Taiwan · Grade 9 · Practice Sheet 12

1. 1.

   Solve for x: 8x + 13 = 61.

   Formula:Solving a Linear Equation

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

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2. 2.

   Find the force needed to accelerate a 47 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   NT$ 4,600 is invested at 10% 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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4. 4.

   Find the momentum of a 40 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the circumference of a circle whose radius is 16 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   Find the force needed to accelerate a 41 kg mass at 4.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A cylinder has radius 3 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   An object has mass 234.6 g and volume 46 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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9. 9.

   NT$ 168 is shared in the ratio 5 : 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 force of 181 N acts on an area of 5.4 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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11. 11.

    A value changes from 38 to 69. 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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12. 12.

    A wave has frequency 92 Hz and wavelength 0.69 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    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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14. 14.

    Find the circumference of a circle whose radius is 8 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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15. 15.

    NT$ 1,800 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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16. 16.

    A car travels 310 km in 5 hours. Find its average speed.

    Formula:Speed

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

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17. 17.

    Solve for x: 9x + 12 = 66.

    Formula:Solving a Linear Equation

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

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18. 18.

    Find the gravitational potential energy of a 37 kg object raised 40 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    NT$ 2,900 is invested at 4% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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20. 20.

    NT$ 135 is shared in the ratio 3 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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