35 Basic C1 Questions


The following is a list of basic C1 questions that students should be able to tackle if they are prepared for the C1 AS-Level Maths exam. They have been designed to cover the techniques that will be needed in order to tackle typical C1 questions in a C1 maths exam. However, these questions do not necessarily resemble the type of C1 exam question students might be faced with, these questions should be used to practice those techniques needed. Having said that, early questions in a C1 exam may look a lot like the questions you see here.

 

c1 maths practice Simplify \sqrt{112}.

c1 maths practice Evaluate x^0.

c1 maths practice Factorise 2x^2-x-3.

c1 maths practice Solve the inequality 2x-5 \textgreater  3x-4.

c1 maths practice Rationalise the denominator of \frac{6}{\sqrt{2}}.

c1 maths practice How many roots does the graph of x^2-4x+2 have?

c1 maths practice Evaluate 4^{\frac{3}{2}}.

c1 maths practice Let m(x)=3x^2+4x+5. Find \frac{dm}{dx} and \frac{d^2m}{dx^2}.

c1 maths practice Sketch the graph of f(x)=\frac{1}{x}.

c1 maths practice Solve the simultaneous equations x^2+y^2=5 and x+2y=3.

c1 maths practice The first term of a sequence is 58 and the common difference is -2. Find the 107th term.

c1 maths practice Rationalise the denominator of \frac{\sqrt{8}}{\sqrt{5}-2}.

c1 maths practice Find the set of values of k for which the quadratic kx^2-kx+8 has two different roots.

c1 maths practice Integrate 2x^5-x^7+3.

c1 maths practice Evaluate \left(\frac{64}{27}\right)^{-\frac{1}{3}}.

c1 maths practice Factorise x^2-9y^2.

c1 maths practice Sketch the graph of y=x^3.

c1 maths practice The first 10 terms of a sequence, whose common difference is 4, adds up to 210. Find the first term.

c1 maths practice Simplify 15x^3y^2\div 5x^2y^3.

c1 maths practice Differentiate 3x^{\frac{1}{2}}-4x^{-\frac{1}{2}}.

c1 maths practice Solve the inequality 6x^2-7x-3\leq 0.

c1 maths practice Using the quadratic formula, solve the equation 3x^2-5x+1=0. Leave your answer in surd form.

c1 maths practice Sketch the graph of f(x)=x^2(3-x).

c1 maths practice If 4^{3y-6}=8^y, find the value of y.

c1 maths practice Integrate 6x^{\frac{3}{2}}-7x^{\frac{2}{5}}.

c1 maths practice Let U_n=n^2-n. Find \sum_{i=1}^5U_i.

c1 maths practice Solve by completing the square: x^2-8x+12=0

c1 maths practice Differentiate \frac{x^3+2x}{x^2}.

c1 maths practice Write (4-\sqrt{3})^2 in the form a+b\sqrt{c}.

c1 maths practice Sketch the graph of y=x^3+x^2-20x.

c1 maths practice Write 2x^2+8x-4 in the form a(x+b)^2+c.

c1 maths practice Find the equation of the tangent to the curve of y=\frac{16}{x^2}-\sqrt{x} when x=4.

c1 maths practice The curve of y=f(x) such that f and passes though the point (1,4). Find the equation for y.

c1 maths practice A line passes through the points A(10,3) and B(2,7). Find the midpoint of AB and the equation of the line that passes through A and B.

c1 maths practice Sketch the graph of f(x)=\frac{1}{x-4}.

 

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