Chile · Grado 9 · Practice Sheet 29

1. 1.

   A bag has 21 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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2. 2.

   Find the force needed to accelerate a 8 kg mass at 1.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   Find the momentum of a 40 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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4. 4.

   Find the force needed to accelerate a 26 kg mass at 5.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A bag has 8 equally likely marbles, of which 5 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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6. 6.

   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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7. 7.

   A car travels 196 km in 2 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

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

   Formula:Volume of a Cone

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

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9. 9.

   Find the gravitational potential energy of a 28 kg object raised 23 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    An object has mass 315 g and volume 45 cm³. Find its density.

    Formula:Density

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

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11. 11.

    $280 is shared in the ratio 4 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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12. 12.

    $2,000 is invested at 7.5% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

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

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13. 13.

    A current of 3 A flows through a 54 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A device runs at 134 V drawing 4.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A cylinder has radius 14 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    A device runs at 77 V drawing 0.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A value changes from 157 to 117. 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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18. 18.

    A bag has 13 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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19. 19.

    A right-angled triangle has legs of 6 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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20. 20.

    A value changes from 85 to 108. 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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