Taiwan · Grade 9 · Practice Sheet 50

1. 1.

   A bag has 25 equally likely marbles, of which 10 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.

   Find the gravitational potential energy of a 3 kg object raised 27 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A cylinder has radius 14 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   Solve for x: 5x + 6 = 16.

   Formula:Solving a Linear Equation

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

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5. 5.

   A force of 114 N moves an object 40 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the momentum of a 22 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Find the circumference of a circle whose radius is 30 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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8. 8.

   A wave has frequency 348 Hz and wavelength 3.6 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A cylinder has radius 13 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    A force of 198 N acts on an area of 3.5 m². Find the pressure.

    Formula:Pressure

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

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11. 11.

    A cone has base radius 9 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    Find the gravitational potential energy of a 28 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    An object has mass 158 g and volume 20 cm³. Find its density.

    Formula:Density

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

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14. 14.

    NT$ 800 is invested at 4% 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.

    NT$ 186 is shared in the ratio 4 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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16. 16.

    Find the force needed to accelerate a 32 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A 23 kg object moves at 7 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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18. 18.

    Find the momentum of a 11 kg object moving at 23 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Find the force needed to accelerate a 46 kg mass at 1.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A value changes from 53 to 168. 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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