Russia · Grade 12 · Practice Sheet 15

1. 1.

   A wave has frequency 339 Hz and wavelength 1.06 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   A triangle has sides a = 6 cm and b = 10 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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3. 3.

   In a triangle, a = 11, b = 5 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   A wave has frequency 506 Hz and wavelength 1.58 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A device runs at 216 V drawing 4.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 10 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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7. 7.

   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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8. 8.

   A device runs at 42 V drawing 9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A triangle has sides a = 16 cm and b = 8 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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10. 10.

    Find the force needed to accelerate a 37 kg mass at 6.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    In a triangle, a = 15, b = 11 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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12. 12.

    A body starts at 15 m/s and accelerates at 5.1 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    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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14. 14.

    Find the gravitational potential energy of a 47 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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15. 15.

    Find the force needed to accelerate a 48 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A body starts at 0 m/s and accelerates at 2.3 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A wave has frequency 393 Hz and wavelength 2.34 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A current of 5.3 A flows through a 31 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the momentum of a 31 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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