China · Grade 9 · Practice Sheet 8

1. 1.

   Solve for x: 2x + 16 = 30.

   Formula:Solving a Linear Equation

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

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2. 2.

   ¥2,900 is invested at 5% 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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3. 3.

   A cylinder has radius 14 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   Find the circumference of a circle whose radius is 22 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   A value changes from 193 to 209. 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.

   An object has mass 45.9 g and volume 17 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A right-angled triangle has legs of 15 cm and 16 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   A bag has 17 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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9. 9.

   A force of 10 N moves an object 39 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A value changes from 61 to 165. 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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11. 11.

    A cone has base radius 7 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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12. 12.

    ¥56 is shared in the ratio 3 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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13. 13.

    A bag has 22 equally likely marbles, of which 3 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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14. 14.

    A force of 60 N acts on an area of 6.2 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    Find the gravitational potential energy of a 10 kg object raised 9 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A force of 257 N acts on an area of 5.4 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the circumference of a circle whose radius is 22 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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18. 18.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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19. 19.

    A wave has frequency 163 Hz and wavelength 4.44 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    A current of 4.6 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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