Japan · Grade 9 · Practice Sheet 31

1. 1.

   Find the momentum of a 55 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A current of 1.3 A flows through a 27 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

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

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   Find the gravitational potential energy of a 50 kg object raised 20 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   ¥4,900 is invested at 5% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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6. 6.

   A force of 178 N acts on an area of 7.2 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A bag has 29 equally likely marbles, of which 25 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.

   A force of 81 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the force needed to accelerate a 11 kg mass at 7.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A train moves at 58 km/h for 3.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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11. 11.

    A right-angled triangle has legs of 13 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    A train moves at 24 km/h for 4.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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13. 13.

    ¥3,800 is invested at 5% simple interest per year for 6 years. Find the interest earned.

    Formula:Simple Interest

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

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14. 14.

    A value changes from 184 to 131. 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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15. 15.

    ¥500 is invested at 5% compound interest per annum for 2 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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16. 16.

    An object has mass 66.3 g and volume 13 cm³. Find its density.

    Formula:Density

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

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17. 17.

    A current of 2.1 A flows through a 41 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    A 18 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    ¥259 is shared in the ratio 3 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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20. 20.

    Find the force needed to accelerate a 56 kg mass at 7.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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