Pakistan · Class 10 · Practice Sheet 16

1. 1.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 7 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A 8 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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3. 3.

   A force of 177 N acts on an area of 3.2 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A wave has frequency 492 Hz and wavelength 2.98 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A device runs at 54 V drawing 8.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   An object has mass 11.7 g and volume 9 cm³. Find its density.

   Formula:Density

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

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7. 7.

   Find the momentum of a 40 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   ₨2,700 is invested at 7.5% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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9. 9.

   A device runs at 79 V drawing 9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    Solve using the quadratic formula: x² − 3x − 10 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    A force of 20 N moves an object 16 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A wave has frequency 137 Hz and wavelength 3.46 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    ₨1,600 is invested at 3% 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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14. 14.

    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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15. 15.

    A device runs at 62 V drawing 5.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    An object with initial velocity 15 m/s accelerates at 1.9 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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17. 17.

    A force of 261 N acts on an area of 5.3 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    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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19. 19.

    Solve using the quadratic formula: x² + 7x + 6 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    In a triangle, a = 7, b = 5 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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