Greece · Grade 12 · Practice Sheet 42

1. 1.

   Find the population standard deviation of: 11, 9, 7, 10, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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2. 2.

   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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3. 3.

   A force of 218 N acts on an area of 5.1 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A force of 72 N moves an object 11 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

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

   Formula:Sum of a Geometric Series

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

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6. 6.

   A population of 3,300 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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7. 7.

   A force of 42 N moves an object 18 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Two masses 4,900 kg and 340 kg are 12 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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9. 9.

   Find the force needed to accelerate a 18 kg mass at 3.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Find the gravitational potential energy of a 4 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A triangle has sides a = 6 cm and b = 9 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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12. 12.

    In a triangle, a = 14, b = 13 and the included angle C = 110°. 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.

    €1,400 is invested at 5% 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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14. 14.

    A current of 1.2 A flows through a 40 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Find the momentum of a 15 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    €2,100 is invested at 4% compound interest per annum for 2 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.

    A force of 360 N acts on an area of 6.9 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 3 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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19. 19.

    Find the momentum of a 21 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    Find the population standard deviation of: 13, 16, 5, 19, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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