India · Class 11 · Practice Sheet 17

1. 1.

   A wave has frequency 31 Hz and wavelength 3.69 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Solve using the quadratic formula: x² + 9x + 20 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   Find the force needed to accelerate a 47 kg mass at 4.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   Find the gravitational potential energy of a 5 kg object raised 28 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A device runs at 228 V drawing 2.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A triangle has sides a = 8 cm and b = 9 cm with an included angle C = 120°. 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.

   Find the force needed to accelerate a 42 kg mass at 4.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A body starts at 18 m/s and accelerates at 4.5 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 10 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    In a triangle, a = 13, b = 12 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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11. 11.

    Find the momentum of a 37 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A triangle has sides a = 16 cm and b = 18 cm with an included angle C = 60°. 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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13. 13.

    Two masses 6,100 kg and 450 kg are 8 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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14. 14.

    Find the population standard deviation of: 16, 10, 10, 4, 18 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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15. 15.

    A current of 3 A flows through a 12 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A wave has frequency 192 Hz and wavelength 3.46 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A triangle has sides a = 12 cm and b = 11 cm with an included angle C = 120°. 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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18. 18.

    A device runs at 104 V drawing 5.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 7 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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20. 20.

    A right-angled triangle has legs of 19 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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