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Here are two functions - OCR - GCSE Maths - Question 11 - 2020 - Paper 6
Question 11
Here are two functions. Function A: Input → × 3 → + 15 → Output Function B: Input → + 11 → × 2 → Output (a)(i) Jo chooses a number, x. She inputs x into each func... show full transcript
Worked Solution & Example Answer:Here are two functions - OCR - GCSE Maths - Question 11 - 2020 - Paper 6
Step 1
(a)(i) Work out the value of x.
Answer
To find the value of x, we first set the outputs of Function A and Function B equal to each other:
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Function A output: [ 3x + 15 ]
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Function B output: [ 2(x + 11) ]
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Set them equal:
[ 3x + 15 = 2(x + 11) ] -
Expand the right side:
[ 3x + 15 = 2x + 22 ] -
Rearranging gives:
[ 3x - 2x = 22 - 15 ] [ x = 7 ]
Thus, ( x = 7 ).
Step 2
(a)(ii) Explain why there is no other input that gives two outputs that are equal.
Answer
The functions A and B are linear functions that can be expressed in the form of straight lines. Since they have different slopes (3 for Function A and 2 for Function B), they can only intersect at one point. Since we found that ( x = 7 ) is the only solution where their outputs are equal, no other input can provide equal outputs. Therefore, there can't be another number that gives the same outputs because each function is uniquely defined by its coefficients.
Step 3
(b) Find the value of p and the value of q.
Answer
To ensure that Function A and Function C yield equal outputs for any input number, we set up an equation:
- Function A output: [ 3x + 15 ]
- Function C output: [ x + p \times q ]
Set these equal:
[ 3x + 15 = x + p \times q ]
Rearranging gives:
[ 3x - x + 15 = pq ]
[ 2x + 15 = pq ]
To satisfy this for all x, set ( p = 2 ) and ( q = 15 ).
Thus, the values are:
- ( p = 2 )
- ( q = 15 ).