United Kingdom · Year 8 · Practice Sheet 7

1. 1.

   Find the circumference of a circle whose radius is 27 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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2. 2.

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

   Formula:Pythagorean Theorem

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

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3. 3.

   Find the circumference of a circle whose radius is 10 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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4. 4.

   A force of 399 N acts on an area of 1.1 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A current of 2.6 A flows through a 54 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   Solve for x: 5x + 8 = 48.

   Formula:Solving a Linear Equation

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

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7. 7.

   A value changes from 83 to 131. 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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8. 8.

   An object has mass 109.2 g and volume 13 cm³. Find its density.

   Formula:Density

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

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9. 9.

   A cylinder has radius 13 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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10. 10.

    A triangle has a base of 16 cm and a height of 9 cm. Find its area.

    Formula:Area of a Triangle

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

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11. 11.

    A right-angled triangle has legs of 15 cm and 3 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    A triangle has a base of 5 cm and a height of 9 cm. Find its area.

    Formula:Area of a Triangle

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

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13. 13.

    Find the circumference of a circle whose radius is 19 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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14. 14.

    A cylinder has radius 9 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    Find the mean (average) of these numbers: 24, 77, 95, 82, 28.

    Formula:Arithmetic Mean

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

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16. 16.

    Solve for x: 4x + 12 = 20.

    Formula:Solving a Linear Equation

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

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17. 17.

    An object has mass 387.1 g and volume 49 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Find the mean (average) of these numbers: 51, 84, 59, 17, 83.

    Formula:Arithmetic Mean

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

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19. 19.

    An object has mass 165.6 g and volume 46 cm³. Find its density.

    Formula:Density

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

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20. 20.

    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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