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TMUA coordinate geometry questions
All 36 coordinate geometry questions from the TMUA past papers, 2016 to 2023, newest first, each with a worked solution.
2023
- P1 Q5 · The following shape has two lines of reflectional symmetry. MNOP is a square of perimeter 40 cm.…
- P1 Q13 · Point P lies on the circle with equation (x-2)² + (y-1)² = 16. Point Q lies on the circle with…
- P1 Q16 · A right-angled triangle has vertices at (2, 3), (9, -1) and (5, k). Find the sum of all the…
- P2 Q7 · The graph of the line ax + by = c is drawn, where a, b and c are real non-zero constants. Which…
- P2 Q8 · A student draws a triangle that is acute-angled or obtuse-angled but not right-angled. The student… hard
- P2 Q14 · Three lines are given by the equations: ax + by + c = 0 bx + cy + a = 0 cx + ay + b = 0 where a, b… hard
2022
- P1 Q2 · Find the complete set of values of p for which the equation x² - 2px + y² - 6y - p² + 8p + 9 = 0…
- P1 Q14 · A circle has centre O and radius 6. P, Q and R are points on the circumference with angle POQ ≥… hard
- P1 Q19 · Circle C₁ is defined as x² + y² = 25. A second circle C₂ has radius 4 and centre (a, b) where -2 ≤…
- P2 Q4 · The point P has coordinates (p, q), and the equation of a circle is x² + 2fx + y² + 2gy + h = 0…
- P2 Q11 · A kite PQRS has diagonals meeting at O, with OP = x, OQ = y, OR = x, OS = z Which of the following…
- P2 Q19 · A polygon has n vertices, where n ≥ 3. It has the following properties: Every vertex of the… hard
2021
- P1 Q1 · Two circles have the same radius. The centre of one circle is (-2, 1). The centre of the other…
- P1 Q20 · Find the length of the curve with equation 2log₁₀(x - y) = log₁₀(2 - 2x) + log₁₀(y + 5) hard
- P2 Q2 · A(0,2) and C(4,0) are opposite vertices of the square ABCD. What is the equation of the straight…
- P2 Q7 · A circle has equation (x-9)² + (y+2)² = 4 A square has vertices at (1,0), (1,2), (-1,2) and…
- P2 Q15 · A circle has equation x² + ax + y² + by + c = 0 where a, b and c are non-zero real constants.…
2020
- P1 Q16 · The circle C₁ has equation (x+2)² + (y-1)² = 3. The circle C₂ has equation (x-4)² + (y-1)² = 3.…
- P2 Q7 · Consider the following conditions on a parallelogram PQRS, labelled anticlockwise:…
- P2 Q11 · A spiral line is drawn as shown. Starting from the point (-2, 0) it travels down to (-2, -2),…
2019
- P1 Q6 · The circles with equations (x+4)² + (y+1)² = 64 and (x-8)² + (y-4)² = r², where r > 0 have exactly…
- P1 Q18 · Find the shortest distance between the curve y = x² + 4 and the line y = 2x - 2.
- P2 Q10 · PQRS is a quadrilateral, labelled anticlockwise. Which one of the following is a necessary but not…
2018
- P1 Q3 · Find the shortest distance between the two circles with equations: (x + 2)² + (y - 3)² = 18 (x -…
- P1 Q16 · The curve C has equation y = x² + bx + 2, where b ≥ 0. Find the value of b that minimises the…
- P2 Q5 · The two diagonals of the quadrilateral Q are perpendicular. Consider the following statements:…
2017
- P1 Q3 · A line l has equation y = 6 - 2x. A second line is perpendicular to l and passes through the point…
- P1 Q6 · A tangent to the circle x² + y² = 144 passes through the point (20, 0) and crosses the positive…
- P1 Q9 · A circle has equation x² + y² - 18x - 22y + 178 = 0 A regular hexagon is drawn inside this circle…
- P2 Q2 · PQRS is a rectangle. The coordinates of P and Q are (0,6) and (1,8) respectively. The…
2016
- P1 Q9 · The line segment joining the points (3, 3) and (7, 5) is a diameter of a circle. This circle is…
- P1 Q20 · The diagram shows a square-based pyramid with base PQRS and vertex O. All the edges of the pyramid… hard
- P2 Q9 · Triangles ABC and XYZ have the same area . Which of these extra conditions, taken independently,…
- P2 Q16 · In the figure, PQRS is a trapezium with PQ parallel to SR. The diagonals of the trapezium meet at…
- P2 Q19 · Some identical unit cubes are used to construct a three-dimensional object by gluing them together…
- P2 Q20 · Each interior angle of a regular polygon with n sides is (3)/(4) of each interior angle of a…