Greece · Grade 9 · Practice Sheet 50

1. 1.

   A bag has 24 equally likely marbles, of which 13 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.

   €174 is shared in the ratio 3 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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3. 3.

   An object has mass 151.9 g and volume 31 cm³. Find its density.

   Formula:Density

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

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4. 4.

   Find the circumference of a circle whose radius is 9 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   A wave has frequency 744 Hz and wavelength 1.22 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A bag has 21 equally likely marbles, of which 12 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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7. 7.

   A device runs at 59 V drawing 0.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   An object has mass 188 g and volume 40 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A device runs at 50 V drawing 8.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the force needed to accelerate a 36 kg mass at 8.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 480 N acts on an area of 8.3 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    €2,500 is invested at 5% compound interest per annum for 2 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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13. 13.

    An object has mass 231 g and volume 30 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A device runs at 232 V drawing 0.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the force needed to accelerate a 10 kg mass at 1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    €500 is invested at 4% compound interest per annum for 4 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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17. 17.

    A current of 4.9 A flows through a 32 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Find the gravitational potential energy of a 34 kg object raised 37 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A cone has base radius 4 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A circle has a radius of 15 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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