KS3/IGCSE Solving Quadratics

KS3/IGCSE Solving Quadratics

LO: Be able to factorise a quadratic

Be able to solve a quadratic equation

Recognise and use the Quadratic Formula

Multiple Select

Pick two numbers that

ADD to make 5 and MULTIPLY to make 6

• 2

• 5

• 1

• 3

Multiple Select

Pick two numbers that

ADD to make 8 and MULTIPLY to make 15

• 6

• 2

• 5

• 3

Multiple Select

Pick two numbers that

ADD to make 24 and MULTIPLY to make 80

• 10

• 4

• 20

• 8

Multiple Select

Pick two numbers that

ADD to make 18 and MULTIPLY to make 80

• 10

• 4

• 20

• 8

Multiple Choice

Expand:

 $4(d+2f)$  

• 4d + 2f

• 4d + 8f

• 4d2f

• 4d2f

Multiple Choice

Expand and simplify

 $2(a+b)$  

• 2ab

• 2a + b

• 2a + 2b

• 2(ab)

Multiple Select

Which of these statements are equivalent to

 $8x+24$  

• 8(x + 24)

• 8(x + 3)

• 4(2x + 3)

• 4(2x + 6)

Multiple Choice

Expand and simplify:

 $7(a+b)+3a$  

• 7a + 7b + 3a

• 13a

• 10ab + 3a

• 10a + 7b

Expanding Double Brackets

THE TRICK!

ADD to find the value in front of x

MULTIPLY to find the end value

Multiple Choice

Expand and Simplify

 $\left(x+3\right)\left(x+4\right)$  

•  $x^2+7x+12$  

•  $x^2+5x+12$  

•  $x^2+12x+7$  

•  $x^2+3x+4x+12$  

Multiple Choice

Expand and Simplify

 $\left(x+9\right)\left(x+2\right)$  

•  $x^2+18x+11$  

•  $x^2+11x+18$  

•  $x^2+10x+11$  

•  $x^2+9x+2x+18$  

Multiple Choice

Expand and Simplify

 $\left(x+9\right)\left(x-2\right)$  

•  $x^2+11x-18$  

•  $x^2+11x+18$  

•  $x^2+7x-18$  

•  $x^2-7x-18$  

Factorising

Pick TWO numbers that

ADD to make the value in front of x

MULTIPLY to make the end value

Multiple Select

Pick two numbers that

ADD to make 8

MULTIPLY to make 12

• 2

• 3

• 4

• 6

Multiple Select

Pick two numbers that

ADD to make -8

MULTIPLY to make -20

• 2

• 10

• -10

• -2

Multiple Select

Pick the solutions to

$$\left(x+3\right)\left(x-5\right)=0$$  

• $$x=3$$  

• $$x=-3$$  

• $$x=5$$  

• $$x=-5$$  

Multiple Select

Pick the solutions to

$$x\left(x+2\right)=0$$  

• $$x=0$$  

• $$x=1$$  

• $$x=-2$$  

• $$x=2$$  

Multiple Select

Pick the solutions to

$$\left(2x+3\right)\left(x-8\right)=0$$  

• $$x=8$$  

• $$x=-3$$  

• $$x=-\frac{3}{2}$$  

• $$x=-\frac{2}{3}$$  

Multiple Select

Pick the solutions to

$$\left(x+4\right)\left(2x-1\right)=0$$  

• $$x=4$$  

• $$x=-\frac{1}{2}$$  

• $$x=-4$$  

• $$x=\frac{1}{2}$$  

Multiple Select

Pick the solutions to

$$5x\left(4x+1\right)=0$$  

• $$x=5$$  

• $$x=-\frac{1}{4}$$  

• $$x=-4$$  

• $$x=0$$  

Multiple Select

Pick the solutions to

$$x^2+8x=0$$  

• $$x=0$$  

• $$x=1$$  

• $$x=-8$$  

• $$x=8$$  

Multiple Select

Pick the solutions to

$$x^2-7x-30=0$$  

• $$x=10$$  

• $$x=3$$  

• $$x=-10$$  

• $$x=-3$$  

Difference of TWO squares

When subtracting two square terms we can factorise by square rooting each term!

Multiple Choice

Factorise

$$x^2-25$$  

• $$\left(x+5\right)\left(x-5\right)$$  

• $$x\left(x-5\right)$$  

• $$\left(x-5\right)\left(x-5\right)$$  

• $$\left(x+5\right)\left(x+5\right)$$  

Multiple Choice

Factorise

$$x^2-81$$  

• $$\left(x+9\right)\left(x+9\right)$$  

• $$x\left(x-9\right)$$  

• $$\left(x-9\right)\left(x+9\right)$$  

• $$x\left(x-81\right)$$  

Multiple Choice

Solve

$$x^2-81=0$$  

• $$x=9$$  

• $$x=0\ and\ x=9$$  

• $$x=-9$$  

• $$x=-9\ and\ x=9$$  

Multiple Choice

Solve

$$x^2-81=0$$  

• $$x=9$$  

• $$x=0\ and\ x=9$$  

• $$x=-9$$  

• $$x=-9\ and\ x=9$$  

ALWAYS SET YOUR QUADRATIC = 0

Before attempting to factorise you must rearrange to make your quadratic equal zero!

Multiple Choice

Solve

$$x^2+5x=24$$  

• $$x=8\ and\ x=-3$$  

• $$x=-8\ and\ x=3$$  

• $$x=12\ and\ x=-2$$  

• $$x=2\ and\ x=-12$$  

QUADRATIC FORMULA

We can solve Quadratics using a special formula known as the Quadratic Formula! We are given this in the exam so there is no need to memorise....we just need to know how to use it.

Multiple Select

Pick the TWO solutions

• $$x=2$$

• $$x=-\frac{1}{3}$$

• $$x=-2$$

• $$x=\frac{1}{3}$$

Multiple Choice

Determine the values of
a, b, and c for
the quadratic equation: 
4x² – 8x = 3
*remember right side should =0

• a = 4, b = -8, c = 3
• a = 4, b =-8, c =-3
• a = 4, b = 8, c = 3
• a = 4, b = 8, c = -3

Multiple Choice

Solve using the quadratic formula.
2x² - 9x - 35 = 0

• x = 7/2, x = -6
• x = -5/2, x =5
• x = -3/7, x =6
• x = -5/2, x = 7

Multiple Choice

What should you do first in solving this equation?

x² + 6x - 13 = 3

• Factor

• Write down: a = 1, b = 6, c = -13

• Subtract 3 from both sides.

• Add 3 to both sides.

Multiple Choice

Solve Using the Quadratic Formula
 x² + 4x - 40 = -8

• -10 & -4
• -4 & 10
• -8 & 4
• 8 & -4

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

Multiple Choice

Use the quadratic formula to solve 2x² + 2x - 12

• -2, 3

• 2, 3

• 2, -3

• -2, -3

Multiple Choice

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

• a = 4, b = -8, c = 3

• a = 4, b =-8, c =-3

• a = 4, b = 8, c = 3

• a = 4, b = 8, c = -3

Surd Form

A surd is an expression that includes a square root, cube root or other root symbol. Surds are used to write irrational numbers precisely – because the decimals of irrational numbers do not terminate or recur, they cannot be written exactly in decimal form.

Multiple Select

Select the surd(s)

• $$\sqrt[]{5}$$

• $$\frac{1}{5}$$

• $$5$$

• $$-5$$

Multiple Choice

What is this formula?

• This is the speed of light formula.
• This is the quadratic formula.
• This is the zero product property.
• This is scary.

Multiple Select

Select the surd(s)

• $$2+\sqrt[]{5}$$

• $$1-\sqrt[]{5}$$

• $$\sqrt[]{5}$$

• $$\frac{1}{5}$$

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12 (leaving the answer in surd form)

Multiple Choice

Solve $$w^2+7w+4=0$$  (leaving the answer in surd form)

• $$\frac{-7\pm\sqrt{33}}{2}$$  

• $$\frac{-7\pm\sqrt{65}}{2}$$  

• $$\frac{7\pm\sqrt{33}}{2}$$  

• $$\frac{-7\pm3\sqrt{11}}{2}$$