O-LevelMathematicsCoordinate geometry4024/22 · May/June 2021 · Q610 Marks
PQR is an isosceles triangle with PR = QR. P is the point (1, 5) and Q is the point (5, 1). Angle PRQ is not a right angle. Find the coordinates for one possible position of R. You may use the grid to help you. [Figure 6.A]
- (a)PQR is an isosceles triangle with PR = QR. P is the point (1, 5) and Q is the point (5, 1). Angle PRQ is not a right angle. Find the coordinates for one possible position of R. You may use the grid to help you. [Figure 6.A][2]
- (b)Here are the equations of five curves. y = 2-x² y = x³-2 y = x²+2x-8 y = x³-3x y = x² - 3x Sketches of three of these curves are drawn below. Write the correct equation underneath each sketch. [Figure 6.B][3]
- (c)A is the point (-1, -5) and B is the point (3, 3). Find the equation of the line perpendicular to AB which passes through the midpoint of AB.[5]
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Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [2] (a) (a, a) with a ≠ 1, 3 or 5 SC1 for answer (1, 1) or (5, 5)
- [3] (b) [y =] x² - 3x B1 for each [y =] 2 - x² [y =] x³-2 cao
- [5] (c) y = -1/2 x - 1/2 oe nfww M1 for [gradient AB =] (3-(-5))/(3-(-1)) oe M1 for [gradient M =] 1/(theirgradientAB) B1 for (1, -1) M1 for their (1, -1) substituted into y=their-1/2 x+c oe
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