Russia · Grade 11 · Practice Sheet 7

1. 1.

   A device runs at 23 V drawing 9.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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2. 2.

   Find the sum of the first 7 terms of a geometric series with first term a = 5 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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3. 3.

   A cylinder has radius 14 cm and height 26 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   A wave has frequency 831 Hz and wavelength 1.78 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A right-angled triangle has legs of 18 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A cone has base radius 4 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A force of 106 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the force needed to accelerate a 12 kg mass at 3.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A device runs at 23 V drawing 2.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the force needed to accelerate a 52 kg mass at 1.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 116 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A right-angled triangle has legs of 14 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    ₽3,100 is invested at 3% compound interest per annum for 5 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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14. 14.

    A triangle has sides a = 19 cm and b = 17 cm with an included angle C = 30°. 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.

    A device runs at 47 V drawing 3.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A wave has frequency 260 Hz and wavelength 1.97 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A force of 104 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    Solve using the quadratic formula: x² − 11x + 30 = 0.

    Formula:Quadratic Formula

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

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19. 19.

    Find the population standard deviation of: 13, 18, 12, 10, 14 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    A population of 6,300 grows 3% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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