Transcript x - Burton Borough School

GCSE Maths Starter 15
1. 20 − 12 ÷ 4
2. Solve 4x + 3 = 18 – 2x
3. Tom, Tim and Bill share £60 in the ratio 2:3:5.
Calculate the amount each person receives.
4. p = mq + r, make q the subject
5. Find the mean, median and mode and range
of:
5, 11, 5, 7, 9, 10, 4, 4, 5, 10
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)
Trial and Improvement
Worked Example 1.
Solve x2 - x = 27 (to 1 d.p)
x2 - x
x
27
5
52 - 5 = 20
too small
6
62 - 6 = 30
too big
5.5
5.52 - 5.5 = 24.75
too small
5.6
5.62 - 5.6 = 25.76
too small
5.7
5.72 - 5.7 = 26.79
too small
5.8
5.82 - 5.8 = 27.84
too big
5.75
5.752
x = 5.7
5.7
The Method
1. Make a table similar to
this one. 27 is your
target number.
2. Make an intelligent
guess to find two
positive consecutive
integers that output
values that straddle the
target number.
3. Repeat above with
consecutive 1 d.p.
numbers between 5
and 6. (Trying 5.5 first)
4. One of these is the
- 5.75 = 27.3125
correct 1 d.p solution
but which one?
So the true value must lie in here and all
values are 5.7 when rounded.
5. Compute the mid-point
value to help you
decide.
5.75
5.8
too big
1 d.p.
Worked Example 3.
x+3
x
x
52
Trial and Improvement
cm2
Find the width of the
rectangle to 1 d.p.
x2 + 3x
52
5
52 + 3 x 5 = 40
too small
6
62 + 3 x 6 = 54
too big
5.9
5.92 + 3 x 5.9 = 52.51
too big
5.8
5.82 + 3 x 5.8 = 51.04
too small
5.85
5.852 + 3 x 5.85 = 51.7725
too small
x = 5.9
Remember :midpoint value: too
big  round down
too
small  round up
The Method
1. Make a table similar to
this one. 52 is your
target number.
2. Make an intelligent
guess to find two
positive consecutive
integers that output
values that straddle the
target number.
3. Repeat above with
consecutive 1 d.p.
numbers between
5 and 6.(Trying 5.9)
4. One of these is the
correct 1 d.p solution.
5. Compute the midpoint
output.
6. Too small so round up
Trial and Improvement
Questions
Solve the following problems below by finding a positive solution for x to 1 d.p.
1. x2 + x = 8
2. x3 - x = 180
3. 2x2 - 3x = 1
x = 2.4
x = 5.7
x = 1.8
x+4
4.
x
27 cm2
x = 3.6
2x + 1
5.
Questions 1
x
11 cm2
x = 2.1
Foundation/Higher Exam Type Question Calculator):
1.
Leave
blank
The equation
x3 - 12 = 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.
x = ......................... (4 marks)
(Total 4 marks)
Q1
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 Q3
5.8 (note: This is closer than 5.9)
Lesson 15
Trial and improvement
Mathswatch clip (110).
Exam questions