Ukraine · Grade 9 · Practice Sheet 25

1. 1.

   A value changes from 182 to 65. 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.

   A wave has frequency 425 Hz and wavelength 1.28 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A circle has a radius of 7 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   An object has mass 198.4 g and volume 32 cm³. Find its density.

   Formula:Density

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

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5. 5.

   A right-angled triangle has legs of 15 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   ₴2,900 is invested at 3% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

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

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7. 7.

   A cylinder has radius 7 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the force needed to accelerate a 31 kg mass at 5.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A train moves at 50 km/h for 5.4 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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10. 10.

    Find the gravitational potential energy of a 24 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    A circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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13. 13.

    Find the circumference of a circle whose radius is 5 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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14. 14.

    Find the force needed to accelerate a 26 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A bag has 29 equally likely marbles, of which 21 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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16. 16.

    A force of 368 N acts on an area of 5.1 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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18. 18.

    ₴3,900 is invested at 8% 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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19. 19.

    Find the force needed to accelerate a 10 kg mass at 2.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A device runs at 204 V drawing 7.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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