Singapore · Grade 9 · Practice Sheet 31

1. 1.

   Find the gravitational potential energy of a 44 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A bag has 11 equally likely marbles, of which 8 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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4. 4.

   A car travels 104 km in 2 hours. Find its average speed.

   Formula:Speed

   $v = \dfrac{d}{t}$

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5. 5.

   A train moves at 56 km/h for 2.1 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   A force of 63 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Solve for x: 4x + 5 = 41.

   Formula:Solving a Linear Equation

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

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8. 8.

   A car travels 126 km in 3 hours. Find its average speed.

   Formula:Speed

   $v = \dfrac{d}{t}$

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9. 9.

   A value changes from 121 to 54. 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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10. 10.

    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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11. 11.

    A cone has base radius 3 cm and height 12 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 46 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Solve for x: 6x + 20 = 56.

    Formula:Solving a Linear Equation

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

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14. 14.

    Find the force needed to accelerate a 48 kg mass at 1.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A train moves at 30 km/h for 2.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    A bag has 26 equally likely marbles, of which 21 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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17. 17.

    A current of 3.2 A flows through a 22 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A value changes from 152 to 55. 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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19. 19.

    A bag has 18 equally likely marbles, of which 4 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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20. 20.

    A cylinder has radius 3 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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