Greece · Grade 11 · Practice Sheet 26

1. 1.

   A population of 7,200 grows 2% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
2. 2.

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

   Formula:Sum of a Geometric Series

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

   View formula →
3. 3.

   Two masses 5,600 kg and 680 kg are 6 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 →
4. 4.

   A current of 2.9 A flows through a 31 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
5. 5.

   An object with initial velocity 10 m/s accelerates at 3.3 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
6. 6.

   Find the momentum of a 4 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
7. 7.

   Find the population standard deviation of: 19, 10, 13, 13, 12 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
8. 8.

   A cylinder has radius 10 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

   View formula →
9. 9.

   A cone has base radius 4 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
10. 10.

    A cylinder has radius 9 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
11. 11.

    A right-angled triangle has legs of 12 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

    View formula →
12. 12.

    An object with initial velocity 15 m/s accelerates at 4.3 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
13. 13.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 11 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

    View formula →
14. 14.

    A population of 7,700 grows 5% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
15. 15.

    A triangle has sides a = 12 cm and b = 9 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 →
16. 16.

    A body starts at 6 m/s and accelerates at 2.1 m/s² for 6 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
17. 17.

    A 21 kg object moves at 16 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
18. 18.

    Solve using the quadratic formula: x² + 1x − 2 = 0.

    Formula:Quadratic Formula

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

    View formula →
19. 19.

    An object with initial velocity 14 m/s accelerates at 3.8 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
20. 20.

    €1,500 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 →

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