Germany · Klasse 9 · Practice Sheet 16

1. 1.

   A cone has base radius 11 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   Find the momentum of a 45 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A bag has 27 equally likely marbles, of which 6 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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4. 4.

   A force of 110 N moves an object 38 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A train moves at 39 km/h for 5.3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   Find the momentum of a 12 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A circle has a radius of 10 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   Solve for x: 6x + 4 = 52.

   Formula:Solving a Linear Equation

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

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9. 9.

   Find the force needed to accelerate a 41 kg mass at 1.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the circumference of a circle whose radius is 23 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    Find the momentum of a 31 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Find the force needed to accelerate a 34 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A force of 36 N moves an object 39 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    €112 is shared in the ratio 3 : 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 bag has 22 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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16. 16.

    €40 is shared in the ratio 1 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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17. 17.

    A value changes from 85 to 107. 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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18. 18.

    A cylinder has radius 9 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A cone has base radius 9 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    Solve for x: 9x + 18 = 117.

    Formula:Solving a Linear Equation

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

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