Complete the table for equation x 2 + x = 100 . Trial x 2 + x Comment x = 10 10 2 + 10 = 110 Too big x = 9 9 2 + 9 = _____ _____ x = 9 . 5 9 . 5 2 + 9 . 5 = _____ _____ x = 9 . 6 _____ _____

We have to find the solution of equation x 2 + x = 100 . We will use trial and improvement method. First we will take x = 10 . ⇒ 10 2 + 10 = 110 , this is too big. Now we will take value of x = 9 , 9 2 + 9 = 81 + 9 = 90 . This is very small, so we will take the value between 10 and 9 i.e, 9 . 5 . ⇒ x = 9 . 5 , 9 . 5 2 + 9 . 5 = 99 . 75 Now we will take x = 9 . 6 . ⇒ 9 . 6 2 + 9 . 6 = 101 . 76 So we can conclude that solution of the equation is 9 . 5 which is very close to the correct answer. Hence, we can write the table as Trial x 2 + x Comment x = 10 10 2 + 10 = 110 Too big x = 9 9 2 + 9 = 90 Too small x = 9 . 5 9 . 5 2 + 9 . 5 = 99 . 75 Too small x = 9 . 6 9 . 6 2 + 9 . 6 = 101 . 76 Too big

Complete the table for the equation x 2 + 5 x = 60 Trial x 2 + 5 x Comment x = 5 5 2 + 5 × 5 = 50 Too big x = 6 6 2 + 5 × 6 = _____ _____ x = 5 . 6 5 . 6 2 + 5 × 5 . 6 = _____ _____ x = 5 . 7 _____ _____ x = 5 . 65 _____ _____

We have to find the solution of equation x 2 + 5 x = 60 . We will use trial and improvement method. First we will take x = 5 . ⇒ 5 2 + 5 × 5 = 50 , this is too small. Now we will take value of x = 6 , 6 2 + 5 × 6 = 36 + 30 = 66 . This is too big, so we will take the value between 6 and 5 i.e, 5 . 6 . ⇒ x = 5 . 6 , 5 . 6 2 + 5 × 5 . 6 = 59 . 36 Now we will take x = 5 . 7 . ⇒ x = 5 . 7 , 5 . 7 2 + 5 × 5 . 7 = 60 . 99 Now we will take number x = 5 . 65 . ⇒ x = 5 . 65 , 5 . 65 2 + 5 × 5 . 65 = 60 . 17 So we can conclude that solution of the equation is 5 . 65 which is very close to the correct answer. Hence, we can write the table as Trial x 2 + 5 x Comment x = 5 5 2 + 5 × 5 = 50 Too small x = 6 6 2 + 5 × 6 = 66 Too big x = 5 . 6 5 . 6 2 + 5 × 5 . 6 = 59 . 36 Too small x = 5 . 7 5 . 7 2 + 5 × 5 . 7 = 60 . 99 Too big x = 5 . 65 5 . 65 2 + 5 × 5 . 65 = 60 . 17 Too big

E M B I B E

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 25 - Trial and Improvement>Exercise 1>Q 8

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Earn 100

The shaded area in the shape below is $100 c m^{2}$ . Use trial and improvement to calculate the side length of the square to $1$ decimal place.

Important Questions on Trial and Improvement

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 25 - Trial and Improvement>Starting point>Q ●

How to solve the equation with an unknown on one side?

$3 x + 5 = 32$

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 25 - Trial and Improvement>Starting point>Q ●

How to solve the equation with an unknown on one side?

$22 = 30 - 2 x$

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 25 - Trial and Improvement>Starting point>Q ●

How to expand a single bracket?

$3 (2 x - 5)$

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 25 - Trial and Improvement>Exercise 1>Q 2

Complete the table for equation $x^{2} + x = 100$ .

Trial	$x^{2} + x$	Comment
$x = 10$	$10^{2} + 10 = 110$	Too big
$x = 9$	$9^{2} + 9 =$ _____	_____
$x = 9.5$	$9 . 5^{2} + 9.5 =$ _____	_____
$x = 9.6$	_____	_____

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 25 - Trial and Improvement>Exercise 1>Q 2

Solve the equation $x^{2} + x = 100$ . Give your answer correct to $1$ d.p.

MEDIUM

Lower Secondary Stage 9

IMPORTANT

Cambridge Lower Secondary Maths Stage 9: Student's Book>Chapter 25 - Trial and Improvement>Exercise 1>Q 3

Complete the table for the equation $x^{2} + 5 x = 60$

Trial	$x^{2} + 5 x$	Comment
$x = 5$	$5^{2} + 5 \times 5 = 50$	Too big
$x = 6$	$6^{2} + 5 \times 6 =$ _____	_____
$x = 5.6$	$5 . 6^{2} + 5 \times 5.6 =$ _____	_____
$x = 5.7$	_____	_____
$x = 5.65$	_____	_____