10 f(x) = 4sin²x
(a) Find f(23)
Give your answer correct to 3 significant figures - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 3
Question 10
10 f(x) = 4sin²x
(a) Find f(23)
Give your answer correct to 3 significant figures.
g(x) = 2x – 3
(b) Find fg(34)
Give your answer correct to 3 significant figure... show full transcript
Worked Solution & Example Answer:10 f(x) = 4sin²x
(a) Find f(23)
Give your answer correct to 3 significant figures - Edexcel - GCSE Maths - Question 10 - 2018 - Paper 3
Step 1
Find f(23)
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Answer
To find f(23), substitute x = 23 into the function:
f(23)=4sin2(23)
Using a calculator,
Calculate sin(23).
Square the result.
Multiply by 4.
Calculating gives:
f(23)≈4×(0.3907)2≈4×0.1527≈0.6109
Rounding this to 3 significant figures yields:
f(23)≈0.611
Step 2
Find fg(34)
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Answer
First, find g(34):
g(34)=2(34)−3=68−3=65
Now substitute into f:
f(g(34))=f(65)=4sin2(65)
Using calculator:
Calculate sin(65).
Square the result.
Multiply by 4.
Calculating gives:
f(65)≈4×(0.9063)2≈4×0.8212≈3.2848
Rounding this to 3 significant figures yields:
fg(34)≈3.28
Step 3
Explain why the statement is not fully correct.
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Answer
Ivan's process has an error in his method.
He wrote (x + 4)² = 25 correctly but stopped without considering both potential square root outcomes. The correct equation involves:
x+4=±5
This leads to two possible solutions:
For the positive case: x+4=5⇒x=1
For the negative case: x+4=−5⇒x=−9
Thus, the solutions should include both values: x = 1 and x = -9.
