Ukraine · Grade 9 · Practice Sheet 20

1. 1.

   A wave has frequency 479 Hz and wavelength 2.11 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A cylinder has radius 12 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   A device runs at 9 V drawing 9.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A 13 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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5. 5.

   Solve for x: 8x + 11 = 35.

   Formula:Solving a Linear Equation

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

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6. 6.

   An object has mass 84.5 g and volume 13 cm³. Find its density.

   Formula:Density

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

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7. 7.

   Solve for x: 3x + 7 = 19.

   Formula:Solving a Linear Equation

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

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8. 8.

   Find the force needed to accelerate a 57 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A wave has frequency 841 Hz and wavelength 0.56 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    Find the gravitational potential energy of a 50 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A bag has 10 equally likely marbles, of which 8 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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12. 12.

    An object has mass 194.7 g and volume 33 cm³. Find its density.

    Formula:Density

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

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13. 13.

    ₴1,900 is invested at 8% 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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14. 14.

    A right-angled triangle has legs of 9 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.

    A device runs at 17 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    ₴600 is invested at 4% 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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17. 17.

    Find the momentum of a 7 kg object moving at 5 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A cylinder has radius 14 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    Find the volume of a sphere of radius 8 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: 2x + 13 = 27.

    Formula:Solving a Linear Equation

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

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