Ecuador · Grado 12 · Practice Sheet 18

1. 1.

   $1,000 is invested at 3% 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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2. 2.

   A body starts at 13 m/s and accelerates at 5.1 m/s² for 4 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

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

   Formula:Quadratic Formula

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

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4. 4.

   Find the force needed to accelerate a 6 kg mass at 6.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   An object with initial velocity 5 m/s accelerates at 4.2 m/s² for 2 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

   $s = ut + \tfrac{1}{2}at^2$

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6. 6.

   $3,500 is invested at 5% compound interest per annum for 4 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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7. 7.

   Find the momentum of a 4 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   Find the gravitational potential energy of a 45 kg object raised 30 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A body starts at 7 m/s and accelerates at 2.1 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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10. 10.

    Find the gravitational potential energy of a 40 kg object raised 10 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the force needed to accelerate a 2 kg mass at 0.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A triangle has sides a = 7 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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13. 13.

    In a triangle, a = 14, b = 14 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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14. 14.

    A cone has base radius 8 cm and height 10 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.

    $2,100 is invested at 5% 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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16. 16.

    A force of 110 N acts on an area of 2.8 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    Find the force needed to accelerate a 51 kg mass at 7.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A current of 6.2 A flows through a 9 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    A 40 kg object moves at 2 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A wave has frequency 867 Hz and wavelength 2.22 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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