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1. End of Unit Test on Bivariate Data for S3 Students
2. End of Unit Test on Inverse and Composite Transformations in 2D for S3 Students
3. End of Unit Test on Enlargement and Similarity in 2D for S3 Students
4. End of Unit Test on Collinear Points and Orthogonal Vectors for S3 Students
5. End of Unit Test on Right Angled Triangles for S3 Students
6. End of Unit Test on Percentage Interest and Proportion for S3 Students
7. End of Unit Test on Quadratic Equations for S3 Students
8. End of Unit Test on Simultaneous Equations and Inequalities for S3 Students
9. End of Unit Test on Algebraic Fractions for S3 Students
10. End of Unit Test on Number Bases for S3 Students
11. End of Unit Test on Problems on Sets for S3 Students
Linear and Quadratic Functions Unit Summary
1. Linear function is of the form \(y = mx + c\) where \(m\) = gradient and \(c\) = y-intercept. Examples of linear functions are: \(y = 2x – 1\), \(y = 8\), \(y = 7 – 7x\).
2. Gradient of a straight line: For line joining two points \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\),
Gradient of the line is \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y_{1}-y_{2}}{x_{1}-x_{2}}\)
3. Parallel condition: When lines are parallel, they have the same gradient i.e. Consider two lines \(y = m_{1}x + c_{1}\) and \(y = m_{2}x + c_{2}\). These lines are parallel only and only if \(m_{1} = m_{2}\).
4. Perpendicular condition: When lines are perpendicular, the product of their gradients is –1 i.e. Two lines \(y = m_{1}x + c_{1}\) and \(y = m_{2}x + c_{2}\) are said to be perpendicular if the product of their gradients gives –1. i.e. \(m_{1} \times m_{2} = –1\).
5. Equation of a straight line: The equation of a line \(y = mx + c\) can be obtained when it passes through one point and gradient is given or when it passes through two given points.
For any two points \((x_{1}, y_{1})\) and \((x_{2}, y_{2})\), the equation of line is given by:
\(y-y_{1}=m(x-x_{1})\) or \(y-y_{2}=m(x-x_{2})\), where \(m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{y_{1}-y_{2}}{x_{1}-x_{2}}\).
6. Quadratic function: The expression \(y = ax^{2} + bx + c\), where \(a\), \(b\) and \(c\) are constants and \(a \neq 0\), is called a quadratic function of \(x\) or a function of the second degree (highest power of \(x\) is two).
7. Axis of symmetry: A quadratic function has axis of symmetry \(x = -\frac{b}{2a}\). The axis of symmetry is parallel to the y - axis.
8. Vertex of a quadratic function: Every quadratic function has vertex. The graph turns at its vertex. The vertex is the coordinate \(([h, f(h))\) where \(x = h=-\frac{b}{2a}\) is the axis of symmetry.
For the expression \(y = ax^{2} + bx + c\), if the coefficient of the \(x^{2}\) term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the "U"-shape. If the coefficient of the term \(x^{2}\) is negative, the vertex will be the highest point on the graph, the point at the top of the "∩"-shape.
9. Intercepts of a quadratic function: The intercepts with axes are the points where a quadratic function cuts the axes. There are two intercepts i.e. x-intercept and y-intercept. x-Intercept for any quadratic expression is calculated by letting \(y = 0\) and y-intercept is calculated by letting \(x = 0\)