Sec 3 E-Math Algebraic Expressions & Formulae topical questions

Simplify 7x − 3(2 − x).

Expand and simplify (x + 4)(x − 2).

Factorise (a) 5x² − 10x and (b) x² − 49.

1. (a)Factorise 5x² − 10x.[1]
2. (b)Factorise x² − 49.[2]

Find the value of 2a² − b when a = −3 and b = 5.

The pattern 4, 9, 14, 19, … continues. Write down the nth term and the 20th term.

Expand and simplify 3(2x − 1) − 2(x + 4).

Factorise (a) 4x² − 18x and (b) x² + 7x + 10.

1. (a)Factorise 4x² − 18x.[1]
2. (b)Factorise x² + 7x + 10.[2]

(a) Expand and simplify (x + 3)(x − 3) + (x − 4)². (b) Use your answer to find the value of the expression when x = 2.

1. (a)Expand and simplify.[3]
2. (b)Evaluate at x = 2.[2]

Factorise (a) 2x² + 5x + 2 and (b) 6x² − 7x − 3.

1. (a)Factorise 2x² + 5x + 2.[2]
2. (b)Factorise 6x² − 7x − 3.[2]

Simplify (2x + 3)/6 − (x − 1)/4.

Simplify 3/(x + 2) + 4/(x − 2), writing the answer as a single fraction.

A cylindrical water tank has base radius r cm, height h cm and internal volume V cm³, where V = πr²h. (a) Make h the subject of the formula. (b) Find h when V = 550 cm³ and r = 5 cm, using π = 22/7.

1. (a)Make h the subject.[2]
2. (b)Find h with the given values.[2]

Simplify fully (x² + 6x + 8)/(x + 2) × 3/(x + 4).

Make x the subject of y = (2x + 5)/3.

A tiling pattern is built from L-shapes of squares. Figure 1 uses 4 tiles, and each new figure adds 3 tiles along both arms. (a) Write the nth-term rule for the number of tiles in figure n. (b) Which figure uses exactly 100 tiles? (c) Explain why no figure uses exactly 101 tiles.

1. (a)Write the nth-term rule.[2]
2. (b)Find which figure uses 100 tiles.[2]
3. (c)Explain why 101 is impossible.[2]

The expression E = (x + 5)² − (x − 3)² is given. (a) Simplify E. (b) Hence solve E = 24. (c) Check your solution by substitution into the original expression.

1. (a)Simplify E.[2]
2. (b)Solve E = 24.[2]
3. (c)Check the solution.[2]

(a) Factorise x² − 4 completely. (b) Hence simplify (x² − 4)/(x + 2). (c) For what value of x is the fraction in (b) undefined, and what value does the simplified form take there?

1. (a)Factorise x² − 4.[2]
2. (b)Simplify (x² − 4)/(x + 2).[2]
3. (c)Discuss x = −2.[3]

The cost, in dollars, of producing n bags is C = 15n + 900, and each bag sells for $32. (a) Write the profit P for n bags as a formula. (b) How many bags must be sold for the profit to be $900? (c) Make n the subject of your formula in (a).

1. (a)Write the profit formula.[2]
2. (b)Find n for a $900 profit.[2]
3. (c)Make n the subject.[2]

(a) Show that (2x + 3)² − (2x − 3)² simplifies to 24x. (b) Use your result to evaluate (7.5)² − (1.5)² without expanding.

(a) Factorise 2x² − 8y² completely. (b) Factorise x² − y² + x + y. (c) Use one of your results, or the difference-of-squares identity directly, to evaluate 51² − 49².

1. (a)Factorise 2x² − 8y² completely.[2]
2. (b)Factorise x² − y² + x + y.[3]
3. (c)Evaluate 51² − 49².[2]