1. GCSE Maths Starter 15 20−12÷4 Solve 4x + 3 = 18 – 2x
Tom, Tim and Bill share £60 in the ratio 2:3:5. Calculate the amount each person receives.
p = mq + r, make q the subject
Find the mean, median and mode and range of:
5, 11, 5, 7, 9, 10, 4, 4, 5, 10

2. Lesson 15 Trial and improvement Mathswatch clip (110).
To estimate a solution to an equation (Grade D/C )
EXTN: To form and solve equations using trial and improvement(Grade C)

3. 1 d.p. Solve x2 - x = 27 (to 1 d.p) x x2 - x 27 x = 5.7
Worked Example 1.
Trial and Improvement
The Method
Solve x2 - x = 27 (to 1 d.p)
Make a table similar to this one. 27 is your target number. x
x2 - x 27
2. Make an intelligent guess to find two positive consecutive integers that output values that straddle the target number. 5
= 20
too small 6
= 30
too big
5.5
= 24.75
too small
5.6
= 25.76
too small
3. Repeat above with consecutive 1 d.p. numbers between 5 and 6. (Trying 5.5 first)
5.7
= 26.79
too small
5.8
= 27.84
too big
4. One of these is the correct 1 d.p solution but which one?
too big
5.75 =
So the true value must lie in here and all values are 5.7 when rounded.
x = 5.7
5. Compute the mid-point value to help you decide.
1 d.p.
5.7
5.8
5.75

4. Remember :midpoint value: too big  round down too small  round up
Worked Example 3.
Trial and Improvement
The Method
x + 3
Make a table similar to this one. 52 is your target number.
Find the width of the rectangle to 1 d.p. x
52 cm2
2. Make an intelligent guess to find two positive consecutive integers that output values that straddle the target number. x
x2 + 3x 52 5
x 5 = 40
too small 6
x 6 = 54
too big
5.9
x 5.9 = 52.51
too big
3. Repeat above with consecutive 1 d.p. numbers between and 6.(Trying 5.9)
5.8
x 5.8 = 51.04
too small
5.85
x 5.85 =
too small
4. One of these is the correct 1 d.p solution.
x = 5.9
5. Compute the midpoint output.
Remember :midpoint value: too big  round down too small  round up
6. Too small so round up

5. Questions 1 x = 2.4 x = 5.7 x = 1.8 x = 3.6 x = 2.1 1. x2 + x = 8
Trial and Improvement
Questions
Solve the following problems below by finding a positive solution for x to 1 d.p.
1. x2 + x = 8
x = 2.4
2. x3 - x = 180
x = 5.7
3. 2x2 - 3x = 1
x = 1.8
x + 4 4.
x = 3.6 x
27 cm2
2x + 1
Questions 1 x
11 cm2
x = 2.1 5.

6. has a solution between 4 and 5
Foundation/Higher Exam Type Question Calculator):
Leave
blank Q1
(Total 4 marks) 1.
(4 marks)
x =
The equation
x = 85
has a solution between 4 and 5
Use a trial and improvement method to find the solution, correct to one decimal place.
You must show all of your working.

7. 3) width of rectangle is 7.8cm 4) x = 3.7
N 29 Trial & Improvement
Answers
Exercise 1 1) Generate the equation x(x + 5) = 73 from the information given (length times width of rectangle gives its area).
Use trial & improvement to arrive at a solution of 6.4cm
2) x = 5.3
3) width of rectangle is 7.8cm
4) x = 3.7
Exam Q1 4.6
Exam Q2 4.7
Exam Q (note: This is closer than 5.9)

8. Lesson 15 Trial and improvement Mathswatch clip (110).
Exam questions