New Zealand · Year 9 · Practice Sheet 36

1. 1.

   A cylinder has radius 3 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   Find the momentum of a 44 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A train moves at 23 km/h for 4.5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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4. 4.

   Solve for x: 7x + 4 = 18.

   Formula:Solving a Linear Equation

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

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5. 5.

   A right-angled triangle has legs of 9 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   A value changes from 122 to 110. 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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7. 7.

   A bag has 22 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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8. 8.

   An object has mass 158.6 g and volume 26 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A force of 8 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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10. 10.

    A cone has base radius 3 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    Find the gravitational potential energy of a 42 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Find the momentum of a 11 kg object moving at 21 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A car travels 560 km in 8 hours. Find its average speed.

    Formula:Speed

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

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14. 14.

    A bag has 14 equally likely marbles, of which 9 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 right-angled triangle has legs of 5 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A value changes from 50 to 200. 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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17. 17.

    Find the force needed to accelerate a 5 kg mass at 2.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    $3,500 is invested at 7.5% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

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

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19. 19.

    A device runs at 103 V drawing 1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A force of 41 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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