Egypt · Grade 11 · Practice Sheet 47

1. 1.

   A force of 252 N acts on an area of 8.7 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   Solve using the quadratic formula: x² + 5x + 6 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   Find the momentum of a 48 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 5 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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6. 6.

   Solve using the quadratic formula: x² + 5x − 6 = 0.

   Formula:Quadratic Formula

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

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7. 7.

   A population of 6,600 grows 8% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   In a triangle, a = 10, b = 5 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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9. 9.

   An object has mass 77.4 g and volume 18 cm³. Find its density.

   Formula:Density

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

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10. 10.

    Find the population standard deviation of: 3, 19, 17, 17, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 9 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    A force of 82 N acts on an area of 1 m². Find the pressure.

    Formula:Pressure

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

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13. 13.

    In a triangle, a = 7, b = 15 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    Find the force needed to accelerate a 9 kg mass at 4.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    In a triangle, a = 11, b = 8 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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16. 16.

    A population of 4,400 grows 5% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    Find the momentum of a 10 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Find the sum of the first 8 terms of a geometric series with first term a = 7 and common ratio r = 2.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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19. 19.

    An object has mass 220.8 g and volume 48 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A triangle has sides a = 6 cm and b = 10 cm with an included angle C = 30°. 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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