Canada · Grade 11 · Practice Sheet 12

1. 1.

   An object with initial velocity 7 m/s accelerates at 3 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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2. 2.

   An object has mass 225.6 g and volume 47 cm³. Find its density.

   Formula:Density

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

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3. 3.

   A force of 154 N acts on an area of 0.6 m². Find the pressure.

   Formula:Pressure

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

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4. 4.

   A right-angled triangle has legs of 19 cm and 15 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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5. 5.

   A 6 kg object moves at 14 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   A force of 245 N acts on an area of 4.1 m². Find the pressure.

   Formula:Pressure

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

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7. 7.

   Find the population standard deviation of: 7, 11, 13, 10, 10 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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8. 8.

   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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9. 9.

   A population of 5,500 grows 2% 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.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 5 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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11. 11.

    A right-angled triangle has legs of 20 cm and 16 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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12. 12.

    A device runs at 117 V drawing 8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A force of 14 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    In a triangle, a = 6, b = 10 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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15. 15.

    Solve using the quadratic formula: x² + 9x + 20 = 0.

    Formula:Quadratic Formula

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

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16. 16.

    A force of 23 N moves an object 30 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 force needed to accelerate a 27 kg mass at 2.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    $1,400 is invested at 4% 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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19. 19.

    Find the population standard deviation of: 6, 11, 5, 3, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    Find the sum of the first 6 terms of a geometric series with first term a = 1 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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