A-LevelMathematicsTrigonometry9709/12 · Oct/Nov 2022 · Q35 Marks

Find the set of values of k for which the equation 8x² + kx + 2 = 0 has no real roots.

(a)Find the set of values of k for which the equation 8x² + kx + 2 = 0 has no real roots.[2]
(b)Solve the equation 8 cos² θ – 10 cos θ + 2 = 0 for 0° ≤ θ ≤ 180°.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

M1 Use of b² - 4ac but not just in the quadratic formula. k² - 4 × 8 × 2 [< 0]
A1 Condone '– 8 < k or k < 8', '– 8 < k and k < 8' but not √64. -8 < k < 8 or |k| < 8 or (-8, 8)
M1 OE. Or use of formula or completing the square. Allow use of replacement variable. 2(4cosθ - 1)(cosθ - 1) or (4cosθ - 1)(cosθ - 1)
A1 OE For both answers. cosθ = 2/8, cosθ = 1
SC: If M0, SC B1 available for sight of cosθ = 2/8 and 1
A1 AWRT ISW rejection of 0°. For both answers and no others in the range 0°≤θ≤180°, must be in degrees. [θ =] 0°, 75.5°
SC: If M0 B1 scored, SC B1 available for correct answers.
SC: If M1 A0 scored, SC B1 available for cosθ = 2/8 and θ = 75.5° only, WWW.

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