Greece · Grade 9 · Practice Sheet 7

1. 1.

   A bag has 19 equally likely marbles, of which 16 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 cone has base radius 5 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   An object has mass 58 g and volume 10 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A wave has frequency 90 Hz and wavelength 2.1 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A force of 66 N moves an object 28 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A circle has a radius of 3 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   Find the force needed to accelerate a 9 kg mass at 0.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A train moves at 38 km/h for 2.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

   €2,400 is invested at 6% 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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10. 10.

    Find the circumference of a circle whose radius is 19 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    €1,900 is invested at 6% 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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12. 12.

    Find the gravitational potential energy of a 27 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    A current of 3.3 A flows through a 49 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    Find the circumference of a circle whose radius is 21 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    A wave has frequency 404 Hz and wavelength 2.31 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the force needed to accelerate a 59 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A right-angled triangle has legs of 7 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    Find the force needed to accelerate a 38 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A current of 6.7 A flows through a 34 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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