Question

A. What is an equation?

B. Explain the difference between a linear and a quadratic equation in terms of degree and solution.

C. Give a concise definition of the following:
1. Rate
2. Ratio
3. Proportion

Answer 1

Solution to A:

An equation is a statement of equality of two expressions formulated by applying various algebraic operations such as addition, subtraction, multiplication and division to a set of variables e.g

$$3x^2 +4x-2=y$$

Solution to B:

A linear equation is an equation where the highest degree of the unknown variable is one e.g $2x+4=6$

Whereas a quadratic equation is an equation where the highest degree of the unknown variable is two e.g $4x^2+3x-2=0$

A linear equation has only one solution whereas a quadratic equation has 2 solutions

Solution to C:

1. Ratio is an expression of one measure relative to another e.g in a class with 40 boys and 37 girls, we can say the ratio of boys to girls in the class is 40:37. Ratio can be expressed either as a fraction $({40 \over 30} )$ or in words (40 to 30) or using colon (40:30).
2. Rate is a form of ratio that compares quantities of different types e.g speed is a rate that compares distance and time (km/hr)
3. Proportion is a ratio that relates a part to a whole e.g the proportion of boys in the class above is ${40 \over 40+37} = 0.5195$ or 51.95%