China · Grade 9 · Practice Sheet 10

1. 1.

   An object has mass 16.8 g and volume 7 cm³. Find its density.

   Formula:Density

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

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2. 2.

   A car travels 252 km in 3 hours. Find its average speed.

   Formula:Speed

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

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3. 3.

   An object has mass 25.6 g and volume 8 cm³. Find its density.

   Formula:Density

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

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4. 4.

   Solve for x: 9x + 16 = 115.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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5. 5.

   Find the force needed to accelerate a 14 kg mass at 2.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   ¥140 is shared in the ratio 3 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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7. 7.

   Find the force needed to accelerate a 10 kg mass at 1.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Solve for x: 9x + 18 = 45.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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9. 9.

   A wave has frequency 89 Hz and wavelength 1.91 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A cylinder has radius 13 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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11. 11.

    Find the force needed to accelerate a 57 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A train moves at 25 km/h for 2.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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13. 13.

    A cone has base radius 6 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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14. 14.

    A value changes from 113 to 32. 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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15. 15.

    A wave has frequency 743 Hz and wavelength 4.33 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A cone has base radius 5 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    A right-angled triangle has legs of 12 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Solve for x: 7x + 14 = 63.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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19. 19.

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

    Formula:Pythagorean Theorem

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

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20. 20.

    A value changes from 155 to 69. 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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