Switzerland · Grade 11 · Practice Sheet 15

1. 1.

   A triangle has sides a = 7 cm and b = 10 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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2. 2.

   Find the gravitational potential energy of a 42 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Find the momentum of a 42 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   A body starts at 16 m/s and accelerates at 4.8 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   Two masses 1,800 kg and 220 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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6. 6.

   In a triangle, a = 12, b = 12 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   A wave has frequency 329 Hz and wavelength 1.95 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A population of 3,400 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A force of 499 N acts on an area of 9.6 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A triangle has sides a = 20 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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11. 11.

    A device runs at 221 V drawing 0.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Two masses 5,900 kg and 190 kg are 13 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 13 terms of an arithmetic series with first term a = 6 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    Find the sum of the first 8 terms of a geometric series with first term a = 6 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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15. 15.

    An object has mass 30 g and volume 30 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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16. 16.

    A force of 497 N acts on an area of 9.8 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the population standard deviation of: 12, 13, 6, 15, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    Two masses 1,000 kg and 800 kg are 14 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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19. 19.

    An object with initial velocity 7 m/s accelerates at 4.4 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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20. 20.

    Two masses 3,500 kg and 210 kg are 17 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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