Official Specimen Paper 1
20 questions · 75 min · Difficulty 29
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Questions in this paper
- Question 1The sum of the two values of x that satisfy the simultaneous equations x-3y+1=0 3x^2-7xy=5 is
- Question 2The number of solutions in the interval 0≤θ≤4π of the equation sin^2θ+3cosθ=3 is
- Question 3The perpendicular bisector of the line segment joining the points (2,-6) and (5,4) cuts the x-axis at the point with x-coordinate
- Question 4The complete set of values of x for which (x^2-1)(x-2)>0 is
- Question 5Given that y=-log_(10)(1-x) for x<1, find x in terms of y.
- Question 6It is given that x+2 is a factor of x^3+4cx^2+x(c+1)^2-6. The sum of the possible values of c is
- Question 7A bag contains n red balls, n yellow balls, and n blue balls. One ball is selected at random and not replaced. A second ball is then…
- Question 8Given that a^xb^(2x)c^(3x)=2, where a, b, and c are positive real numbers, then x=
- Question 9The roots of the equation 2x^2-11x+c=0 differ by 2. The value of c is
- Question 10The curve y=cos x is reflected in the line y=1 and the resulting curve is then translated by dfracπ4 units in the positive x-direction. The…
- Question 11The sum of the roots of the equation 2^(2x)-8×2^x+15=0 is
- Question 12The cross-section of a triangular prism is an equilateral triangle with side 2x cm. The length of the prism is d cm. Let the total surface…
- Question 13How many real roots does the equation x^4-4x^3+4x^2-10=0 have?
- Question 14a, b, x, and y are real and positive. a and b are constants. x and y are related. A graph of log y against log x is drawn. For which one of…
- Question 15The smallest possible value of ∫_0^1(x-a)^2d x as a varies is
- Question 16Given that c and d are non-zero integers, the expression frac10^(c-2d)×20^(2c+d)8^c×125^(c+d) is an integer if
- Question 17For what values of the non-zero real number a does the quadratic equation ax^2+(a-2)x=2 have real distinct roots?
- Question 18The angle x is measured in radians and is such that 0≤ x≤π. The total length of any intervals for which -1≤tan x≤1 and sin2x≥0.5 is
- Question 19A geometric series has first term 4 and common ratio r, where 0<r<1. The first, second, and fourth terms of this geometric series form…
- Question 20The coefficient of x^2 in the expansion of (4-x^2)[(1+2x+3x^2)^6-(1+4x^3)^5] is