Portugal · Ano 12 · Practice Sheet 47

1. 1.

   A body starts at 16 m/s and accelerates at 4.1 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 9 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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3. 3.

   An object with initial velocity 7 m/s accelerates at 1.1 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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4. 4.

   A body starts at 17 m/s and accelerates at 1.7 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   Find the sum of the first 3 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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6. 6.

   A wave has frequency 20 Hz and wavelength 2.43 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A cone has base radius 12 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A device runs at 15 V drawing 8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   Solve using the quadratic formula: x² − 7x + 10 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    In a triangle, a = 6, b = 8 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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11. 11.

    Find the sum of the first 6 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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12. 12.

    Find the population standard deviation of: 20, 9, 19, 4, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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13. 13.

    A force of 65 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A body starts at 18 m/s and accelerates at 1.2 m/s² for 11 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A population of 9,000 grows 10% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    Find the population standard deviation of: 14, 3, 8, 20, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    A cone has base radius 6 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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18. 18.

    A current of 5.2 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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20. 20.

    A wave has frequency 361 Hz and wavelength 2.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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