10th Grade PM Chapter 3: Algebra & Indices Test

Algebra and Indices

Simplifying Expressions

• Simplifying the expression a^2 + 2a - 3 gives a^2 + 2a - 3
• Simplifying the expression 2a^2 + 3a - 1 gives 2a^2 + 3a - 1

Index Laws

• The first index law states that a^m × a^n = a^(m+n)
• The second index law states that a^m ÷ a^n = a^(m-n)
• The third index law states that (a^m)^n = a^(m×n)

Expanding and Simplifying

• Expanding and simplifying the expression (a + b)^2 gives a^2 + 2ab + b^2
• Expanding and simplifying the expression (a - b)^2 gives a^2 - 2ab + b^2

Factorising

• Factorising the expression a^2 + 2a - 3 gives (a + 1)(a - 3)
• Factorising the expression 2a^2 + 3a - 1 gives (2a - 1)(a + 1)

Index Laws Applications

• Expressing the expression 5x^3y / 10x^5y^3 with positive indices gives 1/2x^2y^2
• Expressing the expression 6p^6(s^2)^0 / 2(p^4s^2)^2 with positive indices gives 3/p^2s^4

Scientific Notation

• Writing the number 150 000 000 in scientific notation gives 1.5 × 10^8
• Writing the number 0.0000075 in scientific notation gives 7.5 × 10^-6

Distance and Speed

• The largest distance between Earth and Mars is approximately 400 000 000 km
• The speed of light is approximately 300 000 km/s

Test your understanding of algebra and indices with this 5-question multiple-choice quiz, covering topics such as expression simplification and index laws.