Download Homework on analysing questionnaires – grade C

The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
HW1 – Grade C
Trial and Improvement
1.
(a)
x2 + 4x
Factorise
……………...........………………………….....…………………………………….
Answer ………………………………….
(1)
(b)
Solve the inequality
7y < 3y + 6
……………...........………………………….....…………………………………….
……………...........………………………….....…………………………………….
Answer ………………………………….
(2)
(c)
Make r the subject of the formula
p = 3 + 2r
……………...........………………………….....…………………………………….
……………...........………………………….....…………………………………….
……………...........………………………….....…………………………………….
Answer r = ………………………………….
(2)
(Total 5 marks)
2.
Laura is using trial and improvement to find a solution to the equation
x3+ 2x = 60
The table shows her first try. Continue the table to find a solution to the equation.
x
Comment
x3 + 2x
3
33
too small
Give your answer correct to 1 decimal place.
Answer x = ....................................................
(Total 4 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
3.
Gary is using trial and improvement to find a solution to the equation x3– 5x = 56.
This table shows his first two trials.
x
x3 – 5x
Comment
4
44
Too small
5
100
Too big
Continue the table to find a solution to the equation.
Give your answer to 1 decimal place.
Answer x = ................................................................
(Total 3 marks)
4.
Parveen is using trial and improvement to find a solution to the equation
x3 + 7x = 30
This table shows her first two trials.
x
x3 + 7x
Comment
2
22
Too small
3
48
Too big
Continue the table to find a solution to the equation.
Give your answer to 1 decimal place.
Answer .............................................................
(Total 3 marks)
The Robert Smyth School
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The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
5.
Use trial and improvement to find a solution to the equation
x3 – x = 21
Give your answer to one decimal place.
You must show your working.
................................................................................................................................................
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................................................................................................................................................
Answer x = ……………………………….
(Total 4 marks)
6.
A solution of the equation x3 – 8x = 110 lies between x = 5 and x = 6.
Use trial and improvement to find this solution.
Give your answer to one decimal place.
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...............................................................................................................................................
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Answer x = ..................................................................
(Total 3 marks)
The Robert Smyth School
3
The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
7.
Kate and Lee are working out this question.
A solution of the equation x3 + x = 700 lies between 8 and 9.
Use trial and improvement to find this solution, correct to one decimal place.
Kate’s answer is 8.8
Lee’s answer is 8.9
Which answer is correct?
You must show all your working.
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
...............................................................................................................................................
Answer x = ......................................................
(Total 3 marks)
The Robert Smyth School
4
The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
1.
(a)
x(x + 4)
(b)
4y < 6
B1
M1
y = 1.5 oe scores M1A0
y < 1.5
A1
oe
(c)
p – 3 = 2r or p/2 = 3/2 + r
or (p + 3)/2 or (3 – p)/2
M1
(p – 3)/2 or p/2 – 3/2
oe
A1
[5]
2.
3.7
M1,M1,A1,A1
M1 for trying value bigger than 3
M1 for trying 1d.p value between 3 and 4
M1 for sandwiching between 3.7 and 3.8
A1 for testing 3.75 (or other apt 2 dp value) and stating answer
[4]
3.
Trial for 4 < x < 5
B1
Correctly evaluated to at least nearest whole number
2 trials for 4.2  x  4.3 that ‘bracket’ 56
Trials must be correct to or truncated to at least 1 dp
B1
Trial at 4.25 & answer 4.3
B1
[3]
4.
Trial between 2 and 3
B1
Trial between 2.3 and 2.4 inclusive that “bracket” the answer
B1
Trial at 2.35 or 2.36 or 2.37 and 2.4 stated as answer
DB1
In this question final answer on its own will not get any marks
Working must be seen.
All trials must be correctly evaluated either rounded or
truncated to a degree of accuracy that allows comparison.
[3]
5.
Trial above 2.8796
M1
2 gives 6, 3 gives 24
Trial below 2.8796
M1
2.9 gives 21.489, all values to at least l dp
rounded or truncated
Testing a value that justifies 2.9 as answer
2.5 13.125, 2.6  14.976, 2.7  16.983
2.8  19.152, 2.85 gives 20.299
x = 2.9
The Robert Smyth School
DM1
A1
5
The Robert Smyth School
Mathematics Faculty
Topic 9
Solving Equations 2
Innovation & excellence
Dep on any M mark
[4]
6.
Trial between 5 and 6
B1
Trials at 5.3 and 5.4 or better that bracket 110
5.3  106(.47...)
5.4  114(.26...)
B1
Trial at 5.35 and answer 5.3
5.35  110.3(3...)
B1
[3]
7.
Trial at 8.8 or 8.9 (or between)
690(.272) or 713(.869)
B1
Trials at 8.85 (702) and 8.8
or any 2 trials for 8.8 ≤ x ≤ 8.85
which bracket 700
Note: These 2 trials score first B1
also
B1
8.8 or Kate
B1 dep
Dependent on second B1
Alternative method:
Trial at 8.85
M1
702
A1
8.8
A1
[3]
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