Indonesia · Grade 11 · Practice Sheet 6

1. 1.

   An object has mass 114 g and volume 20 cm³. Find its density.

   Formula:Density

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

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2. 2.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 6 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   In a triangle, a = 17, b = 12 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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4. 4.

   Find the population standard deviation of: 8, 15, 10, 10, 16 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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5. 5.

   Find the momentum of a 52 kg object moving at 25 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   A cone has base radius 5 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A population of 3,600 grows 5% per year. Find its size after 7 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   Find the force needed to accelerate a 6 kg mass at 7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A force of 263 N acts on an area of 4.2 m². Find the pressure.

   Formula:Pressure

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

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10. 10.

    A triangle has sides a = 8 cm and b = 14 cm with an included angle C = 45°. 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 momentum of a 31 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A right-angled triangle has legs of 10 cm and 6 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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13. 13.

    Find the sum of the first 4 terms of a geometric series with first term a = 2 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Find the force needed to accelerate a 9 kg mass at 5.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A force of 245 N acts on an area of 5.5 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A device runs at 218 V drawing 7.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the population standard deviation of: 7, 7, 2, 9, 2 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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18. 18.

    A body starts at 12 m/s and accelerates at 1.8 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    A triangle has sides a = 7 cm and b = 15 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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20. 20.

    Find the momentum of a 25 kg object moving at 30 m/s.

    Formula:Momentum

    $p = mv$

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