Argentina · Grado 11 · Practice Sheet 6

1. 1.

   Find the sum of the first 14 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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2. 2.

   Two masses 6,000 kg and 440 kg are 10 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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3. 3.

   A right-angled triangle has legs of 9 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   A 11 kg object moves at 13 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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5. 5.

   A current of 0.6 A flows through a 57 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   An object with initial velocity 15 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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7. 7.

   A 17 kg object moves at 9 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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8. 8.

   An object has mass 217.8 g and volume 33 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A force of 31 N acts on an area of 4.5 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    Find the sum of the first 6 terms of a geometric series with first term a = 7 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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11. 11.

    A current of 2.4 A flows through a 43 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    In a triangle, a = 8, b = 8 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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13. 13.

    A current of 6 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    Find the sum of the first 6 terms of a geometric series with first term a = 4 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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15. 15.

    Find the population standard deviation of: 2, 16, 17, 6, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 3 and common difference d = 3.

    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 gravitational potential energy of a 26 kg object raised 30 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A current of 5 A flows through a 19 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A triangle has sides a = 5 cm and b = 11 cm with an included angle C = 120°. 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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20. 20.

    A cone has base radius 5 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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