Algeria · Grade 11 · Practice Sheet 5

1. 1.

   Find the sum of the first 8 terms of a geometric series with first term a = 2 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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2. 2.

   In a triangle, a = 13, b = 11 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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3. 3.

   A device runs at 131 V drawing 7.2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the momentum of a 24 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

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5. 5.

   Two masses 1,400 kg and 540 kg are 19 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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6. 6.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 11 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

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7. 7.

   A device runs at 84 V drawing 2 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Find the gravitational potential energy of a 8 kg object raised 24 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A cylinder has radius 12 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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10. 10.

    Find the sum of the first 5 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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11. 11.

    In a triangle, a = 11, b = 13 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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12. 12.

    A population of 6,800 grows 5% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the force needed to accelerate a 27 kg mass at 0.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    A cone has base radius 8 cm and height 4 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 volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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16. 16.

    A force of 297 N acts on an area of 8.9 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    DA 3,500 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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18. 18.

    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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19. 19.

    Find the force needed to accelerate a 40 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the momentum of a 20 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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