New Zealand · Year 10 · Practice Sheet 33

1. 1.

   An object has mass 54.4 g and volume 32 cm³. Find its density.

   Formula:Density

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

   View formula →
2. 2.

   A cylinder has radius 9 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

   View formula →
3. 3.

   Solve for x: 2x + 17 = 25.

   Formula:Solving a Linear Equation

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

   View formula →
4. 4.

   A force of 186 N acts on an area of 7.4 m². Find the pressure.

   Formula:Pressure

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

   View formula →
5. 5.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 12 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

   View formula →
6. 6.

   Find the force needed to accelerate a 57 kg mass at 6.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
7. 7.

   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 →
8. 8.

   Solve for x: 3x + 17 = 29.

   Formula:Solving a Linear Equation

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

   View formula →
9. 9.

   An object has mass 59.8 g and volume 23 cm³. Find its density.

   Formula:Density

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

   View formula →
10. 10.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 7 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

    View formula →
11. 11.

    A force of 83 N moves an object 37 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
12. 12.

    A 38 kg object moves at 19 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
13. 13.

    Solve for x: 2x + 2 = 26.

    Formula:Solving a Linear Equation

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

    View formula →
14. 14.

    Find the gravitational potential energy of a 45 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
15. 15.

    Find the force needed to accelerate a 31 kg mass at 2.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
16. 16.

    A wave has frequency 832 Hz and wavelength 1.5 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
17. 17.

    Find the force needed to accelerate a 43 kg mass at 6.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
18. 18.

    A 30 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

    View formula →
19. 19.

    $900 is invested at 5% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

    View formula →
20. 20.

    An object with initial velocity 4 m/s accelerates at 3.3 m/s² for 9 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →

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