AS Core Maths-TAM Online Session 1: Basic Algebra and Uncertainty A couple of warm-up questions before we get started… 1. A quadratic equation has roots What could the equation be? 2. How can you find the radius of the pipe shown if the only measurement you can take is the one marked h? 4 3 x
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AS Core Maths-TAM Online Session 1: Basic Algebra and Uncertainty A couple of warm-up questions before we get started… 1. A quadratic equation has roots.
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AS Core Maths-TAM Online Session 1: Basic Algebra and
Uncertainty
A couple of warm-up questions before we get started…
1. A quadratic equation has roots
What could the equation be?
4 3x
2. How can you find the radius of the pipe shown if the only measurement you can take is the one marked h?
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1. A quadratic equation has roots
What could the equation be?
4 3x
2. How can you find the radius of the pipe shown if the only measurement you can take is the one marked h?
Session Content
• Quadratic equations
- solving, representing, transformations
- completing the square
- discriminant
Simultaneous equations
Inequalities
NB: This is content based on chapters 1 & 4 in the AS Core textbook
Completing the square - Geogebra file
What could the equation be?
Given that the coefficient of x2 is 2, what is the y-intercept?
Features of Completing the Square
Features of Completed the Square Form for a Quadratic
Proving the Quadratic Formula
If a x2+bx+c=0 h𝑡 𝑒𝑛𝑥=−𝑏± √𝑏2− 4 𝑎𝑐2𝑎
The Discriminant
; Discriminant Geogebra File
If b2 – 4ac < 0 then the equation has no real roots
If b2 – 4ac = 0 then the equation has one real root
If b2 – 4ac > 0 then the equation has two real roots
−2 2
1
2
3
x
y
Quadratic graphs & transformations
2f x x
3 2 1 0 1 2 3
f
f 2
f 2
x
x
x
x
−2 2
1
2
3
x
y
2f x x
: f 2 1 : f 2 1
: f 2 1 : f 2 1
A y x B y x
C y x D y x
Simultaneous Equations
−1 1 2 3
2
4
x
y
Q: What does it mean to find the solution of these equations?
and
Inequalities (1)
5 x− 3≤ 10−2 (2− x )
Inequalities (2)
Inequalities (3)
−20 −10 10 20
−6
−4
−2
2
4
6
8
x
y
Session content check Quadratic equations
- solving, representing, transformations
- completing the square
- discriminants
Simultaneous equations
Inequalities
MEI C1 June 201010.
EDEXCEL C1 JUNE 201310. Given the simultaneous equations
2x + y = 1
x2 – 4ky + 5k = 0 where k is a non zero constant, (a) show that x2 + 8kx + k = 0.
(2)
Given that x2 + 8kx + k = 0 has equal roots, (b) find the value of k.
(3)
(c) For this value of k, find the solution of the simultaneous equations. (3)