Spain · Grado 12 · Practice Sheet 41

1. 1.

   A 17 kg object moves at 14 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 8 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   A device runs at 197 V drawing 7.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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5. 5.

   A cone has base radius 7 cm and height 15 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.

   A device runs at 208 V drawing 10 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   Find the force needed to accelerate a 22 kg mass at 3.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   €1,900 is invested at 8% 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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9. 9.

   Find the gravitational potential energy of a 33 kg object raised 40 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    Find the population standard deviation of: 6, 7, 4, 13, 9 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    A force of 95 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A population of 1,900 grows 8% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    €800 is invested at 6% 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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14. 14.

    Solve using the quadratic formula: x² − 9x + 20 = 0.

    Formula:Quadratic Formula

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

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15. 15.

    A triangle has sides a = 18 cm and b = 17 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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16. 16.

    A force of 20 N moves an object 12 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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17. 17.

    Find the sum of the first 7 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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18. 18.

    Find the population standard deviation of: 5, 2, 8, 2, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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19. 19.

    A triangle has sides a = 6 cm and b = 8 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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20. 20.

    A cone has base radius 4 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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