Japan · Grade 9 · Practice Sheet 15

1. 1.

   Find the force needed to accelerate a 54 kg mass at 3.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A train moves at 87 km/h for 3.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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3. 3.

   A cylinder has radius 4 cm and height 28 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 force needed to accelerate a 27 kg mass at 4.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Solve for x: 5x + 9 = 24.

   Formula:Solving a Linear Equation

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

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6. 6.

   A current of 2.9 A flows through a 29 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the momentum of a 28 kg object moving at 30 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Find the gravitational potential energy of a 35 kg object raised 10 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A train moves at 56 km/h for 5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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10. 10.

    ¥1,400 is invested at 3% compound interest per annum for 5 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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11. 11.

    A force of 63 N acts on an area of 8 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A right-angled triangle has legs of 17 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.

    A value changes from 50 to 66. 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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14. 14.

    An object has mass 240.7 g and volume 29 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A cone has base radius 3 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A circle has a radius of 6 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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17. 17.

    A train moves at 46 km/h for 4.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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18. 18.

    Find the force needed to accelerate a 59 kg mass at 5.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A force of 64 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    Find the gravitational potential energy of a 18 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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