O LevelAdditional MathsCambridgeExam QuestionsAlgebra & FunctionsQuadratic Functions

Quadratic Functions (Cambridge O Level Additional Maths)

Exam Questions

1 hour15 questions
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1a
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Write the expression x squared space minus 6 x plus 1 in the form left parenthesis x plus a right parenthesis squared space plus b, where a and b are constants.

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1b
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Hence write down the coordinates of the minimum point on the curve y space equals space x squared space minus 6 x plus 1.

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2
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Solve the inequality left parenthesis x minus 8 right parenthesis left parenthesis x minus 10 right parenthesis space greater than space 35 .

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3
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Solve the equation 2 x minus 11 space square root of x space plus 12 space equals space 0.

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4
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Find the values of k for which the equation x squared space plus space left parenthesis k plus 9 right parenthesis x plus 9 space equals space 0 has two distinct real roots.

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1
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Find the values of the constant k for which the equation left parenthesis 2 k space – space 1 right parenthesis x squared space plus space 6 x space plus space k space plus space 1 space equals space 0 has real roots.

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2
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Find the values of x for which 12 x squared minus 20 x plus 5 space less than space open parentheses 2 x plus 1 close parentheses open parentheses x minus 1 close parentheses.

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3a
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Write 9 x squared space minus 12 x plus 5 in the form p left parenthesis x minus q right parenthesis squared space plus r, where p,space q space and r are constants.

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3b
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Hence write down the coordinates of the minimum point of the curve y space equals space 9 x squared space minus 12 x plus 5.

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4
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Solve 2 x to the power of 2 over 3 end exponent minus x to the power of 1 third end exponent minus 10 equals 0.

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5
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Find the set of values of k for which 4 x squared space minus 4 k x plus 2 k plus 3 space equals space 0 has no real roots.

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6
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Solve 6 x to the power of 2 over 3 end exponent minus 5 x to the power of 1 third end exponent plus 1 equals 0.

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1
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Find the values of k for which the line y space equals space k x plus 3 is a tangent to the curve y space equals space 2 x squared space plus 4 x plus k minus 1.

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2
Sme Calculator6 marks

Find the values of k for which the line y space equals space x minus 3 intersects the curve y space equals space k squared x squared space plus 5 k x plus 1 at two distinct points.

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3
Sme Calculator6 marks

Find the exact values of the constant k for which the line y space equals space 2 x plus 1 is a tangent to the curve y space equals space 4 x to the power of 2 space end exponent plus k x plus k minus 2.

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4
Sme Calculator6 marks

Find the values of k for which the line y space equals space k x minus 7 and the curve y space equals space 3 x squared space plus 8 x plus 5 do not intersect.

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5
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The curve y space equals space 2 x squared space plus k plus 4 intersects the straight line y space equals space left parenthesis k plus 4 right parenthesis x at two distinct points. Find the possible values of k.

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