Egypt · Grade 10 · Practice Sheet 26

1. 1.

   A bag has 11 equally likely marbles, of which 5 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.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   Solve using the quadratic formula: x² − 1x − 6 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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4. 4.

   A force of 56 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A wave has frequency 592 Hz and wavelength 0.39 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A device runs at 150 V drawing 3.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the gravitational potential energy of a 35 kg object raised 30 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A device runs at 59 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A cylinder has radius 6 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    Find the force needed to accelerate a 15 kg mass at 6.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Find the momentum of a 55 kg object moving at 2 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A cone has base radius 8 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    Solve using the quadratic formula: x² + 2x − 15 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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14. 14.

    A force of 81 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A force of 485 N acts on an area of 3 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    Solve using the quadratic formula: x² − 13x + 42 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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17. 17.

    A right-angled triangle has legs of 18 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Find the momentum of a 52 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 415 N acts on an area of 9.9 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    An object with initial velocity 8 m/s accelerates at 4.7 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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