Official 2021 Paper 1
20 questions · 75 min · Difficulty 49
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Questions in this paper
- Question 1Two circles have the same radius. The centre of one circle is (-2,1). The centre of the other circle is (3,-2). The circles intersect at…
- Question 2The curve y=x^3-6x+3 has turning points at x=α and x=β, where β>α. Find ∫_α^β x^3-6x+3 d x
- Question 3An arithmetic progression and a convergent geometric progression each have first term frac12. The sum of the second terms of the two…
- Question 4Find the minimum value of the function 2^(2x)-2^(x+3)+4
- Question 5The function f is such that f(mn)= f(m)f(n)&if mn is a multiple of 3 mn&if mn is not a multiple of 3 for all positive integers m and n…
- Question 6The function f is given by f(x)=(cos x+3)/(7+5cos x-sin^2 x) Find the positive difference between the maximum and the minimum values of…
- Question 7The function f is such that f(0)=0, and xf(x)>0 for all non-zero values of x. It is given that ∫_(-2)^2 f(x) d x=4 and ∫_(-2)^2|f(x)| d x=8…
- Question 8The line y=2x+3 meets the curve y=x^2+bx+c at exactly one point. The line y=4x-2 also meets the curve y=x^2+bx+c at exactly one point. What…
- Question 9Find the area enclosed by the graph of |x|+|y|=1
- Question 10Use the trapezium rule with 3 strips to estimate ∫_(frac12)^2 2log_(10)x d x
- Question 11The function f is given by f(x)=x^(1/7)(x^2-x+1) Find the fraction of the interval 0<x<1 for which f(x) is decreasing.
- Question 12The minimum value of the function x^4-p^2x^2 is -9. p is a real number. Find the minimum value of the function x^2-px+6.
- Question 13The function f is such that, for every integer n ∫_n^(n+1) f(x) d x=n+1 Evaluate Σ_(r=1)^8∫_0^r f(x) d x
- Question 14This question uses radians. Find the number of distinct values of x that satisfy the equation (x+1)(3-x)=2(1-cos(π x))
- Question 15The diagram shows the graph of y=f(x). The graph consists of alternating straight-line segments of gradient 1 and -1 and continues in this…
- Question 16Consider the expansion of (a+bx)^n The third term, in ascending powers of x, is 105x^2. The fourth term, in ascending powers of x, is…
- Question 17Which of the following sketches shows the graph of sin(x^2+y^2)=frac12 where x^2+y^2≤8π?
- Question 18The curve with equation x=y^2-6y+11 is rotated 90°clockwise about the point P to give the curve C. P has x-coordinate -2 and y-coordinate…
- Question 19The equation sin^2(4^(cosθ)×60°)=frac34 has exactly three solutions in the range 0°≤θ≤ x°. What is the range of all possible values of x?
- Question 20Find the length of the curve with equation 2log_(10)(x-y)=log_(10)(2-2x)+log_(10)(y+5)