Colombia · Grado 12 · Practice Sheet 36

1. 1.

   A triangle has sides a = 9 cm and b = 8 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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2. 2.

   Find the gravitational potential energy of a 26 kg object raised 19 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Find the momentum of a 16 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

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

   Formula:Sum of a Geometric Series

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

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5. 5.

   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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6. 6.

   A force of 93 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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7. 7.

   Find the population standard deviation of: 18, 6, 14, 8, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   A wave has frequency 687 Hz and wavelength 3.02 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A cone has base radius 6 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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11. 11.

    Find the momentum of a 54 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Find the force needed to accelerate a 55 kg mass at 2.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A wave has frequency 810 Hz and wavelength 4.06 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    An object with initial velocity 4 m/s accelerates at 3.9 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 11 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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17. 17.

    Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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18. 18.

    Find the force needed to accelerate a 40 kg mass at 3.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A body starts at 1 m/s and accelerates at 3.8 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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