Thailand · Grade 10 · Practice Sheet 6

1. 1.

   Solve using the quadratic formula: x² + 2x − 8 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   An object has mass 28.8 g and volume 24 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A 32 kg object moves at 25 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   A cone has base radius 7 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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5. 5.

   Find the force needed to accelerate a 4 kg mass at 5.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A body starts at 13 m/s and accelerates at 1 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   In a triangle, a = 5, b = 9 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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8. 8.

   A current of 1.3 A flows through a 36 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Find the force needed to accelerate a 45 kg mass at 7.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A force of 45 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A value changes from 33 to 197. 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 59 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    Find the gravitational potential energy of a 35 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Find the force needed to accelerate a 16 kg mass at 6.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A device runs at 95 V drawing 4.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A cone has base radius 6 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    A device runs at 101 V drawing 6.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    In a triangle, a = 8, b = 10 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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19. 19.

    ฿3,800 is invested at 4% 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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20. 20.

    Find the momentum of a 49 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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