O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2016 · Q311 Marks
The table below is for y = x²+x-3. x | -3 | -2 | -1 | 0 | 1 | 2 y | 3 | -1 | -3 | -3 | -1 | 3 [Figure 3.1]
- (a)Using a scale of 2cm to 1 unit on the x-axis for -3 ≤ x ≤ 2 and a scale of 1 cm to 1 unit on the y-axis for -4 ≤ y ≤ 4, plot the points from the table and join them with a smooth curve.[2]
- (b)(i)Use your graph to estimate the solutions of the equation x²+x-3 = 0.[1]
- (b)(ii)Use your graph to estimate the solutions of the equation x²+x− 5 = 0.[2]
- (c)By drawing a tangent, estimate the gradient of the curve at (1,−1).[2]
- (d)(i)The equation x²-x-1=0 can be solved by drawing a straight line on the graph of y = x² + x - 3. Find the equation of this straight line.[2]
- (d)(ii)Draw this straight line and hence solve x² - x - 1 = 0.[2]
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Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [2] (a) Correct graph
- [2] (a) B1 for correct scales and 4 points or wrong scales and all points.
- [1] (b)(i) -2.3±0.5, 1.3 ± 0.5
- [2] (b)(ii) -2.8±0.5, 1.8 ± 0.5
- [2] (b)(ii) M1 for x² + x − 3 = 2 soi
- [2] (c) 2.4 to 3.6
- [2] (c) M1 for tangent at x =1
- [2] (d)(i) y = 2x-2
- [2] (d)(i) B1 for 2x or -2
- [2] (d)(ii) -0.6, 1.6
- [2] (d)(ii) Dependent on line drawn
- [2] (d)(ii) B1 for their line having FT gradient or FT intercept
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