Norway · Grade 12 · Practice Sheet 9

1. 1.

   Find the momentum of a 58 kg object moving at 6 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   kr 2,500 is invested at 3% compound interest per annum for 3 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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3. 3.

   Find the momentum of a 45 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the sum of the first 14 terms of an arithmetic series with first term a = 4 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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5. 5.

   A device runs at 117 V drawing 5.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 8 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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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 device runs at 225 V drawing 4.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A wave has frequency 568 Hz and wavelength 4.15 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    In a triangle, a = 15, b = 17 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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11. 11.

    A current of 3.7 A flows through a 43 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    In a triangle, a = 12, b = 7 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.

    A triangle has sides a = 11 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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14. 14.

    A body starts at 18 m/s and accelerates at 1.8 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Find the gravitational potential energy of a 46 kg object raised 27 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    Find the population standard deviation of: 7, 7, 7, 7, 19 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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19. 19.

    A population of 5,800 grows 8% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 8 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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