Cambodia · Grade 12 · Practice Sheet 6

1. 1.

   A triangle has sides a = 10 cm and b = 5 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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2. 2.

   In a triangle, a = 5, b = 12 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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3. 3.

   A body starts at 19 m/s and accelerates at 4.2 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   In a triangle, a = 7, b = 12 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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5. 5.

   A device runs at 133 V drawing 4.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   ៛ 2,100 is invested at 6% 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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7. 7.

   A wave has frequency 436 Hz and wavelength 2.21 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A cone has base radius 8 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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9. 9.

   ៛ 1,300 is invested at 6% 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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10. 10.

    Find the sum of the first 4 terms of a geometric series with first term a = 3 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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11. 11.

    A force of 113 N acts on an area of 9 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A force of 20 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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13. 13.

    Solve using the quadratic formula: x² − 1x + 0 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A body starts at 8 m/s and accelerates at 2.9 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    An object with initial velocity 14 m/s accelerates at 3.1 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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16. 16.

    A force of 52 N moves an object 15 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    A 26 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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18. 18.

    A force of 64 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    In a triangle, a = 18, b = 9 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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20. 20.

    Find the momentum of a 59 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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