1. Solve quadratic equations using the formula
Grades 7/8
Quadratic Equations
Solve quadratic equations using the formula
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Solve quadratic equations using the formula
Grade
7/8
Prior Knowledge
Solving quadratics by factorising.
Duration
60 minutes (variable; may take longer or extend into second lesson).
Resources
Slides 9 onwards are printable versions of some of the earlier slides.
Equipment
Calculator
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
Introduction
Three quadratic equations; give these to students to tackle. They should be able to complete the first two easily by factorising, but will be stuck with the third. This becomes a presentation of solution using the formula. 15
Factorising
Differentiated practice. “Silver” questions introduce negative co-efficients; “Gold” questions need to be rearranged. It is quite likely that students will need more than the 20 minutes allocated. PRINT SLIDE 9 20
Reasoning
Four differentiated problem questions. Best tackled by students working in pairs or groups if excessive teacher intervention is to be avoided. PRINT SLIDE 10
Examination style question. PRINT SLIDE 11
Plenary
Matching exercise. May be done as a card sort. CLICKING ON EACH ELEMENT IN THE SLIDE COLOURS IT; THERE ARE THREE COLOURED GROUPS. PRINT/CUT OUT SLIDE 12 10
Next Steps
Surds, rationalising denominators.
Assessment
PLC/Reformed Specification/Target 7/Algebra/Quadratic Equations (quadratic formula)

3. Key Vocabulary
Coefficient Formula Round off Simplify Solve/solution

4. Quadratic Equations; formula
Solve
x² + 7x + 12 = 0
x² + 8x + 12 = 0
x² + 9x + 12 = 0
a = 1
b = 9
c = 12
−9+ 81−48
= −1.63 9 9
×1×12 2 ×1
−9− 81−48
= −7.37 2

5. Click on “Bronze”, “Silver” or “Gold” to see answers for that section
Quadratic Equations; formula
Solve these quadratic equations by using the formula Give your answers to three significant figures (note that the examination paper will specify rounding; this is a “clue” that means “use the formula”
BRONZE
SILVER
GOLD
x² + 5x + 2 = 0
x² + 10x + 7 = 0
2x² + 14x + 13 = 0
2x² + 11x + 7 = 0
x² + 7x + 1 = 0
x² − 6x + 3 = 0
x² + x − 5 = 0
3x² − 14x + 13 = 0
2x² − 4x − 9 = 0
x² − 7x + 2 = 0
3x² + 2x = 3
x(x + 5) = 1
2x² = 3x + 4
5x2 = x + 1
2(1 − x2) = 9x
x = −4.56 or x = −0.438
x = −9.24 or x = −0.757
x = −5.90 or x = −1.10
x = −4.77 or x = −0.734
x = −6.85 or x = −0.146
x = or x = 5.45
x = −2.79 or x = 1.79
x = 1.28 or x = 3.39
x = −1.35 or x = 3.35
x = or x = 6.70
x = −1.39 or x = 0.721
x = −5.19 or x = −0.193
x = −0.851 or x = 2.35
x = −0.358 or x = 0.558
x = −4.71 or x = 0.212
Click on “Bronze”, “Silver” or “Gold” to see answers for that section

6. Quadratic Equations; formula
Reasoning
BRONZE
SILVER
The area of the square is the same as the area of the rectangle. Find x.
Solve the equation 2x3 + 2x2 − 8x = 0. x 3
5.63
−2.56 or 1.56 x
x + 5
SILVER
GOLD
The area of the rectangle is 130cm2. Find x.
Solve the equation 2x2 + x = 50.
(x + 5)cm2
−5.26 or 4.76
5.44
(x + 7)cm2
Click on “Bronze”, “Silver” or “Gold” to see answers for that section

7. Examination style question.
Quadratic Equations; formula
Examination style question.
3x + 2
The area of the pentagon is 156.
(a) Show that x2 + 2x − 30 = 0.
(b) Find the length of PQ.
Give your answer to three significant figures.
2x + 1 x
x + 10 Q R S T P

8. Quadratic Equations; formula
Sort into groups…
x2 + 6x + 2 = 0
x2 − 6x + 9 = 0
x2 − 2x + 6 = 0 x y x y y x

9. Solve these quadratic equations by using the formula
Quadratic Equations; formula
Solve these quadratic equations by using the formula
Give your answers to three significant figures (note that the examination paper will specify rounding; this is a “clue” that means “use the formula”
BRONZE
SILVER
GOLD
x² + 5x + 2 = 0
x² + 10x + 7 = 0
2x² + 14x + 13 = 0
2x² + 11x + 7 = 0
x² + 7x + 1 = 0
x² − 6x + 3 = 0
x² + x − 5 = 0
3x² − 14x + 13 = 0
2x² − 4x − 9 = 0
x² − 7x + 2 = 0
3x² + 2x = 3
x(x + 5) = 1
2x² = 3x + 4
5x2 = x + 1
2(1 − x2) = 9x

10. Quadratic Equations; formula
Reasoning
BRONZE
SILVER
The area of the square is the same as the area of the rectangle. Find x.
Solve the equation 2x3 + 2x2 − 8x = 0. x 3 x
x + 5
SILVER
GOLD
The area of the rectangle is 130cm2. Find x.
Solve the equation 2x2 + x = 50.
(x + 5)cm2
(x + 7)cm2

11. Examination style question.
Quadratic Equations; formula
Examination style question.
3x + 2
The area of the pentagon is 156.
(a) Show that x2 + 2x − 30 = 0.
(b) Find the length of PQ.
Give your answer to three significant figures.
2x + 1 x
x + 10 Q R S T P

12. Quadratic Equations; formula
Sort into groups…
x2 + 6x + 2 = 0
x2 − 6x + 9 = 0
x2 − 2x + 6 = 0 x y x y y x