Egypt · Grade 10 · Practice Sheet 47

1. 1.

   An object has mass 69.7 g and volume 17 cm³. Find its density.

   Formula:Density

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

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2. 2.

   A population of 2,500 grows 2% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   A bag has 20 equally likely marbles, of which 18 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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5. 5.

   Find the momentum of a 47 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A device runs at 140 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A current of 4.2 A flows through a 20 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   A cone has base radius 8 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    An object has mass 32.2 g and volume 23 cm³. Find its density.

    Formula:Density

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

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11. 11.

    A device runs at 231 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A current of 5.7 A flows through a 25 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the gravitational potential energy of a 39 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    In a triangle, a = 18, b = 16 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 3 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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16. 16.

    A body starts at 4 m/s and accelerates at 1.7 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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17. 17.

    Find the momentum of a 31 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A body starts at 3 m/s and accelerates at 1.4 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    Find the force needed to accelerate a 7 kg mass at 2.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 12 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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