New Zealand · Year 8 · Practice Sheet 40

1. 1.

   $189 is shared in the ratio 5 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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2. 2.

   An object has mass 18.9 g and volume 21 cm³. Find its density.

   Formula:Density

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

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3. 3.

   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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4. 4.

   A triangle has a base of 28 cm and a height of 17 cm. Find its area.

   Formula:Area of a Triangle

   $A = \tfrac{1}{2} b h$

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5. 5.

   $500 is invested at 6% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

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

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6. 6.

   A current of 7.5 A flows through a 26 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the mean (average) of these numbers: 17, 21, 19, 14.

   Formula:Arithmetic Mean

   $\bar{x} = \dfrac{\sum x}{n}$

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8. 8.

   A train moves at 36 km/h for 5.6 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

   Solve for x: 3x + 6 = 27.

   Formula:Solving a Linear Equation

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

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10. 10.

    A right-angled triangle has legs of 6 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    A force of 323 N acts on an area of 7.7 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A bag has 22 equally likely marbles, of which 16 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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13. 13.

    Solve for x: 6x + 2 = 38.

    Formula:Solving a Linear Equation

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

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14. 14.

    A cylinder has radius 11 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    An object has mass 90 g and volume 45 cm³. Find its density.

    Formula:Density

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

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16. 16.

    Find the mean (average) of these numbers: 76, 53, 12, 21.

    Formula:Arithmetic Mean

    $\bar{x} = \dfrac{\sum x}{n}$

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17. 17.

    A right-angled triangle has legs of 15 cm and 9 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    $2,600 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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19. 19.

    A cylinder has radius 2 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    Solve for x: 9x + 14 = 59.

    Formula:Solving a Linear Equation

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

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