O-LevelAdditional MathematicsIndices and surds4037/22 · May/June 2013 · Q56 Marks

Calculators must not be used in this question. The diagram shows a trapezium ABCD in which AD = 7cm and AB = (4+ √5)cm. AX is perpendicular to DC with DX = 2cm and XC = xcm. Given that the area of trapezium ABCD is 15(√5+ 2)cm², obtain an expression for x in the form a + b√5, where a and b are integers.

Calculators must not be used in this question. The diagram shows a trapezium ABCD in which AD = 7cm and AB = (4+ √5)cm. AX is perpendicular to DC with DX = 2cm and XC = xcm. Given that the area of trapezium ABCD is 15(√5+ 2)cm², obtain an expression for x in the form a + b√5, where a and b are integers.[6]

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Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

[B1] AX = √45
[B1] AX = 3√5
[M1] (1/2)(4+√5+2+x) x their √45 soi
[M1] 15(√5+2) = (1/2)(4+√5+2+x) x their √45 or better
[M1] Correctly divide their equation by their √5 or their √45 and rationalise denominator
[A1] completion to 4+3√5 www

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