Colombia · Grado 12 · Practice Sheet 31

1. 1.

   Find the sum of the first 5 terms of a geometric series with first term a = 1 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

   View formula →
2. 2.

   Find the population standard deviation of: 10, 7, 18, 7, 20 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
3. 3.

   In a triangle, a = 18, b = 15 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
4. 4.

   A 4 kg object moves at 24 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
5. 5.

   $700 is invested at 6% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

   View formula →
6. 6.

   A device runs at 210 V drawing 1.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
7. 7.

   A triangle has sides a = 5 cm and b = 12 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

   View formula →
8. 8.

   Find the sum of the first 8 terms of a geometric series with first term a = 7 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

   View formula →
9. 9.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 4 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

   View formula →
10. 10.

    A current of 5.3 A flows through a 34 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
11. 11.

    Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

    View formula →
12. 12.

    A 17 kg object moves at 5 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
13. 13.

    Find the force needed to accelerate a 28 kg mass at 3.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
14. 14.

    In a triangle, a = 12, b = 5 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
15. 15.

    A current of 5.7 A flows through a 8 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
16. 16.

    In a triangle, a = 7, b = 13 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
17. 17.

    Find the momentum of a 42 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
18. 18.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 9 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

    View formula →
19. 19.

    Find the gravitational potential energy of a 19 kg object raised 29 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
20. 20.

    An object with initial velocity 13 m/s accelerates at 5 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.