Spain · Grado 11 · Practice Sheet 33

1. 1.

   A triangle has sides a = 5 cm and b = 12 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.

   Find the sum of the first 18 terms of an arithmetic series with first term a = 10 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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3. 3.

   A body starts at 2 m/s and accelerates at 3.2 m/s² for 8 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   A force of 87 N moves an object 25 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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5. 5.

   A 37 kg object moves at 17 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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6. 6.

   A wave has frequency 310 Hz and wavelength 4.82 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   A body starts at 17 m/s and accelerates at 5.1 m/s² for 6 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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8. 8.

   A device runs at 238 V drawing 9.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   A right-angled triangle has legs of 6 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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10. 10.

    A device runs at 111 V drawing 1.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    Find the gravitational potential energy of a 23 kg object raised 16 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    An object has mass 316.8 g and volume 44 cm³. Find its density.

    Formula:Density

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

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13. 13.

    €3,100 is invested at 6% 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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14. 14.

    A body starts at 15 m/s and accelerates at 2.8 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

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

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A population of 1,400 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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17. 17.

    A device runs at 41 V drawing 2.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    A force of 34 N acts on an area of 1.8 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    A body starts at 6 m/s and accelerates at 5.8 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A right-angled triangle has legs of 15 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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