Belgium · Year 9 · Practice Sheet 28

1. 1.

   A wave has frequency 607 Hz and wavelength 1.62 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A bag has 17 equally likely marbles, of which 2 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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3. 3.

   A right-angled triangle has legs of 13 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   €2,900 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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5. 5.

   €90 is shared in the ratio 4 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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6. 6.

   A cylinder has radius 3 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   A current of 6.4 A flows through a 27 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Find the momentum of a 39 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

   €3,300 is invested at 8% 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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10. 10.

    A device runs at 195 V drawing 6.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the force needed to accelerate a 56 kg mass at 2.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A cylinder has radius 14 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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13. 13.

    Find the gravitational potential energy of a 13 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A wave has frequency 174 Hz and wavelength 0.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the gravitational potential energy of a 16 kg object raised 11 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A car travels 588 km in 7 hours. Find its average speed.

    Formula:Speed

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

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17. 17.

    An object has mass 255.6 g and volume 36 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Find the force needed to accelerate a 10 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    Solve for x: 5x + 15 = 75.

    Formula:Solving a Linear Equation

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

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