Vietnam · Grade 12 · Practice Sheet 6

1. 1.

   A triangle has sides a = 10 cm and b = 20 cm with an included angle C = 30°. 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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2. 2.

   A cone has base radius 5 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   A population of 2,100 grows 8% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   VND 1,800 is invested at 5% 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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5. 5.

   A current of 2.9 A flows through a 23 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A force of 82 N acts on an area of 3.1 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the sum of the first 3 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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8. 8.

   A triangle has sides a = 15 cm and b = 20 cm with an included angle C = 30°. 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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9. 9.

   Solve using the quadratic formula: x² − 5x + 6 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A device runs at 78 V drawing 9.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A force of 106 N moves an object 40 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    Two masses 7,800 kg and 570 kg are 4 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.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 8 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    A force of 16 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A population of 2,000 grows 10% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    A force of 71 N moves an object 16 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the momentum of a 47 kg object moving at 27 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A current of 6.5 A flows through a 20 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A device runs at 178 V drawing 1.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the momentum of a 40 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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