Taiwan · Grade 9 · Practice Sheet 7

1. 1.

   A right-angled triangle has legs of 10 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   Find the momentum of a 4 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A value changes from 182 to 242. 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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4. 4.

   A circle has a radius of 10 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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5. 5.

   Find the gravitational potential energy of a 7 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   A circle has a radius of 14 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   A car travels 165 km in 3 hours. Find its average speed.

   Formula:Speed

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

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8. 8.

   A device runs at 228 V drawing 4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A train moves at 68 km/h for 3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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10. 10.

    A 5 kg object moves at 17 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    NT$ 2,800 is invested at 8% 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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12. 12.

    A device runs at 29 V drawing 7.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A cylinder has radius 10 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    A bag has 26 equally likely marbles, of which 12 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.

    NT$ 108 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.

    A car travels 304 km in 4 hours. Find its average speed.

    Formula:Speed

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

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17. 17.

    Find the force needed to accelerate a 36 kg mass at 2.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A cone has base radius 11 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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19. 19.

    A force of 310 N acts on an area of 9.3 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Find the momentum of a 57 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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