Japan · Grade 7 · Practice Sheet 1

1. 1.

   A bag has 28 equally likely marbles, of which 5 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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2. 2.

   A right-angled triangle has legs of 13 cm and 3 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   ¥1,800 is invested at 10% 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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4. 4.

   A train moves at 65 km/h for 4.8 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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5. 5.

   One item costs ¥20.96. Find the total cost of 11 items.

   Formula:Total Cost

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

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6. 6.

   A bag has 9 equally likely marbles, of which 7 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 right-angled triangle has legs of 3 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   A car travels 320 km in 5 hours. Find its average speed.

   Formula:Speed

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

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9. 9.

   A circle has a radius of 20 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    Solve for x: 2x + 4 = 14.

    Formula:Solving a Linear Equation

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

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11. 11.

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

    Formula:Area of a Square

    $A = s^2$

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12. 12.

    ¥2,600 is invested at 3% 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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13. 13.

    Find the circumference of a circle whose radius is 9 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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14. 14.

    Solve for x: 8x + 6 = 86.

    Formula:Solving a Linear Equation

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

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15. 15.

    Find the circumference of a circle whose radius is 26 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    A triangle has a base of 7 cm and a height of 24 cm. Find its area.

    Formula:Area of a Triangle

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

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17. 17.

    What is 25% of 270?

    Formula:Percentage of a Quantity

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

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18. 18.

    Find 1/2 of 12.

    Formula:Fraction of a Quantity

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

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19. 19.

    A triangle has a base of 27 cm and a height of 24 cm. Find its area.

    Formula:Area of a Triangle

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

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20. 20.

    Find the perimeter of a rectangle measuring 30 m by 15 m.

    Formula:Perimeter of a Rectangle

    $P = 2(l + w)$

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