Netherlands · Year 11 · Practice Sheet 13

1. 1.

   In a triangle, a = 13, b = 7 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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2. 2.

   A 31 kg object moves at 14 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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3. 3.

   Find the population standard deviation of: 14, 17, 3, 11, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   An object has mass 105.6 g and volume 22 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A cone has base radius 9 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   Find the force needed to accelerate a 48 kg mass at 6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A force of 104 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A current of 6.3 A flows through a 20 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 9 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    A cone has base radius 3 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    Find the sum of the first 4 terms of a geometric series with first term a = 1 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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12. 12.

    A population of 7,400 grows 5% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    An object with initial velocity 9 m/s accelerates at 2.4 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    Find the force needed to accelerate a 52 kg mass at 6.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

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

    Formula:Quadratic Formula

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

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16. 16.

    A cone has base radius 8 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    Two masses 5,400 kg and 640 kg are 8 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.

    A force of 43 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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19. 19.

    A device runs at 56 V drawing 8.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A wave has frequency 394 Hz and wavelength 4.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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