Ireland · Year 9 · Practice Sheet 46

1. 1.

   A bag has 27 equally likely marbles, of which 18 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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2. 2.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A wave has frequency 291 Hz and wavelength 2.87 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A car travels 651 km in 7 hours. Find its average speed.

   Formula:Speed

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

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5. 5.

   A train moves at 20 km/h for 1.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   A right-angled triangle has legs of 12 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A cone has base radius 5 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A cylinder has radius 5 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   A right-angled triangle has legs of 5 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    A bag has 26 equally likely marbles, of which 4 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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11. 11.

    A force of 86 N moves an object 32 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A right-angled triangle has legs of 9 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    Find the gravitational potential energy of a 8 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A wave has frequency 765 Hz and wavelength 4.61 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    A train moves at 92 km/h for 4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    A wave has frequency 546 Hz and wavelength 2.6 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A device runs at 17 V drawing 4.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A bag has 22 equally likely marbles, of which 10 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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19. 19.

    A circle has a radius of 7 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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20. 20.

    Solve for x: 8x + 14 = 54.

    Formula:Solving a Linear Equation

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

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