Portugal · Ano 10 · Practice Sheet 8

1. 1.

   A triangle has sides a = 14 cm and b = 19 cm with an included angle C = 45°. 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.

   In a triangle, a = 11, b = 7 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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3. 3.

   A cone has base radius 8 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   A wave has frequency 270 Hz and wavelength 0.39 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the gravitational potential energy of a 30 kg object raised 4 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   A cone has base radius 10 cm and height 19 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.

   A cylinder has radius 6 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 5 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   A body starts at 16 m/s and accelerates at 1.6 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    A 38 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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11. 11.

    A device runs at 224 V drawing 6.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the force needed to accelerate a 52 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    A force of 28 N moves an object 2 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    A force of 434 N acts on an area of 4.9 m². Find the pressure.

    Formula:Pressure

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

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15. 15.

    A wave has frequency 687 Hz and wavelength 3.72 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A device runs at 195 V drawing 7.5 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    €3,300 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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18. 18.

    Find the momentum of a 11 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A population of 6,600 grows 5% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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20. 20.

    Solve for x: 3x + 19 = 46.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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