Taiwan · Grade 11 · Practice Sheet 29

1. 1.

   In a triangle, a = 16, b = 10 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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2. 2.

   A triangle has sides a = 16 cm and b = 8 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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3. 3.

   A cone has base radius 2 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   A current of 7.7 A flows through a 40 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Find the momentum of a 24 kg object moving at 17 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A force of 9 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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7. 7.

   In a triangle, a = 16, b = 8 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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8. 8.

   A triangle has sides a = 5 cm and b = 10 cm with an included angle C = 60°. 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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9. 9.

   A device runs at 147 V drawing 7.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    NT$ 2,800 is invested at 8% 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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11. 11.

    A cylinder has radius 4 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    A force of 112 N acts on an area of 5.3 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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13. 13.

    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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14. 14.

    A wave has frequency 585 Hz and wavelength 4.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    An object has mass 27 g and volume 27 cm³. Find its density.

    Formula:Density

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

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16. 16.

    An object with initial velocity 9 m/s accelerates at 2.7 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    A wave has frequency 845 Hz and wavelength 3.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    Find the momentum of a 46 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A force of 106 N moves an object 31 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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