Austria · Klasse 10 · Practice Sheet 25

1. 1.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 12 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   Find the force needed to accelerate a 29 kg mass at 6.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
3. 3.

   In a triangle, a = 7, b = 14 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

   View formula →
4. 4.

   A population of 8,900 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
5. 5.

   A body starts at 18 m/s and accelerates at 4.2 m/s² for 11 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

   View formula →
6. 6.

   Find the force needed to accelerate a 40 kg mass at 7.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
7. 7.

   A force of 26 N moves an object 18 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
8. 8.

   A current of 0.7 A flows through a 17 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
9. 9.

   Solve using the quadratic formula: x² − 9x + 18 = 0.

   Formula:Quadratic Formula

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

   View formula →
10. 10.

    A right-angled triangle has legs of 5 cm and 13 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

    View formula →
11. 11.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 1 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

    View formula →
12. 12.

    A 29 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
13. 13.

    A cylinder has radius 3 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
14. 14.

    A wave has frequency 877 Hz and wavelength 1.23 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
15. 15.

    A cylinder has radius 3 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
16. 16.

    A force of 91 N moves an object 33 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
17. 17.

    In a triangle, a = 9, b = 5 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
18. 18.

    Find the force needed to accelerate a 46 kg mass at 2.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
19. 19.

    Find the gravitational potential energy of a 50 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
20. 20.

    An object has mass 163.3 g and volume 23 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.