France · Classe 9 · Practice Sheet 16

1. 1.

   A right-angled triangle has legs of 7 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A 3 kg object moves at 13 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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3. 3.

   €1,000 is invested at 6% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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4. 4.

   A value changes from 108 to 131. 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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5. 5.

   A 14 kg object moves at 15 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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6. 6.

   Find the momentum of a 31 kg object moving at 27 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Find the circumference of a circle whose radius is 30 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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8. 8.

   A wave has frequency 773 Hz and wavelength 1.07 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A 35 kg object moves at 5 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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10. 10.

    Find the force needed to accelerate a 33 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A car travels 238 km in 7 hours. Find its average speed.

    Formula:Speed

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

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12. 12.

    Solve for x: 5x + 1 = 61.

    Formula:Solving a Linear Equation

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

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13. 13.

    Find the force needed to accelerate a 23 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A train moves at 61 km/h for 3.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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15. 15.

    Solve for x: 2x + 6 = 24.

    Formula:Solving a Linear Equation

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

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16. 16.

    A cone has base radius 8 cm and height 8 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 bag has 26 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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18. 18.

    Find the momentum of a 36 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A wave has frequency 872 Hz and wavelength 4.73 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A circle has a radius of 8 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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