Belgium · Year 9 · Practice Sheet 39

1. 1.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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2. 2.

   A force of 86 N moves an object 21 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the gravitational potential energy of a 19 kg object raised 11 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A wave has frequency 431 Hz and wavelength 0.27 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A circle has a radius of 24 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   Find the circumference of a circle whose radius is 25 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

   A car travels 105 km in 3 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   Solve for x: 7x + 13 = 97.

   Formula:Solving a Linear Equation

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

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9. 9.

   Find the force needed to accelerate a 22 kg mass at 3.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    An object has mass 315.4 g and volume 38 cm³. Find its density.

    Formula:Density

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

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11. 11.

    A device runs at 114 V drawing 5.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A car travels 371 km in 7 hours. Find its average speed.

    Formula:Speed

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

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13. 13.

    €95 is shared in the ratio 3 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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14. 14.

    A right-angled triangle has legs of 18 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A value changes from 69 to 129. 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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16. 16.

    A bag has 17 equally likely marbles, of which 9 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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17. 17.

    Solve for x: 5x + 20 = 30.

    Formula:Solving a Linear Equation

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

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18. 18.

    A cylinder has radius 3 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    €330 is shared in the ratio 5 : 5. Find each share.

    Formula:Dividing in a Ratio

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

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20. 20.

    A value changes from 92 to 31. 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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