Lebanon · Grade 11 · Practice Sheet 3

1. 1.

   A device runs at 218 V drawing 7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   A triangle has sides a = 12 cm and b = 11 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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3. 3.

   In a triangle, a = 18, b = 13 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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4. 4.

   Find the population standard deviation of: 4, 4, 11, 20, 12 (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 8,100 grows 2% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Find the momentum of a 18 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 4 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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8. 8.

   LL 800 is invested at 4% compound interest per annum for 4 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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9. 9.

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

   Formula:Momentum

   $p = mv$

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10. 10.

    A cone has base radius 6 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 1 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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12. 12.

    Find the force needed to accelerate a 48 kg mass at 0.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the momentum of a 28 kg object moving at 19 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    Find the force needed to accelerate a 48 kg mass at 4.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A right-angled triangle has legs of 3 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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16. 16.

    In a triangle, a = 5, b = 13 and the included angle C = 80°. 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 wave has frequency 178 Hz and wavelength 3.57 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A cylinder has radius 2 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    In a triangle, a = 10, b = 10 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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20. 20.

    A wave has frequency 739 Hz and wavelength 1.45 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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