China · Grade 11 · Practice Sheet 19

1. 1.

   Find the gravitational potential energy of a 23 kg object raised 26 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A cylinder has radius 13 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   A wave has frequency 381 Hz and wavelength 3.79 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   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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5. 5.

   A wave has frequency 632 Hz and wavelength 0.36 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A triangle has sides a = 7 cm and b = 20 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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7. 7.

   ¥3,400 is invested at 3% 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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8. 8.

   A force of 58 N moves an object 29 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A device runs at 172 V drawing 4.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Find the population standard deviation of: 9, 2, 9, 16, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Find the momentum of a 56 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A wave has frequency 621 Hz and wavelength 4.14 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    ¥1,400 is invested at 5% 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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14. 14.

    An object has mass 15 g and volume 5 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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15. 15.

    A right-angled triangle has legs of 15 cm and 5 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A body starts at 19 m/s and accelerates at 2.5 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    A cylinder has radius 2 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    An object has mass 121.5 g and volume 15 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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19. 19.

    A body starts at 18 m/s and accelerates at 2 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    An object with initial velocity 11 m/s accelerates at 2 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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