Argentina · Grado 11 · Practice Sheet 46

1. 1.

   Solve using the quadratic formula: x² + 5x − 6 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 9 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   A force of 81 N moves an object 30 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   Find the gravitational potential energy of a 25 kg object raised 25 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the sum of the first 7 terms of a geometric series with first term a = 4 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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6. 6.

   Find the momentum of a 23 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A device runs at 225 V drawing 5.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 1 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   A cylinder has radius 5 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    Find the gravitational potential energy of a 22 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the force needed to accelerate a 49 kg mass at 3.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    An object has mass 41.5 g and volume 5 cm³. Find its density.

    Formula:Density

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

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13. 13.

    Solve using the quadratic formula: x² − 1x − 30 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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15. 15.

    Two masses 2,900 kg and 560 kg are 4 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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16. 16.

    A force of 150 N acts on an area of 2.7 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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17. 17.

    An object with initial velocity 5 m/s accelerates at 4.7 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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19. 19.

    Find the sum of the first 5 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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20. 20.

    A right-angled triangle has legs of 18 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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