Spain · Grado 11 · Practice Sheet 22

1. 1.

   A force of 324 N acts on an area of 7.8 m². Find the pressure.

   Formula:Pressure

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

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2. 2.

   Find the momentum of a 17 kg object moving at 18 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   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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4. 4.

   Find the force needed to accelerate a 36 kg mass at 7.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   €3,400 is invested at 6% compound interest per annum for 2 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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6. 6.

   A right-angled triangle has legs of 13 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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7. 7.

   A body starts at 17 m/s and accelerates at 3.8 m/s² for 10 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   Find the force needed to accelerate a 58 kg mass at 0.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A cone has base radius 2 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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10. 10.

    Find the population standard deviation of: 9, 5, 2, 5, 20 (to 2 d.p.).

    Formula:Standard Deviation (Population)

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

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11. 11.

    A cone has base radius 2 cm and height 24 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.

    A current of 2.9 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A wave has frequency 573 Hz and wavelength 0.54 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    Two masses 7,900 kg and 510 kg are 14 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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15. 15.

    In a triangle, a = 5, b = 14 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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16. 16.

    A population of 8,900 grows 3% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    In a triangle, a = 16, 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 sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 4.

    Formula:Sum of a Geometric Series

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

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19. 19.

    A body starts at 1 m/s and accelerates at 3.4 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 6 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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