United States · Grade 9 · Practice Sheet 40

1. 1.

   $114 is shared in the ratio 1 : 5. Find each share.

   Formula:Dividing in a Ratio

   $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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2. 2.

   Find the gravitational potential energy of a 21 kg object raised 26 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   $189 is shared in the ratio 5 : 2. Find each share.

   Formula:Dividing in a Ratio

   $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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4. 4.

   A train moves at 34 km/h for 1.8 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   Find the force needed to accelerate a 60 kg mass at 6.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A wave has frequency 861 Hz and wavelength 5 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the force needed to accelerate a 35 kg mass at 1.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A device runs at 152 V drawing 9.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A current of 4.2 A flows through a 31 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A force of 32 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    Find the force needed to accelerate a 6 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A device runs at 36 V drawing 9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    An object has mass 89.1 g and volume 11 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A force of 66 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    $3,000 is invested at 4% compound interest per annum for 3 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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16. 16.

    A value changes from 50 to 52. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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17. 17.

    A device runs at 52 V drawing 7.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the gravitational potential energy of a 35 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A bag has 11 equally likely marbles, of which 5 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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20. 20.

    A car travels 138 km in 3 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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