Italy · Classe 10 · Practice Sheet 13

1. 1.

   A triangle has sides a = 6 cm and b = 10 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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2. 2.

   A value changes from 158 to 258. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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3. 3.

   A 25 kg object moves at 23 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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4. 4.

   Find the sum of the first 9 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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5. 5.

   Solve using the quadratic formula: x² + 7x + 12 = 0.

   Formula:Quadratic Formula

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

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6. 6.

   In a triangle, a = 14, b = 5 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   A value changes from 126 to 148. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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8. 8.

   A wave has frequency 72 Hz and wavelength 1.33 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A body starts at 9 m/s and accelerates at 5.9 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    A wave has frequency 396 Hz and wavelength 3.4 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the gravitational potential energy of a 6 kg object raised 19 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Find the force needed to accelerate a 58 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A bag has 23 equally likely marbles, of which 12 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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14. 14.

    A cone has base radius 4 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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15. 15.

    A right-angled triangle has legs of 11 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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16. 16.

    A device runs at 238 V drawing 8.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    An object has mass 97.2 g and volume 36 cm³. Find its density.

    Formula:Density

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

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18. 18.

    A population of 3,300 grows 10% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    €1,300 is invested at 8% 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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20. 20.

    A bag has 15 equally likely marbles, of which 12 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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