Denmark · Grade 11 · Practice Sheet 23

1. 1.

   A population of 2,900 grows 3% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   Solve using the quadratic formula: x² − 3x + 0 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A triangle has sides a = 8 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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4. 4.

   A wave has frequency 336 Hz and wavelength 0.52 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A cylinder has radius 3 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   A population of 6,000 grows 8% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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7. 7.

   Find the gravitational potential energy of a 12 kg object raised 11 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   An object with initial velocity 10 m/s accelerates at 2.6 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   A population of 4,800 grows 10% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    In a triangle, a = 14, b = 17 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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11. 11.

    An object with initial velocity 9 m/s accelerates at 3.9 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    Find the momentum of a 15 kg object moving at 14 m/s.

    Formula:Momentum

    $p = mv$

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13. 13.

    A device runs at 141 V drawing 0.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    In a triangle, a = 11, b = 16 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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15. 15.

    Find the force needed to accelerate a 52 kg mass at 5.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A force of 15 N moves an object 24 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the momentum of a 24 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 295 N acts on an area of 2.1 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Find the force needed to accelerate a 41 kg mass at 5.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    An object has mass 125.4 g and volume 22 cm³. Find its density.

    Formula:Density

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

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