Official 2020 Paper 1
20 questions · 75 min · Difficulty 37
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Questions in this paper
- Question 1Which of the following is an expression for the first derivative with respect to x of (x^3-5x^2)/(2x√ x)
- Question 2(2x+1) and (x-2) are factors of 2x^3+px^2+q. What is the value of 2p+q?
- Question 3Find the complete set of values of x for which (x+4)(x+3)(1-x)>0 (x+2)(x-2)<0
- Question 4The 1st, 2nd and 3rd terms of a geometric progression are also the 1st, 4th and 6th terms, respectively, of an arithmetic progression. The…
- Question 5The curve S has equation y=px^2+6x-q where p and q are constants. S has a line of symmetry at x=-frac14 and touches the x-axis at exactly…
- Question 6Find the maximum value of the function f(x)=frac15^(2x)-4(5^x)+7
- Question 7Given that 2^(3x)=8^((y+3)) and 4^((x+1))=frac16^((y+1))8^((y+3)) what is the value of x+y?
- Question 8The function f is defined for all real x as f(x)=(p-x)(x+2) Find the complete set of values of p for which the maximum value of f(x) is…
- Question 9The quadratic expression x^2-14x+9 factorises as (x-α)(x-β), where α and β are positive real numbers. Which quadratic expression can be…
- Question 10The following sequence of transformations is applied to the curve y=4x^2. 1. Translation by 3 -5 2. Reflection in the x-axis 3. Stretch…
- Question 11The quadratic function shown passes through (2,0) and (q,0), where q>2. What is the value of q such that the area of region R equals the…
- Question 12How many real solutions are there to the equation 3cos x=√ x where x is in radians?
- Question 13Find the coefficient of x^2y^4 in the expansion of (1+x+y^2)^7.
- Question 14The area enclosed between the line y=mx and the curve y=x^3 is 6. What is the value of m?
- Question 15Find the positive difference between the two real values of x for which (log_2 x)^4+12(log_2(frac1x))^2-2^6=0
- Question 16The circle C_1 has equation (x+2)^2+(y-1)^2=3. The circle C_2 has equation (x-4)^2+(y-1)^2=3. The straight line l is a tangent to both C_1…
- Question 17Let c>0. Find the complete set of values of m in terms of c such that the graphs of y=mx+c and y=√ x have two points of intersection.
- Question 18Find the number of solutions and the sum of the solutions of the equation 1-2cos^2 x=|cos x| where 0≤ x≤180°.
- Question 19Find the lowest positive integer for which x^2-52x-52 is positive.
- Question 20For how many values of a is the equation (x-a)(x^2-x+a)=0 satisfied by exactly two distinct values of x?