Thailand · Grade 10 · Practice Sheet 36

1. 1.

   A body starts at 1 m/s and accelerates at 4.5 m/s² for 12 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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2. 2.

   In a triangle, a = 16, b = 7 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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3. 3.

   A triangle has sides a = 5 cm and b = 8 cm with an included angle C = 45°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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4. 4.

   ฿1,000 is invested at 8% 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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5. 5.

   A device runs at 174 V drawing 3.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   Find the momentum of a 19 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A value changes from 45 to 65. 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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8. 8.

   A force of 358 N acts on an area of 5 m². Find the pressure.

   Formula:Pressure

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

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9. 9.

   Find the force needed to accelerate a 13 kg mass at 3.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    A value changes from 198 to 233. 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 4 cm and height 14 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.

    A population of 6,300 grows 2% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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13. 13.

    A cylinder has radius 13 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    Solve using the quadratic formula: x² − 7x + 12 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    An object with initial velocity 15 m/s accelerates at 3.6 m/s² for 4 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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16. 16.

    A current of 4.6 A flows through a 6 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    In a triangle, a = 17, b = 9 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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18. 18.

    Find the gravitational potential energy of a 19 kg object raised 33 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Find the force needed to accelerate a 7 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Solve for x: 3x + 10 = 37.

    Formula:Solving a Linear Equation

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

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