A-Level CAIE Mathematics AS 2.1 Algebra Question Bank

[Maximum number: 8]

The polynomial p(x) is defined by

\mathrm{p}(x)=a x^{3}+b x-10,

where a and b are constants. It is given that (x+2) is a factor of p(x) and that the remainder is -55 when p(x) is divided by ( x+3 ).

(a)

Find the values of a and b.

[ 5 ]

(b)

Hence factorise p(x) completely.

[ 3 ]

[Maximum number: 4]

Solve the inequality |3 x-7|<|4 x+5|.

(a)

Sketch, on the same diagram, the graphs of y=|3 x-5| and y=x+2.

[ 2 ]

(b)

Solve the equation |3 x-5|=x+2.

[ 3 ]

(a)

Solve the inequality |2 x-7|<|2 x-9|.

[ 3 ]

[Maximum number: 3]

The polynomial f(x) is defined by

f(x)=x^{4}-3 x^{3}+5 x^{2}-6 x+11

Find the quotient and remainder when f(x) is divided by $\left(x^{2}+2\right)$ .

[Maximum number: 3]

The polynomial p(x) is defined by

\mathrm{p}(x)=4 x^{3}+(k+1) x^{2}-m x+3 k

where k and m are constants. Given that (x+1) is a factor of p(x), express m in terms of k.

[Maximum number: 4]

Solve the inequality |3 x-2|<|x+5|.

[Maximum number: 3]

Solve the equation |x+a|=|2 x-5 a|, giving x in terms of the positive constant a.

[Maximum number: 3]

Solve the equation |0.4 x-0.8|=2.

[Maximum number: 3]

Find the quotient and the remainder when $2 x^{3}+3 x^{2}+10$ is divided by (x+2).

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