Japan · Grade 9 · Practice Sheet 27

1. 1.

   A cylinder has radius 13 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   A train moves at 63 km/h for 1.5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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3. 3.

   Find the circumference of a circle whose radius is 23 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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4. 4.

   ¥232 is shared in the ratio 5 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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5. 5.

   A bag has 25 equally likely marbles, of which 7 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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6. 6.

   A cylinder has radius 9 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   Find the momentum of a 17 kg object moving at 22 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A bag has 17 equally likely marbles, of which 11 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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9. 9.

   A right-angled triangle has legs of 4 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    Solve for x: 4x + 18 = 42.

    Formula:Solving a Linear Equation

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

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11. 11.

    Find the force needed to accelerate a 33 kg mass at 2.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A device runs at 138 V drawing 4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the force needed to accelerate a 6 kg mass at 7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A right-angled triangle has legs of 4 cm and 19 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A value changes from 25 to 150. 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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16. 16.

    A force of 66 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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17. 17.

    A right-angled triangle has legs of 15 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    ¥2,800 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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19. 19.

    Solve for x: 3x + 10 = 28.

    Formula:Solving a Linear Equation

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

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20. 20.

    An object has mass 50.4 g and volume 6 cm³. Find its density.

    Formula:Density

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

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