Belgium · Year 10 · Practice Sheet 37

1. 1.

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

   Formula:Quadratic Formula

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

   View formula →
2. 2.

   Solve for x: 3x + 4 = 19.

   Formula:Solving a Linear Equation

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

   View formula →
3. 3.

   A wave has frequency 433 Hz and wavelength 0.96 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
4. 4.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 5 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

   View formula →
5. 5.

   €2,800 is invested at 8% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

   View formula →
6. 6.

   A force of 71 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
7. 7.

   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 →
8. 8.

   A value changes from 144 to 85. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

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

   View formula →
9. 9.

   A force of 25 N moves an object 37 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

   View formula →
10. 10.

    Solve for x: 7x + 1 = 64.

    Formula:Solving a Linear Equation

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

    View formula →
11. 11.

    A cone has base radius 5 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
12. 12.

    An object with initial velocity 4 m/s accelerates at 4.8 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
13. 13.

    A 20 kg object moves at 18 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
14. 14.

    A cone has base radius 4 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 →
15. 15.

    Find the gravitational potential energy of a 6 kg object raised 8 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
16. 16.

    A force of 123 N acts on an area of 6.9 m². Find the pressure.

    Formula:Pressure

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

    View formula →
17. 17.

    Find the sum of the first 12 terms of an arithmetic series with first term a = 11 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

    View formula →
18. 18.

    €2,600 is invested at 6% simple interest per year for 6 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

    View formula →
19. 19.

    A 15 kg object moves at 12 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
20. 20.

    A force of 400 N acts on an area of 9.7 m². Find the pressure.

    Formula:Pressure

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

    View formula →

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