GCSE Maths · Higher · Chapter 17: Quadratic equations · Lesson 3

The quadratic formula

Grades 5–8About 50 minutesCalculator allowed44 marks

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NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Work out $- 6 - (- 4)$ .
[1 mark]
Answer
A2
Last lesson
Solve $x^{2} - 4 x - 21 = 0$ .
[1 mark]
Answer
A3
From chapter 2
A price rises from £80 to £100. Find the percentage increase.
[1 mark]
Answer
A4
From chapter 7
$A$ and $B$ are 16 cm apart. Points the same distance from $A$ and $B$ form a line. How far from $A$ does it cross $A B$ ?
[1 mark]
Answer

Grades 5–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Solve $x^{2} + x - 11 = 0$ . Give your answers correct to 2 decimal places.

Hint

a = 1

b = 1

c = - 11

. Put brackets round every value in

\frac{- b \pm b ^{2} - 4 a c}{2 a}

B1
Solve $x^{2} - 9 x + 7 = 0$ . Give your answers correct to 2 decimal places.
[3 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$

Example 2

Solve $2 x^{2} + 7 x + 2 = 0$ . Give your answers correct to 2 decimal places.

Hint Work out

b^{2} - 4 a c

first, then divide by

2 a = 4

B2
Solve $4 x^{2} - 5 x - 3 = 0$ . Give your answers correct to 2 decimal places.
[3 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$

Grades 6–7

C1
Work out the discriminant of $3 x^{2} - 2 x + 5 = 0$ . How many real solutions are there?
[2 marks]
Answer $\dots\dots$ solutions $\dots\dots$
C2
Solve $x^{2} + 14 x + 46 = 0$ . Give your answers in the form $a \pm b$ .
[2 marks]
Answer $x = \dots\dots \pm \dots\dots$

C3
Show that $25 x^{2} - 20 x + 4 = 0$ has exactly one solution, and find it.
[2 marks]
Answer $x = \dots\dots$
C4
Solve $2 x^{2} = 3 x + 7$ . Give your answers correct to 3 significant figures.
[3 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$
C5
Solve $x (x + 5) = 3 (x + 4)$ . Give your answers correct to 2 decimal places.
[3 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$
C6
Solve $2 x^{2} - 6 x + 1 = 0$ . Give your answers in the form $\frac{a \pm b}{c}$ , where $a$ , $b$ and $c$ are whole numbers, as simply as possible.
[3 marks]
Answer $x = \dots\dots\dots\dots$

Grades 6–8

D1
Ben solves $x^{2} - 8 x - 5 = 0$ . He writes $x = \frac{- 8 \pm 64 + 20}{2}$ .
Explain Ben's mistake, and solve the equation. Give your answers correct to 2 decimal places.
[3 marks]
Answer $x = \dots\dots$ or $x = \dots\dots$

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can solve a quadratic equation with the quadratic formula.
I can use the discriminant to say how many solutions there are.
I can give exact answers in surd form, simplified.

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