Canada · Grade 12 · Practice Sheet 27

1. 1.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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2. 2.

   Solve using the quadratic formula: x² − 1x − 2 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A cone has base radius 2 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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4. 4.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 7 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   Find the force needed to accelerate a 51 kg mass at 7.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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7. 7.

   Solve using the quadratic formula: x² − 11x + 30 = 0.

   Formula:Quadratic Formula

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

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8. 8.

   A force of 111 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   Find the population standard deviation of: 14, 8, 17, 12, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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10. 10.

    A force of 53 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    A population of 2,300 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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12. 12.

    A device runs at 35 V drawing 4.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    Find the momentum of a 5 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A body starts at 3 m/s and accelerates at 1.6 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A device runs at 31 V drawing 3.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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16. 16.

    A triangle has sides a = 18 cm and b = 8 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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17. 17.

    A force of 91 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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18. 18.

    In a triangle, a = 7, b = 17 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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19. 19.

    Find the gravitational potential energy of a 23 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    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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