CAIE A-Level Mathematics 2.1 Algebra Question Bank

CAIE A-Level Mathematics 2.1 Algebra Question Bank
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise solving modulus equations and inequalities and applying polynomial division, factor and remainder theorems to determine coefficients, factors and real roots.

Exam points

  • split a modulus relation at its critical points and combine only intervals satisfying all conditions
  • divide a polynomial by a linear or quadratic divisor and retain the stated remainder
  • apply p(a) = 0 or p(a) = r to form coefficient equations and complete the factorisation

Covered syllabus points

2.1.1—Modulus equations2.1.2—Polynomial division2.1.3—Factor and remainder theorems

Question 1

Question 1(a)

(a)

（a）Sketch the graph of y=|3 x-6| ．
（a）Sketch the graph of y=|3 x-6| ．

Table for Question 1(a) — CAIE A-Level Mathematics

Question 1(b)

(b)

Solve the inequality 5x-3<|3x-6|.

Question 5(a)

[Maximum number: 3]

The polynomial p(x) is defined by p(x)=9x3+18x2+5x+4\mathrm{p}(x)=9 x^{3}+18 x^{2}+5 x+4.

Find the quotient when p(x) is divided by (3 x+2), and show that the remainder is 6 .

Question 5(a)

[Maximum number: 4]

The polynomial p(x) is defined by

p(x)=ax4+bx3+13x2−35x+15,\mathrm{p}(x)=a x^{4}+b x^{3}+13 x^{2}-35 x+15,

where a and b are constants. It is given that ( 2 x-1 ) and ( x-3 ) are factors of p(x).

Find the values of a and b.