P1 §1. Algebraic expressions

Pure mathematics Year 1

Here's a short introduction to Pure maths 1 Chapter 1 Algebraic expressions.

 

1.1 Index laws: Multiply and divide integer powers.

1.2 Expanding brackets: Expand a single term over brackets and collect like terms. Expand the product of two or three expressions.

1.3 Factorising: Factorise linear, quadratic and simple cubic expressions.

1.4 Negative and fractional indices: Know and use the laws of indices.

1.5 Surds: Simplify and use the rules of surds.

1.6 Rationalising denominators: Rationalise denominators.

1.7 Mixed exercise for chapter 1

1.8 Review exercise for chapter 1

 

Prior knowledge check

 

Q1. [GCSE Maths] Simplify:

(a) $ 4m^2n + 5mn^2 - 2m^2n + mn^2 - 3mn^2 $

(b) $ 3x^2 - 5x + 2 + 3x^2 - 7x - 12 $

 

Answers:

(a) $ 2m^2n + 3mn^2 $

(b) $ 6x^2 - 12x - 10 $

 

Q2. [GCSE Maths] Write as a single power of 2:

(a) $2^5 \times 2^3$

(b) $2^6 \div 2^2$

(c) $ \left( 2^3 \right)^2 $

 

Answers:

(a) $ 2^8 $

(b) $ 2^4 $

(c) $ 2^6 $

 

Q3. [GCSE Maths] Expand:

(a) $ 3(x + 4) $

(b) $ 5(2 - 3x) $

(c) $ 6(2x - 5y) $

 

Answers:

(a) $ 3x + 12 $

(b) $ 10 - 15x $

(c) $ 12x - 30y $

 

Q4. [GCSE Maths] Write down the highest common factor of:

(a) 24 and 16

(b) $ 6x $ and $ 8x^2 $

(c) $ 4xy^2 $ and $ 3xy $

 

Answers:

(a) 8.

(b) $ 2x $.

(c) $ xy $.

 

Q5. [GCSE Maths] Simplify:

(a) $ \frac{ 10x }{ 5 } $

(b) $ \frac{ 20x }{ 2 } $

(c) $ \frac{ 40x }{ 24 } $

 

Answers:

(a) $ 2x $

(b) $ 10x $

(c) $ \frac{ 5x }{ 3 } $

 

Comment: Computer scientists use indices to describe very large numbers. A quantum computer with 1000 qubits (quantum bits) can consider $ 2^{1000} $ values simultaneously. This is greater than the number of particles in the observable universe.