United States · Grade 9 · Practice Sheet 27

1. 1.

   A bag has 8 equally likely marbles, of which 3 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.

   A circle has a radius of 22 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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3. 3.

   $165 is shared in the ratio 2 : 3. Find each share.

   Formula:Dividing in a Ratio

   $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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4. 4.

   Find the force needed to accelerate a 46 kg mass at 4.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A current of 2.1 A flows through a 34 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   A cylinder has radius 5 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   An object has mass 158.7 g and volume 23 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A force of 226 N acts on an area of 9 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A current of 5.8 A flows through a 57 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A cylinder has radius 2 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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11. 11.

    A force of 37 N moves an object 32 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A bag has 28 equally likely marbles, of which 23 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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13. 13.

    An object has mass 68 g and volume 17 cm³. Find its density.

    Formula:Density

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

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14. 14.

    $1,900 is invested at 10% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

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

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15. 15.

    Solve for x: 5x + 17 = 37.

    Formula:Solving a Linear Equation

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

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16. 16.

    An object has mass 217 g and volume 31 cm³. Find its density.

    Formula:Density

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

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17. 17.

    Find the gravitational potential energy of a 41 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    $147 is shared in the ratio 5 : 2. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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19. 19.

    A wave has frequency 149 Hz and wavelength 2.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A force of 107 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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