Russia · Grade 9 · Practice Sheet 1

1. 1.

   A wave has frequency 375 Hz and wavelength 1.3 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Solve for x: 7x + 20 = 69.

   Formula:Solving a Linear Equation

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

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3. 3.

   Find the gravitational potential energy of a 5 kg object raised 13 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A cylinder has radius 14 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   A right-angled triangle has legs of 12 cm and 19 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 7 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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7. 7.

   A cone has base radius 9 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A bag has 14 equally likely marbles, of which 7 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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9. 9.

   A force of 180 N acts on an area of 2.1 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A wave has frequency 397 Hz and wavelength 1.59 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A circle has a radius of 12 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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12. 12.

    A 35 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    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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14. 14.

    Find the circumference of a circle whose radius is 7 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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15. 15.

    Solve for x: 6x + 9 = 21.

    Formula:Solving a Linear Equation

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

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16. 16.

    Find the force needed to accelerate a 10 kg mass at 3.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Find the gravitational potential energy of a 43 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A device runs at 52 V drawing 4.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    An object has mass 167.4 g and volume 31 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A force of 47 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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