Canada · Grade 12 · Practice Sheet 16

1. 1.

   In a triangle, a = 10, b = 8 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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2. 2.

   A force of 250 N acts on an area of 4 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   A population of 8,600 grows 2% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   $2,500 is invested at 3% 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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6. 6.

   A force of 234 N acts on an area of 4.3 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   A wave has frequency 840 Hz and wavelength 4.26 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A body starts at 9 m/s and accelerates at 1.3 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A wave has frequency 92 Hz and wavelength 0.74 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A triangle has sides a = 12 cm and b = 18 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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11. 11.

    Find the sum of the first 8 terms of a geometric series with first term a = 6 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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12. 12.

    Find the force needed to accelerate a 48 kg mass at 1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A device runs at 131 V drawing 9.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    Find the force needed to accelerate a 12 kg mass at 2.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 36 N acts on an area of 2.2 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A wave has frequency 861 Hz and wavelength 2.34 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Find the momentum of a 20 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A body starts at 20 m/s and accelerates at 1.4 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A 27 kg object moves at 15 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A wave has frequency 809 Hz and wavelength 2.7 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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