Bahrain · Grade 12 · Practice Sheet 38

1. 1.

   Find the sum of the first 19 terms of an arithmetic series with first term a = 4 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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2. 2.

   Find the population standard deviation of: 20, 8, 11, 5, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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3. 3.

   A device runs at 240 V drawing 8.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Solve using the quadratic formula: x² + 9x + 20 = 0.

   Formula:Quadratic Formula

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

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5. 5.

   A triangle has sides a = 11 cm and b = 16 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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6. 6.

   A population of 1,000 grows 5% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   An object with initial velocity 2 m/s accelerates at 1.5 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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8. 8.

   A wave has frequency 271 Hz and wavelength 1.77 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A 22 kg object moves at 21 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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10. 10.

    Find the sum of the first 3 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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11. 11.

    A body starts at 20 m/s and accelerates at 2.4 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A triangle has sides a = 13 cm and b = 17 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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13. 13.

    A device runs at 101 V drawing 9.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A triangle has sides a = 10 cm and b = 17 cm with an included angle C = 45°. 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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15. 15.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    In a triangle, a = 7, b = 14 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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17. 17.

    A body starts at 18 m/s and accelerates at 4.9 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    A triangle has sides a = 10 cm and b = 14 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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19. 19.

    Find the force needed to accelerate a 11 kg mass at 2.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A wave has frequency 505 Hz and wavelength 2.02 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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