10 f(x) = 4sin²x
(a) Find f(23)
Give your answer correct to 3 significant figures - Edexcel - GCSE Maths - Question 11 - 2018 - Paper 3
Question 11
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 figures... 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 11 - 2018 - Paper 3
Step 1
Find f(23)
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Answer
To find f(23), substitute 23 into the function:
f(23)=4imesextsin2(23)
Calculate the sine value:
Compute extsin(23) (ensure your calculator is in degrees).
Square the result and multiply by 4 to find f(23).
Round your answer to 3 significant figures.
Step 2
Find fg(34)
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Answer
First, compute g(34):
g(34)=2(34)−3=68−3=65
Now substitute this value into f:
f(g(34))=f(65)=4imesextsin2(65)
Calculate to find the value and round to 3 significant figures.
Step 3
Explain why.
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Answer
Ivan's solution is not fully correct because:
He did not consider both the positive and negative square roots, which arise from squaring a variable.
The correct approach would be:
From (x+4)2=25, take the square root:
x+4=±5
This leads to two equations:
x+4=5 → x=1
x+4=−5 → x=−9
Thus, the solutions should be x=1 and x=−9, highlighting that there are two possible values for x.
