Pakistan · Class 10 · Practice Sheet 44

1. 1.

   A triangle has sides a = 12 cm and b = 18 cm with an included angle C = 45°. 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.

   An object has mass 64.5 g and volume 43 cm³. Find its density.

   Formula:Density

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

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3. 3.

   Find the force needed to accelerate a 59 kg mass at 7.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A force of 35 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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5. 5.

   An object has mass 132.3 g and volume 21 cm³. Find its density.

   Formula:Density

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

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6. 6.

   A population of 5,500 grows 5% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   A device runs at 52 V drawing 9.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A value changes from 72 to 62. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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9. 9.

   A population of 2,800 grows 5% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    A value changes from 174 to 147. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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11. 11.

    A cylinder has radius 10 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    A current of 1.3 A flows through a 56 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A device runs at 97 V drawing 8.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A triangle has sides a = 9 cm and b = 19 cm with an included angle C = 90°. 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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15. 15.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 7 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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16. 16.

    A cone has base radius 11 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    Find the force needed to accelerate a 49 kg mass at 0.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A population of 2,100 grows 8% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    A cylinder has radius 8 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    A triangle has sides a = 17 cm and b = 10 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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