Finland · Grade 12 · Practice Sheet 39

1. 1.

   In a triangle, a = 7, b = 7 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   Find the sum of the first 13 terms of an arithmetic series with first term a = 9 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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3. 3.

   A triangle has sides a = 5 cm and b = 5 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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4. 4.

   Find the force needed to accelerate a 11 kg mass at 0.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the gravitational potential energy of a 15 kg object raised 38 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   A current of 2.7 A flows through a 36 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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7. 7.

   Find the force needed to accelerate a 50 kg mass at 5.3 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A current of 5.5 A flows through a 29 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   €1,100 is invested at 8% compound interest per annum for 3 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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10. 10.

    Find the gravitational potential energy of a 21 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A device runs at 77 V drawing 7.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    €1,400 is invested at 4% compound interest per annum for 5 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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13. 13.

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

    Formula:Quadratic Formula

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

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14. 14.

    A body starts at 13 m/s and accelerates at 3.4 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    Find the population standard deviation of: 5, 16, 11, 16, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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16. 16.

    Solve using the quadratic formula: x² − 6x + 8 = 0.

    Formula:Quadratic Formula

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

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17. 17.

    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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18. 18.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 2 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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19. 19.

    Find the gravitational potential energy of a 31 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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