Ghana · Grade 12 · Practice Sheet 7

1. 1.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 6 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   A wave has frequency 67 Hz and wavelength 1.54 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A triangle has sides a = 6 cm and b = 17 cm with an included angle C = 90°. 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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4. 4.

   A device runs at 54 V drawing 3.8 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   Find the force needed to accelerate a 39 kg mass at 1.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A cone has base radius 2 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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7. 7.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A 4 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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9. 9.

   Solve using the quadratic formula: x² − 4x − 12 = 0.

   Formula:Quadratic Formula

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

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10. 10.

    A force of 47 N moves an object 32 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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11. 11.

    In a triangle, a = 10, b = 8 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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12. 12.

    An object with initial velocity 5 m/s accelerates at 1.7 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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13. 13.

    Find the population standard deviation of: 11, 4, 15, 11, 15 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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14. 14.

    A force of 26 N moves an object 14 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    GH₵ 3,000 is invested at 5% compound interest per annum for 4 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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16. 16.

    An object with initial velocity 15 m/s accelerates at 4.9 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    In a triangle, a = 5, b = 12 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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18. 18.

    Find the population standard deviation of: 7, 19, 8, 13, 10 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A force of 329 N acts on an area of 5.5 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A force of 67 N moves an object 22 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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