Official 2022 Paper 1
20 questions · 75 min · Difficulty 51
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Questions in this paper
- Question 1How many real solutions are there to the equation 2cos^4θ-5cos^2θ+3=0 in the interval 0≤θ≤2π?
- Question 2Find the complete set of values of p for which the equation x^2-2px+y^2-6y-p^2+8p+9=0 describes a circle in the xy-plane.
- Question 3Given the following statements about a function f - f"(x)=a for all x - f(0)=1, f(1)=2 - ∫_0^1 f(x)d x=1 find the value of a.
- Question 4These sectors of circles are similar. The arc length of the smaller sector is 6. The difference between the areas of the sectors is 21…
- Question 5The terms x_n of a sequence follow the rule x_(n+1)=(x_n+p)/(x_n+q) where p and q are real numbers. Given that x_1=3, x_2=5, and x_3=7…
- Question 6Given that ∫_(log_2 5)^(log_2 20)xd x=log_2M what is the value of M?
- Question 7Find the finite area enclosed between the line y=0 and the curve y=x^2-4|x|-12.
- Question 8A geometric sequence has first term a and common ratio r, where a and r are positive integers and r is greater than 1. The sum of the first…
- Question 9This question is about pairs of functions f and g that satisfy f(x)-g(x)&=2sin x f(x)g(x)&=cos^2x for all real numbers x. Across all…
- Question 10A sequence of translations is applied to the graph of y=x^3. Which of the following graphs could be the result of this sequence of…
- Question 11Evaluate Σ_(n=1)^(100)log_(10)(3^(1-n)).
- Question 12A family of quadratic curves is given by y_k=2(x-frac k2)^2+frack^22+4k+3 where k is any real number and y_k is a function of x. All these…
- Question 13Given that (a^3+frac2b^3)(frac2a^3-b^3)=√2 where a and b are real numbers, what is the least value of ab?
- Question 14A circle has centre O and radius 6. P, Q and R are points on the circumference with angle POQ≥dfracπ2. The area of the triangle POQ is 9√3…
- Question 15A rectangle is drawn in the region enclosed by the curves p and q, where p(x)=8-2x^2 q(x)=x^2-2 such that the sides of the rectangle are…
- Question 16The solutions to 7x^4-6x^2+1=0 are ±cosθ and ±cosβ. Which one of the following equations has solutions ±sinθ and ±sinβ?
- Question 17Find the complete set of values of x for which there are two non-congruent triangles with the side lengths and angle as shown in the…
- Question 18It is given that f(x)=x^2(x-1)^2(x-2) g(x)=-p(x-q)^2(x-r)^2 where p, q and r are positive and q<r. Find the set of values of q and r that…
- Question 19Circle C_1 is defined as x^2+y^2=25. A second circle C_2 has radius 4 and centre (a,b) where -2≤ a≤2 -3≤ b≤3. If the centre of C_2 is…
- Question 20n is the number of points of intersection of the graphs y=|x^2-a^2| y=a^2|x-1| where a is a real number. What is the smallest value of n…