Finland · Grade 9 · Practice Sheet 31

1. 1.

   Find the gravitational potential energy of a 9 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   Solve for x: 4x + 20 = 52.

   Formula:Solving a Linear Equation

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

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3. 3.

   €1,100 is invested at 6% compound interest per annum for 4 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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4. 4.

   €100 is shared in the ratio 2 : 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.

   Find the circumference of a circle whose radius is 21 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   A wave has frequency 132 Hz and wavelength 3.19 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Solve for x: 6x + 6 = 78.

   Formula:Solving a Linear Equation

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

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8. 8.

   €60 is shared in the ratio 1 : 4. Find each share.

   Formula:Dividing in a Ratio

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

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9. 9.

   A value changes from 183 to 20. 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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10. 10.

    Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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11. 11.

    A cone has base radius 6 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    A wave has frequency 481 Hz and wavelength 3.52 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    A 7 kg object moves at 9 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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14. 14.

    A current of 1.7 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Find the gravitational potential energy of a 2 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A value changes from 52 to 133. 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.

    A circle has a radius of 5 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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18. 18.

    A current of 3.4 A flows through a 41 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A bag has 10 equally likely marbles, of which 5 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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20. 20.

    €3,100 is invested at 3% compound interest per annum for 4 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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