Egypt · Grade 10 · Practice Sheet 32

1. 1.

   A bag has 26 equally likely marbles, of which 12 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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2. 2.

   An object has mass 108.3 g and volume 19 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A device runs at 38 V drawing 6.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A cone has base radius 11 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   Find the gravitational potential energy of a 16 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   A current of 4.9 A flows through a 50 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Solve for x: 5x + 5 = 60.

   Formula:Solving a Linear Equation

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

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8. 8.

   An object with initial velocity 12 m/s accelerates at 1.4 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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9. 9.

   Solve for x: 6x + 4 = 16.

   Formula:Solving a Linear Equation

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

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10. 10.

    Find the force needed to accelerate a 50 kg mass at 7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A force of 72 N moves an object 30 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 9 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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13. 13.

    Solve for x: 4x + 17 = 61.

    Formula:Solving a Linear Equation

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

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14. 14.

    A population of 7,800 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A cylinder has radius 4 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    A force of 20 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the force needed to accelerate a 49 kg mass at 1.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A cylinder has radius 10 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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19. 19.

    A body starts at 6 m/s and accelerates at 2.4 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A current of 6.5 A flows through a 47 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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