Mexico · Grado 12 · Practice Sheet 27

1. 1.

   A force of 72 N acts on an area of 9.6 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Solve using the quadratic formula: x² + 1x − 2 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   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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4. 4.

   Solve using the quadratic formula: x² + 4x − 12 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   Find the sum of the first 7 terms of a geometric series with first term a = 5 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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7. 7.

   Find the force needed to accelerate a 3 kg mass at 7.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Find the gravitational potential energy of a 34 kg object raised 24 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 11 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Find the gravitational potential energy of a 5 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the population standard deviation of: 10, 4, 6, 9, 16 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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12. 12.

    Find the momentum of a 44 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A body starts at 19 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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14. 14.

    A cone has base radius 2 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    A force of 37 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    A current of 2 A flows through a 40 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A wave has frequency 858 Hz and wavelength 3.03 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A force of 396 N acts on an area of 3.3 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A wave has frequency 218 Hz and wavelength 2.63 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    In a triangle, a = 10, b = 16 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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