Hungary · Grade 9 · Practice Sheet 46

1. 1.

   Find the force needed to accelerate a 42 kg mass at 8.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   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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3. 3.

   A wave has frequency 132 Hz and wavelength 1.15 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A 11 kg object moves at 18 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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5. 5.

   A train moves at 41 km/h for 5.3 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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6. 6.

   Find the circumference of a circle whose radius is 27 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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7. 7.

   Find the gravitational potential energy of a 13 kg object raised 30 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Find the force needed to accelerate a 37 kg mass at 8.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Ft 2,700 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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10. 10.

    Find the force needed to accelerate a 38 kg mass at 8.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Solve for x: 6x + 6 = 54.

    Formula:Solving a Linear Equation

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

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12. 12.

    A force of 5 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A right-angled triangle has legs of 15 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    A cone has base radius 12 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    A right-angled triangle has legs of 10 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A value changes from 30 to 68. 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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17. 17.

    Find the gravitational potential energy of a 48 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Find the circumference of a circle whose radius is 9 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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19. 19.

    A car travels 438 km in 6 hours. Find its average speed.

    Formula:Speed

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

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20. 20.

    Find the gravitational potential energy of a 15 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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