Japan · Grade 11 · Practice Sheet 17

1. 1.

   Find the force needed to accelerate a 60 kg mass at 6.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   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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3. 3.

   Find the gravitational potential energy of a 38 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   ¥2,700 is invested at 6% 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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5. 5.

   Find the population standard deviation of: 16, 18, 12, 17, 3 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

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6. 6.

   Find the sum of the first 6 terms of a geometric series with first term a = 8 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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7. 7.

   An object has mass 100.8 g and volume 24 cm³. Find its density.

   Formula:Density

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

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8. 8.

   A wave has frequency 729 Hz and wavelength 3.97 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A body starts at 13 m/s and accelerates at 3.7 m/s² for 7 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    Solve using the quadratic formula: x² + 1x − 6 = 0.

    Formula:Quadratic Formula

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

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11. 11.

    Find the momentum of a 54 kg object moving at 20 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    In a triangle, a = 15, b = 11 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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13. 13.

    A device runs at 202 V drawing 6.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A cone has base radius 8 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    Find the population standard deviation of: 2, 16, 9, 8, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    Find the momentum of a 11 kg object moving at 8 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A triangle has sides a = 9 cm and b = 10 cm with an included angle C = 30°. 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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18. 18.

    Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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19. 19.

    Find the population standard deviation of: 13, 18, 3, 12, 5 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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20. 20.

    A population of 7,400 grows 2% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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