Exam Review: QUADRATICS, Pure Mathematics 1

Name: Exam Review: QUADRATICS, Pure Mathematics 1
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Solved Exam/Topical Questions on Quadratics: Pure mathematics 1 (AS/A level maths)

Created byFahmi Fariq Muhammadsharif

Last updated 11/2024

English

What you'll learn

The process of completing the square for quadratic functions/equations and use it correctly.
Finding the discriminant of quadratic functions and use it to find the coordinates of intersection(s) between a curve and a line.
Solving quadratic equations, finding axis of symmetry, and solving quadratic inequalities.
Knowing if there is a solution or not for simultaneous equations by using discriminant term of quadratics.
Solving simultaneous equations by substitution if one equation is linear and one is quadratic.
Recognizing and solving equations in x which are quadratic in some function of x.
Finding constants in a quadratic function/equation based on the discriminant term conditions.
Finding a quadratic equation if the plot/graph of the equation is given.
Finding the location/coordinates of vertex of quadratics and to know if it has a maximum or minimum value.

Course content

1 section • 18 lectures • 2h 8m total length

Important Notes on Quadratics and its Fundamentals11:16
Students will be able to recognize quadratic equations, their plot shape, vertex (turning point) location along with knowing if a quadratic equation has real solutions or a repeated solution (two similar solutions). Also, students will be able to know how to use the discriminant term to find the intersection points between a line and quadratic curve.
Expressing quadratics in completing the square form and finding constants4:29
Students will be able to learn the process of expressing quadratic equations in the form of completing the square and use it to find the related constants/parameters.
The use of discriminant term to find the set of constant values of equations9:00
Students will learn on finding the set of possible values of a parameter/coefficient exists in a linear and/or quadratic equation when there are two distinct real solutions between the line and the curve.
Solving quadratic inequalities by using graphical method.4:54
Students will be able to easily get the solution set of a quadratic inequality by means of graphical method.
Solving quadratic inequalities by knowing the x-intercepts/roots of equation9:40
Students will be able to easily solve quadratic inequalities by means of a rapid sketching of their plot after finding the roots/x-intercepts of the quadratic equation.
The use of roots to find parameters via discriminant property of equal roots8:44
Students will learn how to use roots of quadratic equation to derive simultaneous equations and solving them to extract the available parameters/constants in the equations. Also, understand to apply the discriminant term when there are two equal roots.
Finding the set of values of a parameter when a line intersects a curve8:23
Students will be able to use the discriminant term to find the set of possible values of a parameter in the linear equation when there are two real solutions/two intersection points between the line and a quadratic curve.
Finding the set of real values when a line intersects with a quadratic curve5:06
Students will be able to use the discriminant term when there are two real solutions/two intersection points between a line and a quadratic curve.
Finding the roots of disguising quadratic equations by means of power reduction6:45
Students will be able to recognize a disguising quadratic equation and use a new skill of reducing the exponent power to the second power through assumption, thereby solving the quadratic equation.
Finding coordinates of intersection point(s) between a line and a curve7:02
Students will be able to find the coordinates (x and y) of the intersection point(s) between a linear line and a nonlinear curve (quadratic) if exist.
Showing that there are no real solutions to simultaneous equations4:57
Students will be able to extract a new quadratic equation from two simultaneous equations, then use the discriminant term to prove that there are no any real solutions to the simultaneous equations.
Finding the vertex coordinates and stating if it is a maximum or minimum value7:10
Students will be able to sketch a quadratic curve easily and define its vertex coordinates followed by recognizing if the vertex presents a minimum or a maximum value and hence finding its value.
Solving simultaneous equations by substitution with one quadratic equation5:00
Students will be able to solve simultaneous equations with one quadratic equation and one linear equation by method of substitution.
Application of quadratic equation to find the maximum area of geometrical shapes8:35
Students will be able to use a quadratic equation to express the variation in the area of a triangle with variable side lengths. By this, the maximum area of the triangle can be found at a specific length (x).
Finding the equation of axis of symmetry of quadratic equations13:15
Students will be able to find the equation of axis of symmetry (vertical line passing through the vertex) by means converting the quadratic equation to the vertex form a(x-h)^2+k
Finding the equation of a quadratic curve when the vertex point is known4:36
Students will be able to find/derive an equation for a quadratic curve by using the vertex coordinates (which represent x-intercepts) and y-intercept point.
Finding the equation of a quadratic curve from y-intercept and vertex points3:16
Students will be able to find/derive an equation for a quadratic curve by using the vertex coordinates and y-intercept point.
Finding the equation of a quadratic curve from the x- and y-intercepts6:01
Students will be able to find/derive an equation for a quadratic curve by using the roots (x-intercepts) and y-intercept point ony.

Requirements

Basic Math

Description

By taking this course of solving exam questions on quadratics and its related sub-topics, students familiarize with the basic and advanced levels of quadratics. This can help them to successfully pass the first paper (Pure Mathematics 1) in the AS/A math with a very good/excellent grade.

Through this course:

Students will learn the process of completing the square for quadratic functions/equations and use it correctly.

Students will learn finding the discriminant of quadratic functions/equations and use it to find the coordinates of intersection(s) between a curve and a line.

Students will learn solving quadratic equations, finding axis of symmetry, and solving quadratic inequalities.

Students will learn solving simultaneous equations by substitution if one equation is linear and one is quadratic.

Students will learn recognizing and solving equations in x which are quadratic in some function of x.

Students will learn to know if there is a solution or not for simultaneous equations by using discriminant term of quadratics.

Students will learn finding constants in a quadratic function/equation based on the discriminant term conditions.

Students will learn finding a quadratic equation if the plot/graph of the equation is given.

Students will learn finding the location/coordinates of vertex of quadratics and to know if it has a maximum or minimum value.

Who this course is for:

Students who want to learn all about quadratics and solve exam style questions, thereby passing pure mathematics 1 (Paper 1) of AS/A level math successfully.
Learners who want to know everything about quadratics and solve related exam questions in a step by step way, thereby expecting exam questions on pure mathematics.
Students who want to learn solving easy, medium and hard questions on quadratics, the first part of exam questions on pure mathematics.