A partial product refers to any of the multiplication results that lead up to an overall multiplication result.

A binomial is an algebraic expression representing the sum or difference of exactly two unlike terms.

To factorise is to express a term as the product of its factors.

A solution to an equality with one variable is a value for the variable which, when substituted, maintains the equality between the expressions.

Advanced problem solving with algebraic manipulation

Maths

In this unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in the future unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In the prior unit, pupils used the distributive law to find the product of two binomials. In algebraic manipulation, pupils use apply this knowledge in order to factorise quadratics.

Algebraic manipulation

The sum of two consecutive even integers is 506. What is the value of the smallest integer?

I take a number, add 6, and multiply the result by 9. My new number is 900. What was the original number?

The sum of three consecutive integers is 72. What is the largest integer?

If the square of a positive number is decreased by 5, the result is 139. What is the number?

The area of a square is $$49 cm^2$$. What is the perimeter?

The sum of a negative number and half its square is equal to 40. What is the number?

What expression represents the following: I start with a number ($$n$$), subtract 3, and then double the result. 

What expression represents the following: I take a number ($$n$$), multiply it by 5, and then add 10 to the product.

What expression represents the following: I triple a number ($$n$$) and then subtract 4 from it.

Which expression represents the following: I square a number ($$n$$), then subtract twice the number from the square.

Which expression represents the following: I take a number ($$n$$), halve it, and then add the square of the number to this result.

A rectangle has side lengths of $$3x + 5$$ and $$4x - 3$$. Write an expression for the perimeter of the shape.

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