Ukraine · Grade 11 · Practice Sheet 29

1. 1.

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

   Formula:Sum of a Geometric Series

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

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2. 2.

   Solve using the quadratic formula: x² + 5x + 4 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A body starts at 7 m/s and accelerates at 2.9 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the population standard deviation of: 6, 18, 12, 9, 13 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   A population of 4,800 grows 2% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A device runs at 70 V drawing 6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A population of 1,500 grows 10% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A wave has frequency 177 Hz and wavelength 0.64 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the force needed to accelerate a 8 kg mass at 3.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A device runs at 38 V drawing 4.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the momentum of a 20 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A force of 364 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A cylinder has radius 13 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    Find the population standard deviation of: 4, 15, 3, 19, 6 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    A force of 94 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    Find the sum of the first 8 terms of an arithmetic series with first term a = 7 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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17. 17.

    In a triangle, a = 14, b = 6 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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18. 18.

    Find the momentum of a 11 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Solve using the quadratic formula: x² + 3x + 2 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    Find the force needed to accelerate a 10 kg mass at 5.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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