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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) Jo chooses a number, x. She inputs x into each functio... show full transcript
Worked Solution & Example Answer:Here are two functions - OCR - GCSE Maths - Question 11 - 2020 - Paper 6
Step 1
(a)(i) x =
Answer
To find the value of x, we set the outputs of both functions equal:
For Function A: Output = 3x + 15
For Function B: Output = 2(x + 11) = 2x + 22
Setting these equal gives us the equation:
Now, we can solve for x:
- Subtract 2x from both sides:
- Simplifying gives:
- Subtract 15 from both sides:
- Hence, .
Step 2
(a)(ii) Explain why there is no other input that gives two outputs that are equal.
Answer
The functions are linear equations with unique slopes; therefore, their outputs will only be equal at one specific point where they intersect. Since both functions are defined in terms of x, any other input will yield different outputs due to their linear nature. Thus, there cannot be another input that gives equal outputs for Function A and Function B.
Step 3
(b) p =
Answer
To ensure Kai’s function C gives an output equal to Function A for any input, we need:
For Function A: Output = 3x + 15
For Function C: Output = x + p × q
Setting the two outputs equal:
Rearranging gives:
Since we want this to hold true for all x, we must have:
- The coefficient of x on both sides must be equal:
- The coefficient of x should also be 2, requiring that:
Thus, the values are: .