Japan · Grade 9 · Practice Sheet 13

1. 1.

   A value changes from 165 to 206. 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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2. 2.

   An object has mass 53.3 g and volume 41 cm³. Find its density.

   Formula:Density

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

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3. 3.

   Find the gravitational potential energy of a 41 kg object raised 13 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the circumference of a circle whose radius is 13 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   A value changes from 140 to 136. 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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6. 6.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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7. 7.

   A right-angled triangle has legs of 18 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   ¥2,500 is invested at 6% 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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9. 9.

   Solve for x: 2x + 16 = 26.

   Formula:Solving a Linear Equation

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

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10. 10.

    Find the gravitational potential energy of a 3 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A force of 443 N acts on an area of 1.4 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    ¥4,700 is invested at 8% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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13. 13.

    A force of 22 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A train moves at 33 km/h for 5.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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15. 15.

    Solve for x: 4x + 12 = 56.

    Formula:Solving a Linear Equation

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

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16. 16.

    A force of 102 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the circumference of a circle whose radius is 24 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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18. 18.

    A car travels 207 km in 3 hours. Find its average speed.

    Formula:Speed

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

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19. 19.

    A right-angled triangle has legs of 16 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    A cone has base radius 2 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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