Qatar · Grade 11 · Practice Sheet 47

1. 1.

   Find the gravitational potential energy of a 10 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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2. 2.

   A wave has frequency 743 Hz and wavelength 2.05 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A population of 5,600 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   Find the gravitational potential energy of a 41 kg object raised 38 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   In a triangle, a = 10, b = 11 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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6. 6.

   A population of 3,100 grows 5% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   QAR 800 is invested at 6% 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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8. 8.

   A triangle has sides a = 15 cm and b = 20 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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9. 9.

   In a triangle, a = 16, 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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10. 10.

    A wave has frequency 522 Hz and wavelength 4.78 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A body starts at 20 m/s and accelerates at 3.9 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A 9 kg object moves at 3 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A triangle has sides a = 18 cm and b = 11 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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14. 14.

    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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15. 15.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 8 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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17. 17.

    A cylinder has radius 10 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    Find the force needed to accelerate a 9 kg mass at 8.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    Find the sum of the first 5 terms of a geometric series with first term a = 3 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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