Mongolia · Grade 10 · Practice Sheet 27

1. 1.

   Solve using the quadratic formula: x² + 2x − 24 = 0.

   Formula:Quadratic Formula

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

   View formula →
2. 2.

   A value changes from 159 to 95. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

   View formula →
3. 3.

   An object with initial velocity 14 m/s accelerates at 1.6 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
4. 4.

   An object has mass 20.4 g and volume 12 cm³. Find its density.

   Formula:Density

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

   View formula →
5. 5.

   A force of 49 N moves an object 23 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
6. 6.

   A current of 4 A flows through a 49 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
7. 7.

   A triangle has sides a = 15 cm and b = 7 cm with an included angle C = 45°. 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.

   A device runs at 68 V drawing 6.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

   View formula →
9. 9.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
10. 10.

    A triangle has sides a = 10 cm and b = 18 cm with an included angle C = 90°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

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

    View formula →
11. 11.

    A wave has frequency 544 Hz and wavelength 4.52 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
12. 12.

    A cone has base radius 11 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
13. 13.

    Solve for x: 6x + 12 = 66.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

    View formula →
14. 14.

    A force of 62 N acts on an area of 6.5 m². Find the pressure.

    Formula:Pressure

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

    View formula →
15. 15.

    A cylinder has radius 10 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
16. 16.

    A wave has frequency 51 Hz and wavelength 1.23 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
17. 17.

    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 →
18. 18.

    Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

    View formula →
19. 19.

    Find the sum of the first 5 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 →
20. 20.

    Find the volume of a sphere of radius 4 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

    View formula →

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