Russia · Grade 10 · Practice Sheet 6

1. 1.

   Solve for x: 7x + 19 = 40.

   Formula:Solving a Linear Equation

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

   View formula →
2. 2.

   A cone has base radius 6 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
3. 3.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 2 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

   View formula →
4. 4.

   A 36 kg object moves at 18 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
5. 5.

   A cone has base radius 9 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 →
6. 6.

   A triangle has sides a = 5 cm and b = 12 cm with an included angle C = 60°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

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

   View formula →
7. 7.

   Find the force needed to accelerate a 29 kg mass at 3 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
8. 8.

   A force of 88 N acts on an area of 7 m². Find the pressure.

   Formula:Pressure

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

   View formula →
9. 9.

   Find the force needed to accelerate a 16 kg mass at 7.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

   View formula →
10. 10.

    An object has mass 32.9 g and volume 7 cm³. Find its density.

    Formula:Density

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

    View formula →
11. 11.

    A body starts at 14 m/s and accelerates at 3.3 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
12. 12.

    Solve for x: 3x + 18 = 24.

    Formula:Solving a Linear Equation

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

    View formula →
13. 13.

    In a triangle, a = 16, b = 15 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
14. 14.

    A device runs at 136 V drawing 7.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
15. 15.

    A wave has frequency 243 Hz and wavelength 4.11 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

    View formula →
16. 16.

    A force of 129 N acts on an area of 1.6 m². Find the pressure.

    Formula:Pressure

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

    View formula →
17. 17.

    A population of 9,000 grows 3% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

    View formula →
18. 18.

    Find the force needed to accelerate a 23 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
19. 19.

    A device runs at 22 V drawing 3.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
20. 20.

    An object with initial velocity 8 m/s accelerates at 1.2 m/s² for 6 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.