Spain · Grado 11 · Practice Sheet 2

1. 1.

   A force of 77 N moves an object 31 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   An object with initial velocity 4 m/s accelerates at 3.9 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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3. 3.

   €1,600 is invested at 3% 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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4. 4.

   An object has mass 275 g and volume 50 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A triangle has sides a = 20 cm and b = 15 cm with an included angle C = 45°. 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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6. 6.

   In a triangle, a = 11, b = 17 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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7. 7.

   A wave has frequency 244 Hz and wavelength 3.92 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A device runs at 222 V drawing 8.5 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Two masses 5,400 kg and 470 kg are 13 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 4 terms of a geometric series with first term a = 1 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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11. 11.

    Find the gravitational potential energy of a 50 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A force of 97 N moves an object 17 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A cone has base radius 4 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    Find the force needed to accelerate a 43 kg mass at 2.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A device runs at 183 V drawing 6.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A wave has frequency 411 Hz and wavelength 4.42 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the population standard deviation of: 19, 12, 2, 3, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    A cone has base radius 12 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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19. 19.

    €2,500 is invested at 8% compound interest per annum for 3 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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20. 20.

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

    Formula:Quadratic Formula

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

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