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Units and Algebra: Maths Diagnostic

Jackie Grant 7 questions

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Questions in this quiz (7)

  1. 1\(\rm {The \ length \ of \ one \ side \ of \ a \ cube \ is \ 5.00 \ cm. \\ What \ is \ the \ volume \ in \ m^3 \ ?} \)
    1. A\( 1.25 \times 10^2 \ \rm m ^3\)
    2. B\( 1.25 \times 10^{-2} \ \rm m ^3\)
    3. C\( 1.25 \times 10^{-4} \ \rm m ^3\)
    4. D\( 1.25 \times 10^{-6} \ \rm m ^3\)
    5. E\( 1.25 \times 10^{-8} \ \rm m ^3\)
  2. 2\(\rm {The \ density \ of \ aluminium \ is \ 2.70 \ g cm^{−3}, \\ convert \ this \ density \ to \ kg m^{−3}}. \)
    1. A\( 2.70 \times 10^{-9} \ \rm kgm ^{-3}\)
    2. B\( 2.70 \times 10^{-6} \ \rm kgm ^{-3}\)
    3. C\( 2.70 \times 10^{-1} \ \rm kgm ^{-3}\)
    4. D\( 2.70 \times 10^{3} \ \rm kgm ^{-3}\)
    5. E\( 2.70 \times 10^{6} \ \rm kgm ^{-3}\)
  3. 3\( \rm{Calculate \ {\it a} \ in \ ms^{-2}, \ where \ {\it V} = 72 \ km/h \ and \ {\it R} = 2000 \ m, \\ from \ the \ equation \ {\it a} =\frac{ V^2}{R} } \)
    1. A\(2.0 \times 10^{1} { \rm \ ms^{-2}} \)
    2. B\(7.2 \times 10^{2} { \rm \ ms^{-2}} \)
    3. C\(2.6 \times 10^{0} { \rm \ ms^{-2}} \)
    4. D\(2.0 \times 10^{-1} { \rm \ ms^{-2}} \)
    5. E\(7.2 \times 10^{3} { \rm \ ms^{-2}} \)
  4. 4\( {\rm Given} \ \pi r^2v = 5.2 \times 10^{-6} \ \rm {m^3 s^{-1}}, \\ find \ the \ value \ of \ { \it v} \ if \ {\it r} = 3.6 \ mm. \)
    1. A\(1.3 \times 10^{-1} \rm \ m s^{-1} \)
    2. B\(1.3 \times 10^{-7} \rm \ m s^{-1} \)
    3. C\(2.3 \times 10^{-4} \rm \ m s^{-1} \)
    4. D\(4.6 \times 10^{-4} \rm \ m s^{-1} \)
    5. E\(4.6 \times 10^{-7} \rm \ m s^{-1} \)
  5. 5\( \rm The \ mass \ of \ a \ proton \ can \ be \ expressed \ as \ 1.0 {\it \ u}, \ where \ {\it u} \ is \ the \ Atomic \ Mass \ Unit \ and \ 1 \ {\it u} = 1.67\times 10^{−27} kg.
    \\ If \ a \ proton \ has \ a \ mass \ 2,000 \ times \ the \ mass \ of \ an \ electron, \ determine \ the \ energy, \ {\it E}, \ of \ an \ electron \ from \ its \ mass, \ {\it m},
    \\ and \ the \ speed \ of \ light \ {\it c} = 3.0 \times 10^8 m s^{−1}, \ using \ the \ relationship \ between \ energy \ and \ mass \ given \ by \ \it E = mc^2. \)
    1. A\( 7.5 \times 10^{−14} \ \rm kg m^ 2 s^{−2} \)
    2. B\( 1.5 \times 10^{−10} \ \rm kg m^ 2 s^{−2} \)
    3. C\( 2.5 \times 10^{−22} \ \rm kg m^ 2 s^{−2} \)
    4. D\( 2.2 \times 10^{−14} \ \rm kg m^ 2 s^{−2} \)
    5. E\( 5.0 \times 10^{−19} \ \rm kg m^ 2 s^{−2} \)
  6. 6\( P_2 = \rho g h + P_1 \ {\rm and} \ Q = \frac{\pi R^4(P_2−P_1)}{8\eta L}. \\ \rm Eliminate \ {\it P_1} \ and \ {\it P_2} \ and \ write \ an \ equation \ for \ {\it h} \ in \ terms \ of \ \it Q, \ R, \ ρ, \ g, \ \eta \ {\rm and} \ L. \)
    1. A\( h = \frac{8 \eta L Q}{\pi R^4 \rho g} \)
    2. B\( h = \frac{8 \eta L Q}{\pi R^4 } - \rho g \)
    3. C\( h = \frac{8 \eta L Q - \pi R^4}{\pi R^4 \rho g} \)
    4. D\( h = \frac{8 \eta L Q - \pi R^4}{\rho g} \)
    5. E\( h = \frac{ \pi R^4 - 8 \eta L Q -}{ \rho g} \)
  7. 7\( \rm Determine \ the \ uncertainty \ in \ density, \sigma_{\rho}, \ in \ kg m^{−3}, \ of \ a \ cube \ of \ Manganese, \ if \ for \ a \ given \ set \ of \ measurements \\ length \ {\it l} = 3 \ cm, \ mass \ {\it m} = 2 \times 10^{-1} \ kg, \ uncertainty \ in \ length, \ \sigma_{\it l} = 5 \times 10^{-3} m, \ and \ uncertainty \ in \ mass, \ \sigma_{\it m} = 2 \ g, \\ using \ the \ equation \)

    \[ \sigma_\rho = \frac{\it m}{\it l^3}\sqrt{ \left(\frac{\sigma_{\it m}}{\it m}\right)^2 + 3 \left(\frac{\sigma_{\it l}}{\it l} \right)^2} \]
    1. A\( 2 \times 10^3 \rm \ kgm^{−3} \)
    2. B\( 5 \times 10^{-1} \rm \ kgm^{−3} \)
    3. C\( 2 \times 10^0 \rm \ kgm^{−3} \)
    4. D\( 5 \times 10^3 \rm \ kgm^{−3} \)
    5. E\(2 \times 10^{-1} \rm \ kgm^{−3} \)

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If you can not do all of these problems, practice the resources at www.mathscentre.ac.uk
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