Belgium · Year 12 · Practice Sheet 36

1. 1.

   Two masses 1,000 kg and 740 kg are 5 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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2. 2.

   A device runs at 202 V drawing 7.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A triangle has sides a = 14 cm and b = 5 cm with an included angle C = 120°. 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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4. 4.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 11 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A device runs at 240 V drawing 1.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the population standard deviation of: 3, 5, 14, 3, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the momentum of a 8 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   In a triangle, a = 8, b = 17 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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9. 9.

   A body starts at 15 m/s and accelerates at 4.2 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    Find the force needed to accelerate a 58 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A body starts at 8 m/s and accelerates at 5.2 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    Find the population standard deviation of: 8, 16, 11, 3, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A cone has base radius 7 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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14. 14.

    €3,200 is invested at 4% 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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15. 15.

    A current of 4.7 A flows through a 10 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A device runs at 90 V drawing 8.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Two masses 4,000 kg and 440 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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18. 18.

    Solve using the quadratic formula: x² − 2x − 24 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    A body starts at 9 m/s and accelerates at 3.4 m/s² for 12 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A triangle has sides a = 13 cm and b = 9 cm with an included angle C = 45°. 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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