Taiwan · Grade 9 · Practice Sheet 27

1. 1.

   Find the circumference of a circle whose radius is 14 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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2. 2.

   A current of 1.8 A flows through a 56 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   Find the gravitational potential energy of a 3 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   Find the force needed to accelerate a 44 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A value changes from 74 to 104. 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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6. 6.

   A train moves at 83 km/h for 4 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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7. 7.

   A bag has 19 equally likely marbles, of which 11 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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8. 8.

   Find the force needed to accelerate a 2 kg mass at 3.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 106 N moves an object 8 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A wave has frequency 439 Hz and wavelength 0.57 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A right-angled triangle has legs of 9 cm and 5 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    NT$ 100 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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13. 13.

    Solve for x: 9x + 8 = 35.

    Formula:Solving a Linear Equation

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

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14. 14.

    A circle has a radius of 14 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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15. 15.

    A right-angled triangle has legs of 10 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    NT$ 3,100 is invested at 3% compound interest per annum for 3 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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17. 17.

    A cone has base radius 12 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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18. 18.

    A right-angled triangle has legs of 6 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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19. 19.

    A 8 kg object moves at 13 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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20. 20.

    A car travels 144 km in 2 hours. Find its average speed.

    Formula:Speed

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

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