Vietnam · Grade 11 · Practice Sheet 6

1. 1.

   A force of 42 N moves an object 9 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   In a triangle, a = 9, b = 9 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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3. 3.

   A population of 3,200 grows 8% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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4. 4.

   A right-angled triangle has legs of 6 cm and 11 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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5. 5.

   Solve using the quadratic formula: x² − 3x − 18 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   Find the population standard deviation of: 2, 2, 18, 14, 2 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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7. 7.

   Find the gravitational potential energy of a 16 kg object raised 2 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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9. 9.

   VND 800 is invested at 3% compound interest per annum for 3 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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10. 10.

    A device runs at 75 V drawing 2.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A cylinder has radius 4 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    Solve using the quadratic formula: x² − 3x + 2 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    Find the volume of a sphere of radius 7 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    Find the force needed to accelerate a 25 kg mass at 7.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 87 N moves an object 18 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    Find the sum of the first 4 terms of a geometric series with first term a = 3 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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17. 17.

    An object with initial velocity 3 m/s accelerates at 2.5 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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18. 18.

    Find the momentum of a 15 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A force of 94 N acts on an area of 9.8 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    An object has mass 118.5 g and volume 15 cm³. Find its density.

    Formula:Density

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

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