Egypt · Grade 12 · Practice Sheet 7

1. 1.

   A wave has frequency 282 Hz and wavelength 1.74 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Solve using the quadratic formula: x² + 1x − 20 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A device runs at 89 V drawing 3.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A body starts at 10 m/s and accelerates at 3 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   A wave has frequency 582 Hz and wavelength 1.84 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A triangle has sides a = 9 cm and b = 5 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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7. 7.

   A device runs at 167 V drawing 1.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the sum of the first 6 terms of a geometric series with first term a = 7 and common ratio r = 2.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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9. 9.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 12 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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10. 10.

    Find the momentum of a 21 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    Solve using the quadratic formula: x² + 1x − 2 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A force of 68 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A 20 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    A triangle has sides a = 19 cm and b = 10 cm with an included angle C = 90°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

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17. 17.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    A device runs at 32 V drawing 9.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A force of 171 N acts on an area of 0.8 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Solve using the quadratic formula: x² + 4x − 5 = 0.

    Formula:Quadratic Formula

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

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