StepMaths Mock Paper 1
19 questions · 71 min · Difficulty 46 · by StepMaths
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Questions in this paper
- Question 1Given that the coefficient of x^2 in the expansion of (1+x^2)(3-2x)^n is 1323, is n even or odd?
- Question 2The polynomial P(x) has (x-1)^2 as a factor. Given that P(x) is of the form P(x)=2x^4-3x^3+ax^2+bx-6, find a and b.
- Question 3What is the maximum value of √(x^2+y^2) for x and y that satisfy the inequality x^2-30x+y^2-16y≤-253?
- Question 4The function f(x) satisfies the following equation for x≠1: f(x)+xf(1-x)=(x)/(x-1) Given that f(2) can be written as a fraction dfrac ab in…
- Question 5Withdrawn
- Question 6The ratio of the 11th and the 21st terms of an arithmetic progression is 9:8. What is the ratio of the 51st and 91st terms of the…
- Question 7A white wooden cube is made of n^3 identical, smaller cubes, where n is an even number. Each small cube on the surface of the large cube is…
- Question 8How many solutions are there to the equation sin(x)+cos(x)=1 for -2π≤ x≤2π?
- Question 9In the diagram, the radius of the large quadrant is 2. The two semicircles touch each other only once. Find the area inside the quadrant…
- Question 10The equation sin(x)=kx has 5 solutions, where k>0. What is the simplest complete set of conditions that k satisfies when this is true? (You…
- Question 11Let the solutions to the equation 2^(2x+1)-2^x-2^(x+3)+2^2=0 be a and b. Find the value of a+b.
- Question 12A right circular cone has base radius R and height H, where R<H. A cylinder is inscribed in the cone in such a way that the curved surface…
- Question 13How many roots does the equation 3cos^4(x)+2cos^3(x)-7cos(x)+1=0 have in the range 0<x<2π?
- Question 14Let k_t be a sequence of numbers defined by k_1=1 and satisfying frack_(t+1)k_t=2^t Find log_2(k_(100)).
- Question 15At the two points where the line y=k cuts the curve y=x^2, tangents are drawn. It is found that they intersect at the point (0,-2). What is…
- Question 16For what values of x can the following simultaneous equations be solved? 4^(frac xy+frac yx)=32 log_3(x-y)+log_3(x+y)=1
- Question 17A cube has each side length 2 units. An ant walks on the surface of the cube and starts at H. What is the shortest distance it has to…
- Question 18If x+dfrac1x=5 what is the value of x^4+dfrac1x^4?
- Question 19What is the total length of the interval or intervals on which the following inequality is true? -1<(3x+4)/(x-6)<1
- Question 20How many positive integers are there such that x and x+99 are both square numbers?