Colombia · Grado 11 · Practice Sheet 42

1. 1.

   A triangle has sides a = 12 cm and b = 16 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.

   A force of 22 N moves an object 26 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   $3,200 is invested at 3% 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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4. 4.

   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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5. 5.

   Two masses 6,900 kg and 230 kg are 20 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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6. 6.

   Find the force needed to accelerate a 51 kg mass at 1.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   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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8. 8.

   A force of 18 N moves an object 40 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the population standard deviation of: 14, 16, 14, 12, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A cone has base radius 4 cm and height 10 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.

    A current of 2 A flows through a 10 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    Find the sum of the first 6 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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13. 13.

    A triangle has sides a = 6 cm and b = 10 cm with an included angle C = 60°. 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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14. 14.

    In a triangle, a = 8, b = 12 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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15. 15.

    Find the force needed to accelerate a 51 kg mass at 8.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    $900 is invested at 6% 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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17. 17.

    Solve using the quadratic formula: x² + 7x + 12 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    A current of 5.2 A flows through a 15 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the momentum of a 45 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the population standard deviation of: 17, 4, 4, 4, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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