Belgium · Year 11 · Practice Sheet 13

1. 1.

   A device runs at 49 V drawing 0.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   A right-angled triangle has legs of 8 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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3. 3.

   An object with initial velocity 9 m/s accelerates at 4.9 m/s² for 8 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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4. 4.

   A cone has base radius 5 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   €4,000 is invested at 6% 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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6. 6.

   Solve using the quadratic formula: x² − 5x + 4 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 2 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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8. 8.

   €3,300 is invested at 5% compound interest per annum for 4 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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9. 9.

   Find the population standard deviation of: 17, 12, 12, 15, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A wave has frequency 412 Hz and wavelength 4.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A device runs at 119 V drawing 8.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the population standard deviation of: 15, 16, 15, 20, 12 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    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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14. 14.

    A wave has frequency 162 Hz and wavelength 4.23 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

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

    Formula:Exponential Growth

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

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16. 16.

    Two masses 6,700 kg and 660 kg are 3 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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17. 17.

    Find the force needed to accelerate a 34 kg mass at 6.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 40 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the force needed to accelerate a 40 kg mass at 0.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A triangle has sides a = 15 cm and b = 9 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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