Nigeria · Grade 12 · Practice Sheet 49

1. 1.

   A cone has base radius 12 cm and height 9 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.

   An object with initial velocity 8 m/s accelerates at 4.3 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   A cone has base radius 8 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   Find the gravitational potential energy of a 30 kg object raised 24 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A current of 6.7 A flows through a 59 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A device runs at 131 V drawing 2.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   In a triangle, a = 12, b = 6 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   Find the force needed to accelerate a 2 kg mass at 0.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 384 N acts on an area of 5.6 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the momentum of a 8 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the force needed to accelerate a 51 kg mass at 4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A body starts at 13 m/s and accelerates at 5.8 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Two masses 8,000 kg and 600 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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14. 14.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    A triangle has sides a = 5 cm and b = 17 cm with an included angle C = 60°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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16. 16.

    In a triangle, a = 13, 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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17. 17.

    Find the force needed to accelerate a 26 kg mass at 5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 75 N moves an object 29 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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20. 20.

    A body starts at 17 m/s and accelerates at 5.2 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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