accelerate a 7 kg mass at 5.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    Find the gravitational potential energy of a 11 kg object raised 12 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Find the force needed to accelerate a 2 kg mass at 3.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the population standard deviation of: 9, 16, 12, 14, 8 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    A current of 3.7 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    ₦2,100 is invested at 8% compound interest per annum for 5 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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19. 19.

    A force of 116 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    An object with initial velocity 10 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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