Ireland · Year 9 · Practice Sheet 44

1. 1.

   A bag has 23 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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2. 2.

   A force of 152 N acts on an area of 4.2 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A wave has frequency 120 Hz and wavelength 3.78 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   €2,800 is invested at 7.5% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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5. 5.

   Find the circumference of a circle whose radius is 4 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   A train moves at 92 km/h for 5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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7. 7.

   A force of 53 N moves an object 10 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A circle has a radius of 5 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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9. 9.

   A cylinder has radius 7 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A bag has 17 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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11. 11.

    Find the force needed to accelerate a 47 kg mass at 4.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A force of 59 N acts on an area of 5.9 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A wave has frequency 784 Hz and wavelength 4.58 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Solve for x: 4x + 11 = 59.

    Formula:Solving a Linear Equation

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

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15. 15.

    A cylinder has radius 8 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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16. 16.

    Solve for x: 3x + 16 = 37.

    Formula:Solving a Linear Equation

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

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17. 17.

    A car travels 522 km in 6 hours. Find its average speed.

    Formula:Speed

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

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18. 18.

    A value changes from 101 to 159. 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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19. 19.

    Find the force needed to accelerate a 58 kg mass at 8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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