O-LevelAdditional MathematicsQuadratic functions4037/22 · May/June 2023 · Q17 Marks
Solve the inequality 3x²-12x+16 > 3x+4.
- (a)Solve the inequality 3x²-12x+16 > 3x+4.[3]
- (b)(i)Write 3x²-12x+16 in the form a(x+b)² + c where a, b and c are integers.[3]
- (b)(ii)Hence, write down the equation of the tangent to the curve y = 3x² - 12x+16 at the minimum point of the curve.[1]
Mark scheme
Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.
- [B1] 3x²-15x+12 [*0] oe where * is any inequality sign or =
- [M1] Factorises or solves their 3-term quadratic FT their 3-term quadratic
- [A1] x < 1 or x > 4 mark final answer
- [3] 3(x-2)² + 4
- [B2] for 3(x-2)²
- [B1] for (x-2)² or a = 3, b = −2
- [B1] for a(x+b)² + 4 with numerical values of a and b or c = 4
- [B1] y = their 4 STRICT FT their 4 from part (i)
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