Japan · Grade 7 · Practice Sheet 48

1. 1.

   Solve for x: 9x + 4 = 31.

   Formula:Solving a Linear Equation

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

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2. 2.

   A right-angled triangle has legs of 13 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 15 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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4. 4.

   What is 5% of 390?

   Formula:Percentage of a Quantity

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

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5. 5.

   ¥66 is shared in the ratio 3 : 3. Find each share.

   Formula:Dividing in a Ratio

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

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6. 6.

   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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7. 7.

   A triangle has a base of 19 cm and a height of 22 cm. Find its area.

   Formula:Area of a Triangle

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

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8. 8.

   One item costs ¥18.45. Find the total cost of 11 items.

   Formula:Total Cost

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

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9. 9.

   What is 75% of 580?

   Formula:Percentage of a Quantity

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

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10. 10.

    A right-angled triangle has legs of 7 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    Find the perimeter of a rectangle measuring 18 m by 4 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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12. 12.

    Solve for x: 3x + 16 = 49.

    Formula:Solving a Linear Equation

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

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13. 13.

    Find the area of a square with side length 25 cm.

    Formula:Area of a Square

    $A = s^2$

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14. 14.

    Find 1/2 of 38.

    Formula:Fraction of a Quantity

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

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15. 15.

    A train moves at 78 km/h for 3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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16. 16.

    A bag has 16 equally likely marbles, of which 9 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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17. 17.

    Solve for x: 9x + 7 = 79.

    Formula:Solving a Linear Equation

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

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18. 18.

    A value changes from 111 to 60. 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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19. 19.

    ¥1,300 is invested at 4% 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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20. 20.

    A value changes from 162 to 180. 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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