Ukraine · Grade 9 · Practice Sheet 17

1. 1.

   A wave has frequency 663 Hz and wavelength 0.88 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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2. 2.

   Find the momentum of a 41 kg object moving at 16 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   Solve for x: 8x + 12 = 28.

   Formula:Solving a Linear Equation

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

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4. 4.

   A value changes from 186 to 230. 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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5. 5.

   A bag has 23 equally likely marbles, of which 6 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 force of 16 N moves an object 25 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   ₴1,700 is invested at 3% 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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8. 8.

   A force of 176 N acts on an area of 9.4 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   A cone has base radius 10 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    A right-angled triangle has legs of 5 cm and 14 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    Find the force needed to accelerate a 18 kg mass at 1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    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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13. 13.

    A cone has base radius 2 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    A circle has a radius of 4 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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15. 15.

    A device runs at 197 V drawing 9.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A bag has 13 equally likely marbles, of which 9 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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17. 17.

    ₴105 is shared in the ratio 3 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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18. 18.

    A current of 1.2 A flows through a 14 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A wave has frequency 782 Hz and wavelength 0.86 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    Find the force needed to accelerate a 34 kg mass at 4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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