Hungary · Grade 9 · Practice Sheet 31

1. 1.

   A bag has 24 equally likely marbles, of which 18 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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2. 2.

   A cylinder has radius 12 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   A circle has a radius of 13 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   A value changes from 42 to 38. 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.

   Find the force needed to accelerate a 37 kg mass at 5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A force of 64 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Ft 1,200 is invested at 8% 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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8. 8.

   A right-angled triangle has legs of 14 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A bag has 20 equally likely marbles, of which 14 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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11. 11.

    A cone has base radius 3 cm and height 9 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 force of 190 N acts on an area of 1.5 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    A train moves at 25 km/h for 3.7 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    A right-angled triangle has legs of 16 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A train moves at 52 km/h for 2.4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    Ft 2,300 is invested at 8% 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.

    Find the force needed to accelerate a 7 kg mass at 0.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 51 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    Find the momentum of a 55 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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20. 20.

    A current of 7.5 A flows through a 38 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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