11 Questions
The value of if a = 4, b = −2 and c = −3 is:
−5
Simplifying the expression gives:
D
When the brackets are expanded, the expression becomes:
B
The first index law states that is equal to:
E
Which of the following expressions is the same as (5m)^2?
5 × m × 5 × m
3.20405 written to 4 significant figures is?
3.204
Simplify the following.
ab
Expand and simplify the following.
ab
Factorise the following.
ab
Express the following with positive indices.
a. $\frac{1}{2x^2y^2}$ b. $\frac{3}{p^2s^4}$
Simplify the following using the index laws.
ab cd ef
Study Notes
Algebra and Indices
Simplifying Expressions
- Simplifying the expression
a^2 + 2a - 3givesa^2 + 2a - 3 - Simplifying the expression
2a^2 + 3a - 1gives2a^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)^2givesa^2 + 2ab + b^2 - Expanding and simplifying the expression
(a - b)^2givesa^2 - 2ab + b^2
Factorising
- Factorising the expression
a^2 + 2a - 3gives(a + 1)(a - 3) - Factorising the expression
2a^2 + 3a - 1gives(2a - 1)(a + 1)
Index Laws Applications
- Expressing the expression
5x^3y / 10x^5y^3with positive indices gives1/2x^2y^2 - Expressing the expression
6p^6(s^2)^0 / 2(p^4s^2)^2with positive indices gives3/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.
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