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)

10.

AQA C1 Jane 20122.

OCR C1 May 2012

OCR C1 May 20125

OCR C1 June 2012

MEI C1 June 2010