Japan · Grade 11 · Practice Sheet 13

1. 1.

   Find the sum of the first 8 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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2. 2.

   A current of 2.6 A flows through a 9 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the population standard deviation of: 15, 9, 12, 2, 18 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A current of 2.5 A flows through a 23 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A body starts at 10 m/s and accelerates at 2.1 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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6. 6.

   An object with initial velocity 11 m/s accelerates at 2.1 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   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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8. 8.

   Find the momentum of a 49 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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9. 9.

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

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A device runs at 204 V drawing 7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the force needed to accelerate a 41 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A population of 5,300 grows 8% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A triangle has sides a = 16 cm and b = 6 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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14. 14.

    Find the population standard deviation of: 10, 15, 3, 5, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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15. 15.

    Find the momentum of a 25 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 6 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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18. 18.

    Find the sum of the first 3 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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19. 19.

    A cone has base radius 8 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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20. 20.

    A wave has frequency 276 Hz and wavelength 4.09 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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