Australia · Year 9 · Practice Sheet 43

1. 1.

   Find the force needed to accelerate a 40 kg mass at 8.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   Find the gravitational potential energy of a 24 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   A bag has 25 equally likely marbles, of which 16 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 force of 101 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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5. 5.

   A train moves at 47 km/h for 5.8 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   A current of 1.1 A flows through a 10 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   $2,900 is invested at 4% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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8. 8.

   $72 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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9. 9.

   A bag has 28 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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10. 10.

    Find the circumference of a circle whose radius is 17 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    A bag has 24 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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12. 12.

    A right-angled triangle has legs of 7 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    Find the force needed to accelerate a 39 kg mass at 4.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A bag has 28 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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15. 15.

    A device runs at 168 V drawing 0.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    Find the force needed to accelerate a 12 kg mass at 2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A cone has base radius 4 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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18. 18.

    A right-angled triangle has legs of 18 cm and 11 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A cone has base radius 12 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    A current of 4.1 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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