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.