Czechia · Grade 9 · Practice Sheet 45

1. 1.

   Find the momentum of a 48 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   Kč 112 is shared in the ratio 1 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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4. 4.

   An object has mass 147 g and volume 49 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A right-angled triangle has legs of 14 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A cylinder has radius 13 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   A force of 311 N acts on an area of 7.5 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A car travels 118 km in 2 hours. Find its average speed.

   Formula:Speed

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

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9. 9.

   A device runs at 88 V drawing 5.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A current of 1 A flows through a 58 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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11. 11.

    Find the circumference of a circle whose radius is 14 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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12. 12.

    Find the momentum of a 7 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A cone has base radius 9 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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14. 14.

    A right-angled triangle has legs of 20 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    Kč 900 is invested at 3% 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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17. 17.

    Kč 4,900 is invested at 4% 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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18. 18.

    Find the momentum of a 27 kg object moving at 6 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Find the gravitational potential energy of a 18 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A bag has 30 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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