A-Level CAIE Mathematics AS Question Bank

[Maximum number: 3]

Express $2 x^{2}-12 x+7$ in the form $a(x+b)^{2}+c$ , where a, b and c are constants.

(a)

Express $16 x^{2}-24 x+10$ in the form $(4 x+a)^{2}+b$ .

[ 2 ]

(b)

It is given that the equation $16 x^{2}-24 x+10=k$ , where k is a constant, has exactly one root.

Find the value of this root.

[ 2 ]

(a)

Express $x^{2}+6 x+5$ in the form $(x+a)^{2}+b$ , where a and b are constants.

[ 2 ]

(a)

Express $x^{2}+6 x+2$ in the form $(x+a)^{2}+b$ , where a and b are constants.

[ 2 ]

(b)

Hence, or otherwise, find the set of values of x for which $x^{2}+6 x+2>9$ .

[ 2 ]

[Maximum number: 3]

Express $3 x^{2}-12 x+7$ in the form $a(x+b)^{2}+c$ , where a, b and c are constants.

[Maximum number: 3]

Showing all necessary working, solve the equation $4 x-11 x^{\frac{1}{2}}+6=0$ .

[Maximum number: 5]

The function f is defined by $\mathrm{f}(x)=x^{2}-4 x+8$ for $x \in \mathbb{R}$ .

(a)

Express $x^{2}-4 x+8$ in the form $(x-a)^{2}+b$ .

[ 2 ]

(b)

Hence find the set of values of x for which f(x)<9, giving your answer in exact form.

[ 3 ]

[Maximum number: 2]

The equation of a curve is $y=x^{2}-6 x+k$ , where k is a constant.

(a)

Find the set of values of k for which the whole of the curve lies above the x-axis.

[ 2 ]

(a)

Express $4 x^{2}-12 x$ in the form $(2 x+a)^{2}+b$ .

[ 2 ]

(b)

Hence, or otherwise, find the set of values of x satisfying $4 x^{2}-12 x>7$ .

[ 2 ]

(a)

Given that $\frac{1+4^{y}}{3+2^{y}}=5$ , find the value of $2^{y}$ .

[ 3 ]

0 selected

A-Level CAIE Mathematics AS Question Bank is the parent practice page for Mathematics questions organised by syllabus topic. It is built for focused revision: choose a course area, preview the available question style, then build a short practice set when you are ready to work under exam conditions.

Start with broad topic areas such as A-Level CAIE Mathematics, 1. Pure Mathematics 1, 2. Pure Mathematics 2, 4. Mechanics, then narrow the tree when you know which lesson, homework set or mock-exam skill you are targeting. Keeping practice inside the syllabus map helps you see whether a mistake came from knowledge recall, graph interpretation, formula use, command-word depth or mark-scheme wording. After each short set, move to the linked notes page to rebuild weak knowledge before retesting.

Use this entry page as the stable hub for A-Level CAIE Mathematics AS question practice. Detailed topic URLs can help you navigate, but this parent page is the canonical place for the full course-level question bank, related notes and nearby level pages.

Topics to start with

A-Level CAIE Mathematics 1. Pure Mathematics 1 2. Pure Mathematics 2 4. Mechanics 5. Probability & Statistics 1 1.1 Quadratics 1.2 Functions 1.3 Coordinate geometry