Higher June 2018 Paper 2 Q16
16
(a) On the grid, draw the graph of \(x^2 + y^2 = 12.25\)
(b) Hence find estimates for the solutions of the simultaneous equations
\(x^2 + y^2 = 12.25\)
\(2x + y = 1\) (3)
\(x^2 + y^2 = 12.25\)
\(2x + y = 1\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| Correct graph | B2 | for a circle radius 3.5, centre \((0, 0)\) |
| (B1 | for a circle centre \((0, 0)\) of a different radius, or for a circle drawn of radius 3.5 centre not \((0, 0)\) or incomplete correct circle) |
Additional guidance
Circle could be drawn freehand as long as it approximates to a circle
| Answer | Mark | Mark scheme |
|---|---|---|
| \(x = 2.0\), \(y = -2.9\) \(x = -1.2\), \(y = 3.3\) | M1 | for \(2x + y = 1\) drawn, or for correctly eliminating one variable, eg \(x^2 + 1 - 4x + 4x^2 = 12.25\) or \(x^2 + (1 - 2x)^2 = 12.25\) |
| A1 | for the pair of \(x\) values, or the correct pair of \(y\) values, or one correct pair of \(x\)/\(y\) values ft from (a) (dep on B1) | |
| A1 | for both correct pair of \(x\)/\(y\) values, unambiguously matched ft from (a) (dep on B1) |
Additional guidance
\(2x + y = 1\) does not have to be shown
Use professional judgment
Accept values given as coordinates.
Check graph for answers