Philippines · Grade 10 · Practice Sheet 49

1. 1.

   In a triangle, a = 8, b = 18 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   A force of 151 N acts on an area of 8.1 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   An object has mass 308 g and volume 44 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A triangle has sides a = 18 cm and b = 18 cm with an included angle C = 120°. 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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5. 5.

   In a triangle, a = 16, b = 7 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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6. 6.

   A force of 178 N acts on an area of 7.8 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the gravitational potential energy of a 40 kg object raised 34 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 5 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

   $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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9. 9.

   Find the momentum of a 19 kg object moving at 21 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A device runs at 104 V drawing 4.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A 35 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    A body starts at 13 m/s and accelerates at 3.9 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    An object has mass 162 g and volume 18 cm³. Find its density.

    Formula:Density

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

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14. 14.

    A cone has base radius 10 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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15. 15.

    Find the momentum of a 13 kg object moving at 17 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    A right-angled triangle has legs of 19 cm and 7 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    Find the force needed to accelerate a 9 kg mass at 4.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A value changes from 146 to 61. 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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19. 19.

    A current of 2 A flows through a 57 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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20. 20.

    A force of 326 N acts on an area of 6.5 m². Find the pressure.

    Formula:Pressure

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

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