Ukraine · Grade 12 · Practice Sheet 33

1. 1.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 4 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   A population of 1,700 grows 2% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
3. 3.

   A wave has frequency 291 Hz and wavelength 1.27 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
4. 4.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 3 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

   View formula →
5. 5.

   An object with initial velocity 5 m/s accelerates at 4.5 m/s² for 4 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
6. 6.

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

   Formula:Quadratic Formula

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

   View formula →
7. 7.

   A wave has frequency 159 Hz and wavelength 2.5 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
8. 8.

   Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

   View formula →
9. 9.

   Find the population standard deviation of: 4, 2, 19, 6, 6 (to 2 d.p.).

   Formula:Standard Deviation (Population)

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

   View formula →
10. 10.

    A wave has frequency 733 Hz and wavelength 0.66 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
11. 11.

    A force of 499 N acts on an area of 4.1 m². Find the pressure.

    Formula:Pressure

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

    View formula →
12. 12.

    An object with initial velocity 10 m/s accelerates at 3 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
13. 13.

    Solve using the quadratic formula: x² + 9x + 20 = 0.

    Formula:Quadratic Formula

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

    View formula →
14. 14.

    Find the force needed to accelerate a 30 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
15. 15.

    A device runs at 214 V drawing 1.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
16. 16.

    In a triangle, a = 14, b = 6 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
17. 17.

    Solve using the quadratic formula: x² + 6x + 5 = 0.

    Formula:Quadratic Formula

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

    View formula →
18. 18.

    A device runs at 197 V drawing 2.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
19. 19.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 2 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

    View formula →
20. 20.

    Find the force needed to accelerate a 58 kg mass at 2.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →

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