Ghana · Grade 11 · Practice Sheet 15

1. 1.

   Solve using the quadratic formula: x² + 4x − 5 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   An object with initial velocity 2 m/s accelerates at 2.5 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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3. 3.

   A device runs at 218 V drawing 5.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   A body starts at 1 m/s and accelerates at 2.6 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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5. 5.

   An object with initial velocity 9 m/s accelerates at 1.5 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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6. 6.

   A triangle has sides a = 16 cm and b = 8 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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7. 7.

   Find the force needed to accelerate a 30 kg mass at 8.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A current of 4.4 A flows through a 50 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

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

   Formula:Quadratic Formula

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

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10. 10.

    A wave has frequency 241 Hz and wavelength 1.91 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

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

    Formula:Volume of a Cone

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

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12. 12.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 2 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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13. 13.

    A population of 4,100 grows 5% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    A force of 99 N moves an object 20 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    A body starts at 19 m/s and accelerates at 2.1 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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16. 16.

    Find the force needed to accelerate a 29 kg mass at 2.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    In a triangle, a = 11, b = 13 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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18. 18.

    A device runs at 182 V drawing 8.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A cone has base radius 12 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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20. 20.

    An object has mass 201.6 g and volume 28 cm³. Find its density.

    Formula:Density

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

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