Austria · Klasse 11 · Practice Sheet 38

1. 1.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 8 and common difference d = 2.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   In a triangle, a = 5, b = 14 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 →
3. 3.

   An object has mass 65.1 g and volume 21 cm³. Find its density.

   Formula:Density

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

   View formula →
4. 4.

   Find the sum of the first 5 terms of a geometric series with first term a = 5 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

   View formula →
5. 5.

   Find the population standard deviation of: 19, 2, 6, 17, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
6. 6.

   A population of 2,300 grows 10% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
7. 7.

   In a triangle, a = 7, b = 8 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 →
8. 8.

   An object has mass 436.1 g and volume 49 cm³. Find its density.

   Formula:Density

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

   View formula →
9. 9.

   Find the force needed to accelerate a 35 kg mass at 7.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
10. 10.

    A force of 117 N moves an object 5 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
11. 11.

    €1,100 is invested at 6% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

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

    View formula →
12. 12.

    Two masses 7,300 kg and 610 kg are 15 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

    View formula →
13. 13.

    €2,600 is invested at 8% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

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

    View formula →
14. 14.

    Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

    View formula →
15. 15.

    A current of 0.9 A flows through a 4 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
16. 16.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 12 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

    View formula →
17. 17.

    A cone has base radius 3 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
18. 18.

    A body starts at 17 m/s and accelerates at 6 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
19. 19.

    €500 is invested at 5% compound interest per annum for 4 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

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

    View formula →
20. 20.

    An object has mass 61.5 g and volume 15 cm³. Find its density.

    Formula:Density

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

    View formula →

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