Ireland · Year 8 · Practice Sheet 36

1. 1.

   Solve for x: 6x + 10 = 58.

   Formula:Solving a Linear Equation

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

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2. 2.

   A right-angled triangle has legs of 10 cm and 4 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   A train moves at 35 km/h for 4.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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4. 4.

   A right-angled triangle has legs of 20 cm and 14 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   €198 is shared in the ratio 1 : 5. Find each share.

   Formula:Dividing in a Ratio

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

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6. 6.

   A value changes from 83 to 226. 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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7. 7.

   What is 50% of 590?

   Formula:Percentage of a Quantity

   $\text{result} = \dfrac{p}{100} \times N$

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8. 8.

   A train moves at 74 km/h for 2.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

   Solve for x: 5x + 10 = 50.

   Formula:Solving a Linear Equation

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

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10. 10.

    A circle has a radius of 9 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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11. 11.

    A bag has 23 equally likely marbles, of which 22 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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12. 12.

    An object has mass 170.1 g and volume 27 cm³. Find its density.

    Formula:Density

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

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13. 13.

    A bag has 12 equally likely marbles, of which 2 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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14. 14.

    A current of 4.7 A flows through a 37 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    A bag has 10 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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16. 16.

    An object has mass 135.3 g and volume 33 cm³. Find its density.

    Formula:Density

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

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17. 17.

    A current of 3 A flows through a 36 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    Solve for x: 4x + 13 = 37.

    Formula:Solving a Linear Equation

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

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19. 19.

    A value changes from 144 to 122. 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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20. 20.

    €3,800 is invested at 10% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

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

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