United Arab Emirates · Grade 11 · Practice Sheet 16

1. 1.

   A triangle has sides a = 5 cm and b = 5 cm with an included angle C = 60°. 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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2. 2.

   A 24 kg object moves at 7 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   Find the force needed to accelerate a 29 kg mass at 1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A right-angled triangle has legs of 15 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Find the force needed to accelerate a 37 kg mass at 3.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A cylinder has radius 7 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the force needed to accelerate a 43 kg mass at 7.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   Find the population standard deviation of: 13, 3, 10, 18, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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10. 10.

    AED 1,100 is invested at 5% compound interest per annum for 2 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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11. 11.

    A force of 80 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    An object has mass 34.8 g and volume 29 cm³. Find its density.

    Formula:Density

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

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13. 13.

    A current of 3.9 A flows through a 47 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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14. 14.

    A force of 101 N moves an object 3 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A triangle has sides a = 13 cm and b = 6 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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16. 16.

    In a triangle, a = 10, b = 17 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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17. 17.

    An object with initial velocity 4 m/s accelerates at 4.2 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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18. 18.

    Find the momentum of a 5 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 235 N acts on an area of 2.4 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Solve using the quadratic formula: x² − 2x − 15 = 0.

    Formula:Quadratic Formula

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

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