Japan · Grade 9 · Practice Sheet 6

1. 1.

   A wave has frequency 21 Hz and wavelength 4.62 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the circumference of a circle whose radius is 12 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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3. 3.

   An object has mass 140.4 g and volume 36 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A train moves at 81 km/h for 2.5 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   A circle has a radius of 19 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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6. 6.

   A value changes from 32 to 157. 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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7. 7.

   ¥40 is shared in the ratio 3 : 1. Find each share.

   Formula:Dividing in a Ratio

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

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8. 8.

   A wave has frequency 613 Hz and wavelength 4.81 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A bag has 20 equally likely marbles, of which 2 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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10. 10.

    Find the circumference of a circle whose radius is 20 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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11. 11.

    An object has mass 118.8 g and volume 44 cm³. Find its density.

    Formula:Density

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

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12. 12.

    A current of 5 A flows through a 32 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    Find the circumference of a circle whose radius is 14 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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14. 14.

    Solve for x: 2x + 10 = 30.

    Formula:Solving a Linear Equation

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

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15. 15.

    ¥3,500 is invested at 3% 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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16. 16.

    ¥1,700 is invested at 5% compound interest per annum for 3 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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17. 17.

    A train moves at 93 km/h for 3.6 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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18. 18.

    Find the gravitational potential energy of a 31 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    ¥700 is invested at 5% compound interest per annum for 3 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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20. 20.

    A cone has base radius 7 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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