# Mathematics Grade 11 Investigation Term 1

Mathematics Grade 11 Investigation Term 1: Equations and Roots 2023, and 2021 Investigations.

In grade 11 mathematics, learners are introduced to various concepts related to equations and roots. Equations and roots form an essential part of algebra, and mastering these concepts is important for success in higher-level mathematics.

## Mathematics Grade 11 Investigation Term 1

During term 1, learners are expected to investigate equations and roots through a range of activities and assessments. Here is an overview of the topics covered in this investigation:

1. Solving linear equations: Learners will be introduced to the concept of linear equations, which are equations of the form ax + b = c. They will learn how to solve linear equations using a range of methods, including balancing both sides of the equation, and isolating the variable.
2. Graphing linear equations: Learners will learn how to graph linear equations using a range of techniques, including finding the x- and y-intercepts, and using slope-intercept form.
3. Quadratic equations: Learners will be introduced to quadratic equations, which are equations of the form ax² + bx + c = 0. They will learn how to solve quadratic equations using a range of methods, including factoring, completing the square, and using the quadratic formula.
4. Roots of quadratic equations: Learners will learn how to find the roots of quadratic equations, which are the values of x that make the equation equal to zero. They will also learn how to graph quadratic equations using techniques such as finding the vertex and axis of symmetry.
5. Applications of equations and roots: Finally, learners will investigate various applications of equations and roots in real-life scenarios, including optimization problems, finding the maximum or minimum values of a function, and analyzing data.

Throughout this investigation, learners will be expected to develop their problem-solving skills, analytical thinking, and ability to apply mathematical concepts to real-world situations. By the end of term 1, learners should have a solid understanding of equations and roots, and be able to use these concepts in a range of mathematical contexts.

## 2023: Grade 11 Mathematics Investigation

### Answers (NB: For Guiding Purposes)

To solve the quadratic equation 12𝑥^2 + 5𝑥 − 2 = 0 using the quadratic formula, we need to first identify the values of a, b, and c in the general quadratic equation form, which is ax^2 + bx + c = 0.

In this case, a = 12, b = 5, and c = -2.

𝑥 = (−𝑏 ± √𝑏^2 − 4𝑎𝑐) / 2𝑎

Substituting the values of a, b, and c in the quadratic formula, we get:

𝑥 = (−5 ± √5^2 − 4(12)(−2)) / 2(12)

Simplifying the equation further:

𝑥 = (−5 ± √169) / 24

𝑥 = (-5 + 13) / 24 or 𝑥 = (-5 – 13) / 24

Solving for 𝑥, we get:

𝑥 = 1/3 or 𝑥 = -2/3

Therefore, the solutions to the quadratic equation 12𝑥^2 + 5𝑥 − 2 = 0 are 𝑥 = 1/3 or 𝑥 = -2/3.

Are the roots equal or unequal?

The roots of the given quadratic equation 12𝑥^2 + 5𝑥 − 2 = 0 are unequal. One root is 𝑥 = 1/3, and the other is 𝑥 = -2/3. This is because the discriminant (the expression inside the square root in the quadratic formula) is greater than zero. If the discriminant is zero, then the roots would be equal.

Questions: