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TMUA graphs and transformations questions
All 16 graphs and transformations questions from the TMUA past papers, 2016 to 2023, newest first, each with a worked solution.
2023
- P1 Q11 · It is given that f(x) = x² - 6x. The curves y = f(kx) and y = f(x - c) have the same minimum…
- P1 Q20 · The diagram shows the graph of y = f(x). The function f attains its maximum value of 2 at x = 1,… hard
2022
- P1 Q10 · A sequence of translations is applied to the graph of y = x³. Which of the following graphs could…
- P1 Q18 · It is given that f(x) = x²(x-1)²(x-2) g(x) = -p(x-q)²(x-r)² where p, q and r are positive and q… hard
- P1 Q20 · n is the number of points of intersection of the graphs y = |x² - a²| y = a²|x - 1| where a is a… hard
- P2 Q18 · Four graphs P, Q, R and S show y = (cos x)^cos x, y = (sin x)^sin x, y = (cos x)^sin x, y = (sin… hard
2021
- P1 Q9 · Find the area enclosed by the graph of |x| + |y| = 1
- P1 Q17 · Which of the following sketches shows the graph of sin(x² + y²) = (1)/(2) where x² + y² ≤ 8π? All…
- P1 Q18 · The curve with equation x = y² - 6y + 11 is rotated 90^∘ clockwise about the point P to give the… hard
2020
- P1 Q10 · The following sequence of transformations is applied to the curve y = 4x²: 1. Translation by…
- P2 Q5 · Which one of the following shows the graph of y = (2^x)/(1 + 2^x) (Dotted lines indicate…
2019
- P1 Q20 · What is the complete range of values of k for which the curves with equations y = x³ - 12x and y =… hard
- P2 Q20 · When the graph of the function y = f(x), defined on the real numbers, is reflected in the y-axis…