New Zealand · Year 7 · Practice Sheet 41

1. 1.

   A train moves at 27 km/h for 5.1 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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2. 2.

   A value changes from 45 to 155. 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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3. 3.

   A circle has a radius of 23 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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4. 4.

   A right-angled triangle has legs of 4 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   $297 is shared in the ratio 5 : 4. 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 car travels 208 km in 2 hours. Find its average speed.

   Formula:Speed

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

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7. 7.

   Find the circumference of a circle whose radius is 29 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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8. 8.

   A triangle has a base of 11 cm and a height of 30 cm. Find its area.

   Formula:Area of a Triangle

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

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9. 9.

   $87 is shared in the ratio 1 : 2. Find each share.

   Formula:Dividing in a Ratio

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

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10. 10.

    A triangle has a base of 18 cm and a height of 7 cm. Find its area.

    Formula:Area of a Triangle

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

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11. 11.

    What is 12% of 170?

    Formula:Percentage of a Quantity

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

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12. 12.

    A right-angled triangle has legs of 6 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    A value changes from 127 to 91. 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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14. 14.

    Find the area of a square with side length 17 cm.

    Formula:Area of a Square

    $A = s^2$

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15. 15.

    Find the perimeter of a rectangle measuring 35 m by 14 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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16. 16.

    Solve for x: 9x + 2 = 65.

    Formula:Solving a Linear Equation

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

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17. 17.

    Find the perimeter of a rectangle measuring 15 m by 4 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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18. 18.

    A car travels 207 km in 3 hours. Find its average speed.

    Formula:Speed

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

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19. 19.

    A triangle has a base of 23 cm and a height of 27 cm. Find its area.

    Formula:Area of a Triangle

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

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20. 20.

    A bag has 8 equally likely marbles, of which 1 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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