United Kingdom · Year 11 · Practice Sheet 13

1. 1.

   A force of 493 N acts on an area of 4.7 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   A wave has frequency 554 Hz and wavelength 2.36 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A right-angled triangle has legs of 16 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   Find the gravitational potential energy of a 37 kg object raised 29 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   An object has mass 298.9 g and volume 49 cm³. Find its density.

   Formula:Density

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

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6. 6.

   Find the force needed to accelerate a 16 kg mass at 1.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   £2,100 is invested at 8% 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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9. 9.

   Find the sum of the first 7 terms of a geometric series with first term a = 8 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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10. 10.

    An object has mass 309.6 g and volume 36 cm³. Find its density.

    Formula:Density

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

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11. 11.

    An object with initial velocity 11 m/s accelerates at 1.4 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Find the population standard deviation of: 11, 18, 3, 19, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A current of 2.8 A flows through a 44 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A device runs at 166 V drawing 9.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    An object has mass 327.6 g and volume 39 cm³. Find its density.

    Formula:Density

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

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16. 16.

    Find the force needed to accelerate a 49 kg mass at 2.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    £1,600 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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18. 18.

    Find the force needed to accelerate a 51 kg mass at 3.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A population of 9,000 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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20. 20.

    A cylinder has radius 13 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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