Applications of Quadratics (Ex 5H)

Year 10 Mathematics Core · Cambridge Ch 5, §5H · Mr Wong

Name

Class

Date

Learning intentions.

Set up a quadratic equation from a worded problem
Solve it by factorising (rearrange → factorise → Null Factor Law)
Check the validity of each solution and reject any that don't fit the context

The four steps

1. Define a variable ("Let $x$ be …"). 2. Write an equation. 3. Solve by factorising. 4. Choose the valid solution(s) and check they are reasonable (e.g. a length must be positive).

Part A — Rectangle dimensions

1. A rectangle has area $40\ \text{m}^2$ and its length is $3$ m more than its width. Let the width be $x$ m. Write an equation, solve it, and state the dimensions.

2. A rectangle has area $24\ \text{m}^2$ and its length is $5$ m more than its width. Find the dimensions.

3. A rectangle has area $63\ \text{m}^2$ and its length is $2$ m less than its width. Find the dimensions.

Part B — Triangles

4. A triangle has area $10\ \text{cm}^2$ and its base is $1$ cm more than its height. Find the height and base. (Area $=\tfrac12\,bh$.)

5H — continued

Part C (number problems) · Part D (Pythagoras) · Challenge

Name

Part C — Number problems

5. A positive number is $12$ less than its own square. Find the number.

6. Two consecutive even integers have a product of $168$. Find the two integers (positive case).

Part D — Pythagoras

7. A right-angled triangle has legs of length $x$ cm and $(x+7)$ cm, and hypotenuse $13$ cm. Form a quadratic equation and find $x$. (Use $a^2+b^2=c^2$.)

Challenge

8. A rectangular garden bed measures $x$ m by $(x+6)$ m and has an area of $91\ \text{m}^2$. Find its dimensions, clearly rejecting the invalid solution.