Lebanon · Grade 12 · Practice Sheet 42

1. 1.

   A wave has frequency 664 Hz and wavelength 3.1 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   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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3. 3.

   Find the momentum of a 3 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   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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5. 5.

   A population of 4,400 grows 2% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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6. 6.

   A current of 5.7 A flows through a 29 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   In a triangle, a = 8, b = 16 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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8. 8.

   A device runs at 123 V drawing 9.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Two masses 2,300 kg and 710 kg are 11 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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10. 10.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 9 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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11. 11.

    A cone has base radius 9 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 11 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    Find the sum of the first 4 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

    A 21 kg object moves at 17 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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15. 15.

    An object with initial velocity 11 m/s accelerates at 4.1 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    In a triangle, a = 17, b = 8 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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17. 17.

    A wave has frequency 246 Hz and wavelength 4.57 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the force needed to accelerate a 19 kg mass at 3.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Find the gravitational potential energy of a 13 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A device runs at 161 V drawing 1.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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