United Kingdom · Year 11 · Practice Sheet 29

1. 1.

   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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2. 2.

   An object has mass 378 g and volume 42 cm³. Find its density.

   Formula:Density

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

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3. 3.

   An object with initial velocity 1 m/s accelerates at 1.7 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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4. 4.

   A device runs at 124 V drawing 3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A cone has base radius 12 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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6. 6.

   An object has mass 86.4 g and volume 48 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A current of 7.2 A flows through a 34 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   Solve using the quadratic formula: x² − 7x + 6 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the force needed to accelerate a 7 kg mass at 3.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    Two masses 3,500 kg and 680 kg are 5 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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11. 11.

    Find the momentum of a 52 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A population of 3,500 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A wave has frequency 477 Hz and wavelength 2.48 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A body starts at 9 m/s and accelerates at 1.1 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    A cylinder has radius 3 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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16. 16.

    In a triangle, a = 10, b = 12 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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17. 17.

    An object has mass 27.2 g and volume 16 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Find the sum of the first 20 terms of an arithmetic series with first term a = 5 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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20. 20.

    A force of 366 N acts on an area of 1.5 m². Find the pressure.

    Formula:Pressure

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

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