Bangladesh · Class 12 · Practice Sheet 48

1. 1.

   ৳ 2,300 is invested at 4% 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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2. 2.

   A device runs at 12 V drawing 3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   In a triangle, a = 7, b = 18 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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4. 4.

   Find the gravitational potential energy of a 39 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   ৳ 1,500 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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6. 6.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   An object with initial velocity 1 m/s accelerates at 2.3 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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8. 8.

   A 5 kg object moves at 18 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   Find the momentum of a 2 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    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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11. 11.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 7 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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12. 12.

    Find the sum of the first 7 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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13. 13.

    Find the force needed to accelerate a 25 kg mass at 5.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A device runs at 144 V drawing 6.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Solve using the quadratic formula: x² − 2x − 15 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    Find the force needed to accelerate a 53 kg mass at 5.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    An object with initial velocity 8 m/s accelerates at 2.8 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    A force of 67 N moves an object 17 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A force of 462 N acts on an area of 5.3 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A device runs at 225 V drawing 2.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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