United Kingdom · Year 9 · Practice Sheet 50

1. 1.

   An object has mass 69 g and volume 23 cm³. Find its density.

   Formula:Density

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

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2. 2.

   A cylinder has radius 10 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   Find the force needed to accelerate a 4 kg mass at 3.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A right-angled triangle has legs of 17 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   A train moves at 53 km/h for 3.2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   A force of 164 N acts on an area of 3.5 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A value changes from 102 to 241. 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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8. 8.

   Find the momentum of a 21 kg object moving at 23 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   A train moves at 100 km/h for 3.1 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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10. 10.

    Find the force needed to accelerate a 11 kg mass at 7.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A cone has base radius 11 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    £800 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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13. 13.

    An object has mass 255 g and volume 30 cm³. Find its density.

    Formula:Density

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

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14. 14.

    £216 is shared in the ratio 2 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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15. 15.

    A force of 275 N acts on an area of 7.3 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A train moves at 75 km/h for 2.1 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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17. 17.

    A wave has frequency 185 Hz and wavelength 3.99 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A circle has a radius of 17 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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19. 19.

    Find the circumference of a circle whose radius is 6 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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20. 20.

    A circle has a radius of 22 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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