United Kingdom · Year 12 · Practice Sheet 18

1. 1.

   Solve using the quadratic formula: x² + 2x − 3 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 3 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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3. 3.

   A cone has base radius 9 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   Find the gravitational potential energy of a 27 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A wave has frequency 890 Hz and wavelength 4.68 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A device runs at 64 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the population standard deviation of: 19, 18, 9, 20, 9 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   A body starts at 1 m/s and accelerates at 1.6 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A population of 7,800 grows 5% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    £1,600 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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12. 12.

    Find the momentum of a 32 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the gravitational potential energy of a 31 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the population standard deviation of: 7, 2, 5, 8, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A current of 3.5 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    Find the momentum of a 1 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A force of 19 N moves an object 35 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    A force of 254 N acts on an area of 2.3 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    An object with initial velocity 13 m/s accelerates at 4.5 m/s² for 3 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 4,200 kg and 280 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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