Italy · Classe 10 · Practice Sheet 5

1. 1.

   A wave has frequency 401 Hz and wavelength 3.96 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A cylinder has radius 4 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   Find the gravitational potential energy of a 47 kg object raised 40 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A current of 7.3 A flows through a 55 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A force of 256 N acts on an area of 1.4 m². Find the pressure.

   Formula:Pressure

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

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6. 6.

   A value changes from 197 to 227. 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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7. 7.

   €3,500 is invested at 5% compound interest per annum for 3 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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8. 8.

   €900 is invested at 10% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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9. 9.

   Find the force needed to accelerate a 54 kg mass at 3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 309 N acts on an area of 7.5 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A body starts at 4 m/s and accelerates at 3.3 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A wave has frequency 48 Hz and wavelength 1.99 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the gravitational potential energy of a 34 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A bag has 12 equally likely marbles, of which 3 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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15. 15.

    A device runs at 67 V drawing 5.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the gravitational potential energy of a 29 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A cone has base radius 7 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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18. 18.

    Find the force needed to accelerate a 57 kg mass at 6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Solve for x: 5x + 12 = 42.

    Formula:Solving a Linear Equation

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

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20. 20.

    A right-angled triangle has legs of 10 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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