China · Grade 12 · Practice Sheet 23

1. 1.

   A cone has base radius 8 cm and height 18 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.

   ¥1,100 is invested at 5% 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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3. 3.

   Find the momentum of a 5 kg object moving at 22 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the gravitational potential energy of a 43 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A device runs at 127 V drawing 9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A current of 4.5 A flows through a 43 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Solve using the quadratic formula: x² − 7x + 10 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   A force of 12 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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9. 9.

   In a triangle, a = 14, b = 17 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    A body starts at 14 m/s and accelerates at 3 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    Find the momentum of a 34 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Two masses 5,100 kg and 110 kg are 10 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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13. 13.

    A population of 3,800 grows 3% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    ¥3,200 is invested at 4% compound interest per annum for 4 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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16. 16.

    A force of 129 N acts on an area of 4.4 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Two masses 7,300 kg and 170 kg are 2 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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18. 18.

    Find the gravitational potential energy of a 35 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A device runs at 163 V drawing 3.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the force needed to accelerate a 55 kg mass at 4.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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