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It is some examples questions to practise further maths GCSE aqa
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Materials required for examination Items included with question papers Mathematical Formulae (Pink or Green) Nil Advice to Candidates You must ensure that your answers to parts of questions are clearly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers without working may not gain full credit.
1. f( x ) = 2 x^3 + x^2 โ 5 x + c , where c is a constant. Given that f(1) = 0, ( a ) find the value of c , (2) ( b ) factorise f( x ) completely, (4) ( c ) find the remainder when f( x ) is divided by (2 x โ 3). (2)
4. f( x ) = 2 x^3 + 3 x^2 โ 29 x โ 60. ( a ) Find the remainder when f( x ) is divided by ( x + 2). (2) ( b ) Use the factor theorem to show that ( x + 3) is a factor of f( x ). (2) ( c ) Factorise f( x ) completely. (4)
5****. f( x ) = x^3 + 4 x^2 + x โ 6. ( a ) Use the factor theorem to show that ( x + 2) is a factor of f( x ). (2) ( b ) Factorise f( x ) completely. (4) ( c ) Write down all the solutions to the equation x^3 + 4 x^2 + x โ 6 = 0. (1)
7. f( x ) = 2 x^3 โ 3 x^2 โ 39 x + 20 ( a ) Use the factor theorem to show that ( x + 4) is a factor of f ( x ). (2) ( b ) Factorise f ( x ) completely. (4) 8. f( x ) = (3 x โ 2)( x โ k ) โ 8 where k is a constant. ( a ) Write down the value of f ( k ). (1) When f( x ) is divided by ( x โ 2) the remainder is 4. ( b ) Find the value of k. (2) ( c ) Factorise f ( x ) completely. (3)
9. f ( x ) = x^4 + 5 x^3 + ax + b , where a and b are constants. The remainder when f( x ) is divided by ( x โ 2) is equal to the remainder when f( x ) is divided by ( x + 1). ( a ) Find the value of a. (5) Given that ( x + 3) is a factor of f( x ), ( b ) find the value of b. (3)
