Ecuador · Grado 11 · Practice Sheet 33

1. 1.

   Find the momentum of a 26 kg object moving at 23 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   An object has mass 62.5 g and volume 25 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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3. 3.

   A current of 3.9 A flows through a 26 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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4. 4.

   A right-angled triangle has legs of 17 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   A force of 106 N moves an object 38 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A device runs at 57 V drawing 6.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A current of 4.9 A flows through a 13 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A triangle has sides a = 7 cm and b = 12 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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9. 9.

   In a triangle, a = 9, b = 17 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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10. 10.

    A population of 8,300 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A wave has frequency 654 Hz and wavelength 1.05 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    Two masses 4,100 kg and 470 kg are 7 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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13. 13.

    $1,600 is invested at 3% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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14. 14.

    Find the sum of the first 5 terms of a geometric series with first term a = 3 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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15. 15.

    A body starts at 18 m/s and accelerates at 3.6 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    A device runs at 184 V drawing 5.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    $1,700 is invested at 5% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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18. 18.

    Two masses 4,100 kg and 790 kg are 14 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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19. 19.

    A triangle has sides a = 8 cm and b = 7 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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20. 20.

    An object has mass 100 g and volume 20 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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