Taiwan · Grade 10 · Practice Sheet 25

1. 1.

   A cylinder has radius 11 cm and height 20 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   A cone has base radius 12 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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3. 3.

   NT$ 2,500 is invested at 6% compound interest per annum for 4 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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4. 4.

   A value changes from 98 to 175. 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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5. 5.

   A wave has frequency 886 Hz and wavelength 2.11 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A cone has base radius 10 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   An object has mass 72.9 g and volume 27 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A device runs at 63 V drawing 5.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A body starts at 5 m/s and accelerates at 3.7 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    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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11. 11.

    A value changes from 85 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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12. 12.

    Find the momentum of a 16 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A current of 6.3 A flows through a 22 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    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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15. 15.

    A cone has base radius 8 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    A bag has 18 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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17. 17.

    A cylinder has radius 5 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    Find the gravitational potential energy of a 26 kg object raised 28 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Solve using the quadratic formula: x² − 8x + 12 = 0.

    Formula:Quadratic Formula

    $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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20. 20.

    A force of 13 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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