Podcast
Questions and Answers
Simplify: 2³ x 2⁴, expressing all answers in positive indices
Simplify: 2³ x 2⁴, expressing all answers in positive indices
2⁷
Simplify: e⁴ x e¹³, expressing all answers in positive indices
Simplify: e⁴ x e¹³, expressing all answers in positive indices
e¹⁷
Simplify: $\frac{2^7}{2^4}$, expressing all answers in positive indices
Simplify: $\frac{2^7}{2^4}$, expressing all answers in positive indices
2³
Simplify: $\frac{a^{12}}{a^8}$, expressing all answers in positive indices
Simplify: $\frac{a^{12}}{a^8}$, expressing all answers in positive indices
Simplify: (2³)², expressing all answers in positive indices
Simplify: (2³)², expressing all answers in positive indices
Simplify: (b⁵)⁷, expressing all answers in positive indices
Simplify: (b⁵)⁷, expressing all answers in positive indices
Simplify: (2³ x 3⁴)⁵, expressing all answers in positive indices
Simplify: (2³ x 3⁴)⁵, expressing all answers in positive indices
Simplify: (a⁴b³c⁵)⁷, expressing all answers in positive indices
Simplify: (a⁴b³c⁵)⁷, expressing all answers in positive indices
Simplify: $(\frac{a^2}{3^3})^5$, expressing all answers in positive indices
Simplify: $(\frac{a^2}{3^3})^5$, expressing all answers in positive indices
Simplify: $(\frac{a^2b^5}{c^6})^3$, expressing all answers in positive indices
Simplify: $(\frac{a^2b^5}{c^6})^3$, expressing all answers in positive indices
Simplify: b⁰, expressing all answers in positive indices
Simplify: b⁰, expressing all answers in positive indices
Simplify: $\frac{(2a^3)^3}{a^9}$, expressing all answers in positive indices
Simplify: $\frac{(2a^3)^3}{a^9}$, expressing all answers in positive indices
Simplify: $\frac{2b^{-3}}{b^{-5}}$, expressing all answers in positive indices
Simplify: $\frac{2b^{-3}}{b^{-5}}$, expressing all answers in positive indices
Simplify: $\frac{(a^3c^7)^3a^{-2}}{(a^2b^5)^2}$, expressing all answers in positive indices
Simplify: $\frac{(a^3c^7)^3a^{-2}}{(a^2b^5)^2}$, expressing all answers in positive indices
Simplify: $\frac{(3a^3b^2)^{-2}}{(2a^2b^3)^3}$, expressing all answers in positive indices
Simplify: $\frac{(3a^3b^2)^{-2}}{(2a^2b^3)^3}$, expressing all answers in positive indices
Simplify: $(\frac{(a^4b^2)^3}{b^{-4}c^2})^3$
Simplify: $(\frac{(a^4b^2)^3}{b^{-4}c^2})^3$
Complete the table: Decimal Notation 87 300 000
Complete the table: Decimal Notation 87 300 000
Complete the table: Decimal Notation 0.000 000 2301
Complete the table: Decimal Notation 0.000 000 2301
Complete the table: Scientific Notation 8.01 x 10⁵
Complete the table: Scientific Notation 8.01 x 10⁵
Complete the table: 9.21 x 10⁻⁵
Complete the table: 9.21 x 10⁻⁵
Expand: 2(x + 4)
Expand: 2(x + 4)
Expand: 4(x + 3) – 3(x + 4)
Expand: 4(x + 3) – 3(x + 4)
Expand: -3(x - 4) – 2(x − 3)
Expand: -3(x - 4) – 2(x − 3)
Expand: (x + 4)(x + 3)
Expand: (x + 4)(x + 3)
Expand: (3y + 2)(y – 2)
Expand: (3y + 2)(y – 2)
Expand and simplify: (x + 4)²
Expand and simplify: (x + 4)²
Expand and simplify: (x + 3)(x - 3)
Expand and simplify: (x + 3)(x - 3)
Expand and simplify: (3x + 8)(3x – 8)
Expand and simplify: (3x + 8)(3x – 8)
Factorise the following: 6x + 48
Factorise the following: 6x + 48
Factorise the following: 5x³ – 55x
Factorise the following: 5x³ – 55x
Factorise the following: 6x³ + 24x²
Factorise the following: 6x³ + 24x²
Factorise the following: -10x² + 45x
Factorise the following: -10x² + 45x
Factorise the following: -6x⁴ – 46x²
Factorise the following: -6x⁴ – 46x²
Factorise the following: 2x(x - 7) + 3(x - 7)
Factorise the following: 2x(x - 7) + 3(x - 7)
Factorise the following: 3x(x – 1) – 4(x – 1)
Factorise the following: 3x(x – 1) – 4(x – 1)
Rearrange to make y the subject: a = y + b
Rearrange to make y the subject: a = y + b
Rearrange to make y the subject: a = √(cdy + b)
Rearrange to make y the subject: a = √(cdy + b)
Flashcards
Product of Powers Rule
Product of Powers Rule
When multiplying powers with the same base, add the exponents. x^m * x^n = x^(m+n)
Power of a Power Rule
Power of a Power Rule
When raising a power to a power, multiply the exponents. (x^m)^n = x^(m*n)
Quotient of Powers Rule
Quotient of Powers Rule
When dividing powers with the same base, subtract the exponents. x^m / x^n = x^(m-n)
Zero exponent
Zero exponent
Signup and view all the flashcards
Distributive Property
Distributive Property
Signup and view all the flashcards
FOIL Method
FOIL Method
Signup and view all the flashcards
Factorising
Factorising
Signup and view all the flashcards
Study Notes
- Revision topics are based on traffic light Exercise 3.1 – 3.7
- Try all the questions, highlight in the traffic light to show competency, ask for help if marked red, and for further practice refer to the textbook and choose one easy and one difficult question to challenge yourself.
Index Laws (3.1 & 3.2)
- Simplify expressions expressing all answers in positive indices:
- Examples include: 2³ x 2⁴, a³ x a⁸, e⁴ x e¹³, 2⁷/2⁴, a¹²/a⁸, a¹⁰/a⁷, (2³)², (a³)^5, (b⁵)⁷ ,(2³ x 3⁴)⁵, (a³b⁵)², (a⁴b³c⁵)⁷, (a/3b)⁵, (a²b/b⁵)³, (a²b⁵c/c⁶)⁵, b⁰, a⁵c⁴/a⁵, (2a³)³/a⁹, b⁻⁵, a⁴/a³, 2b⁻³/b⁻⁵, (a³c⁷)³a⁻²/(a²b⁵)², (3a³b²)⁻²/(2a²b³)³, ((a⁴b⁵c²)³)/(b⁻⁴c²)
Scientific Notation (3.3)
- Convert between decimal notation and scientific notation
- Determine the rank from smallest to largest
- Examples include: 87 300 000, 0.000 000 2301, 8.01 x 10⁵, 9.21 x 10⁻⁵
Binomial Expansion (3.5)
-
Expand the following expressions:
-
Examples include: 2(x + 4), 2(x – 5), -3(x + 5), 4(x + 3) – 3(x + 4), 3(x – 5) – 2(x + 5), 4(x + 3) – 3(x – 5), -3(x – 4) – 2(x – 3), (x + 4)(x + 3), (x + 5)(x – 2), (3y + 2)(y – 2), (2y – 3)(3y – 7)
-
A square garden with side length of x is to be enlarged where length is increased by 4 metres and width by 1 metre.
-
Draw a diagram of the new garden
-
State the equation that gives the area of the new garden, in its expanded and simplified form.
-
A garden bed has a width of 8 metres and length of 6 metres and is to be enlarged by x in both its length and width.
-
Draw a diagram of the new garden
-
State the equation that gives the area of the new garden in its expanded and simplified form
Expanding Special Brackets (3.6)
- Expand and simplify
- Examples include: (x + 4)², (x + 7)², (x – 8)², (x – 5)², (2x + 3)², (3x + 5)², (x + 3)(x – 3), (x – 7)(x + 7), (3x + 8)(3x – 8)
Factorise (3.7)
- Factorise the following expressions
- Examples include: 6x + 48, 6x + 21, 12x – 42, 5x³ – 55x, 4x³ – 16x², 6x³ + 24x², -10x² + 45x, -12x³ – 32x, -6x⁴ – 46x², 2x(x – 7) + 3(x – 7), 3x(x – 1) – 4(x – 1), 2x(x + 2) + 7(x + 2)
Rearranging Formula (3.4)
- Rearrange the following formulas to make y the subject:
- Examples include: a = y + b, a = y – b, a = y x b, a = by + c, a = by – c, a = y/b + c, a = (y + b)², a = √(y + b), a = √(cdy + b)
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
