Bangladesh · Class 12 · Practice Sheet 32

1. 1.

   In a triangle, a = 14, b = 8 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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2. 2.

   A body starts at 8 m/s and accelerates at 3.9 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   Find the population standard deviation of: 18, 13, 12, 2, 17 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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4. 4.

   A device runs at 166 V drawing 1.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   An object with initial velocity 12 m/s accelerates at 1.7 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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6. 6.

   A body starts at 19 m/s and accelerates at 3.3 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A cone has base radius 2 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A device runs at 98 V drawing 5.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   ৳ 1,400 is invested at 4% compound interest per annum for 2 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.

    A body starts at 6 m/s and accelerates at 1.4 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    A force of 21 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A population of 1,500 grows 3% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Solve using the quadratic formula: x² − 1x − 30 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A wave has frequency 564 Hz and wavelength 2.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the force needed to accelerate a 38 kg mass at 1.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    Find the population standard deviation of: 16, 7, 5, 13, 11 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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17. 17.

    ৳ 3,900 is invested at 8% compound interest per annum for 2 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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18. 18.

    Find the gravitational potential energy of a 30 kg object raised 22 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A device runs at 90 V drawing 6.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Find the momentum of a 40 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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