Nepal · Class 10 · Practice Sheet 27

1. 1.

   Solve for x: 2x + 8 = 28.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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2. 2.

   A device runs at 22 V drawing 2.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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3. 3.

   A cone has base radius 3 cm and height 22 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 2.8 A flows through a 37 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   Find the force needed to accelerate a 37 kg mass at 3.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A force of 9 N moves an object 18 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Solve for x: 6x + 18 = 48.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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8. 8.

   A bag has 8 equally likely marbles, of which 1 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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9. 9.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 3 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    A force of 61 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A right-angled triangle has legs of 13 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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12. 12.

    A device runs at 97 V drawing 6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A body starts at 17 m/s and accelerates at 5.5 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    Find the force needed to accelerate a 60 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Solve using the quadratic formula: x² + 0x − 9 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    An object has mass 128 g and volume 16 cm³. Find its density.

    Formula:Density

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

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17. 17.

    Solve using the quadratic formula: x² − 6x + 5 = 0.

    Formula:Quadratic Formula

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

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18. 18.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 8 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    A wave has frequency 418 Hz and wavelength 1.49 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 12 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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