Ireland · Year 7 · Practice Sheet 45

1. 1.

   Find the perimeter of a rectangle measuring 27 m by 21 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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2. 2.

   Solve for x: 5x + 6 = 21.

   Formula:Solving a Linear Equation

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

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3. 3.

   A value changes from 25 to 225. 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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4. 4.

   One item costs €9.47. Find the total cost of 19 items.

   Formula:Total Cost

   $\text{total} = \text{price} \times \text{quantity}$

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5. 5.

   €90 is shared in the ratio 5 : 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 circle has a radius of 11 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   Find the area of a square with side length 19 cm.

   Formula:Area of a Square

   $A = s^2$

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8. 8.

   Find the perimeter of a rectangle measuring 44 m by 4 m.

   Formula:Perimeter of a Rectangle

   $P = 2(l + w)$

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9. 9.

   Find the area of a square with side length 8 cm.

   Formula:Area of a Square

   $A = s^2$

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10. 10.

    A bag has 13 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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11. 11.

    A car travels 135 km in 3 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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12. 12.

    Find the mean (average) of these numbers: 44, 53, 59, 37, 39.

    Formula:Arithmetic Mean

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

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13. 13.

    Solve for x: 4x + 5 = 13.

    Formula:Solving a Linear Equation

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

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14. 14.

    €1,400 is invested at 6% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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15. 15.

    Find the perimeter of a rectangle measuring 24 m by 35 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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16. 16.

    A triangle has a base of 5 cm and a height of 23 cm. Find its area.

    Formula:Area of a Triangle

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

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17. 17.

    A right-angled triangle has legs of 11 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    Find the mean (average) of these numbers: 86, 44, 31, 10, 19.

    Formula:Arithmetic Mean

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

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19. 19.

    A car travels 474 km in 6 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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20. 20.

    Solve for x: 6x + 5 = 65.

    Formula:Solving a Linear Equation

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

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