Official 2019 Paper 1
20 questions · 75 min · Difficulty 37
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Questions in this paper
- Question 1f(x) is a quadratic function in x. The graph of y=f(x) passes through the point (1,-1) and has a turning point at (-1,3). Find an…
- Question 2Find the complete set of values of the real constant k for which the expression x^2+kx+2x+1-2k is positive for all real values of x.
- Question 3Find the coefficient of x in the expression: &(1+x)^0+(1+x)^1+(1+x)^2+(1+x)^3 & +…+(1+x)^(79)+(1+x)^(80)
- Question 4The sequence x_n is given by: x_1=10 x_(n+1)=√(x_n) n≥1 What is the value of x_(100)? [Note that a^(b^c) means a^((b^c))]
- Question 5S is a geometric sequence. The sum of the first 6 terms of S is equal to 9 times the sum of the first 3 terms of S. The 7th term of S is…
- Question 6The circles with equations (x+4)^2+(y+1)^2=64 (x-8)^2+(y-4)^2=r^2 r>0 have exactly one point in common. Find the difference between the two…
- Question 7A curve has equation y=(2q-x^2)(2qx+3) The gradient of the curve at x=-1 is a function of q. Find the value of q which minimises the…
- Question 8The function f is such that 0<f(x)<1 for 0≤ x≤1. The trapezium rule with n equal intervals is used to estimate ∫_0^1 f(x) d x and produces…
- Question 9p is a positive constant. Find the area enclosed between the curves y=p√ x and x=p√ y.
- Question 10Evaluate ∫_(-1)^3|x|(1-x) d x
- Question 11Find the sum of the real values of x that satisfy the simultaneous equations: log_3(xy^2)=1 (log_3 x)(log_3 y)=-3
- Question 12It is given that (d V)/(d t)=(24π(t-1))/((1+√ t)) t≥1 and V=7 when t=1. Find the value of V when t=9.
- Question 13Find the maximum value of 4^(sin x)-4×2^(sin x)+frac174 for real x.
- Question 14x satisfies the simultaneous equations sin2x+√3cos2x=-1 and √3sin2x-cos2x=√3 where 0°≤ x≤360°. Find the sum of the possible values of x.
- Question 15Find the real non-zero solution to the equation frac2^((9^x))8^((3^x))=frac14
- Question 16Given that 2∫_0^1 f(x) d x+5∫_1^2 f(x) d x=14 and ∫_0^1 f(x+1) d x=6 find the value of ∫_0^2 f(x) d x
- Question 17Find the fraction of the interval 0≤θ≤π for which the inequality (sin(2θ)-frac12)(sinθ-cosθ)≥0 is satisfied.
- Question 18Find the shortest distance between the curve y=x^2+4 and the line y=2x-2.
- Question 19Find the value of Σ_(k=0)^(90)sin(10+90k)°
- Question 20What is the complete range of values of k for which the curves with equations y=x^3-12x and y=k-(x-2)^2 intersect at three distinct points…