Japan · Grade 7 · Practice Sheet 18

1. 1.

   ¥72 is shared in the ratio 1 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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2. 2.

   A right-angled triangle has legs of 9 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 triangle has a base of 8 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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4. 4.

   Convert 9.56 kilometres into metres.

   Formula:Metric Length Conversion

   $1\,\text{km} = 1000\,\text{m}$

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5. 5.

   ¥800 is invested at 8% 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 bag has 19 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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7. 7.

   A train moves at 46 km/h for 4.9 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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8. 8.

   Solve for x: 3x + 4 = 40.

   Formula:Solving a Linear Equation

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

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9. 9.

   A bag has 10 equally likely marbles, of which 4 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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10. 10.

    A circle has a radius of 21 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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11. 11.

    Solve for x: 9x + 9 = 108.

    Formula:Solving a Linear Equation

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

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12. 12.

    Find the area of a square with side length 12 cm.

    Formula:Area of a Square

    $A = s^2$

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13. 13.

    A triangle has a base of 7 cm and a height of 12 cm. Find its area.

    Formula:Area of a Triangle

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

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14. 14.

    One item costs ¥2.04. Find the total cost of 4 items.

    Formula:Total Cost

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

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15. 15.

    What is 15% of 130?

    Formula:Percentage of a Quantity

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

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16. 16.

    Find 3/5 of 65.

    Formula:Fraction of a Quantity

    $\text{result} = \dfrac{a}{b} \times N$

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17. 17.

    A triangle has a base of 20 cm and a height of 29 cm. Find its area.

    Formula:Area of a Triangle

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

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18. 18.

    Find 4/5 of 25.

    Formula:Fraction of a Quantity

    $\text{result} = \dfrac{a}{b} \times N$

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19. 19.

    ¥3,200 is invested at 6% 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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20. 20.

    A train moves at 38 km/h for 5.4 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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