DPiD Maths Mock Set 1 Paper 2
20 questions · 75 min · Difficulty 59 · by DPiD Maths
Read the questions freely. Sign in to answer them, start a timed paper and save your progress.
Questions in this paper
- Question 1What is the smallest prime divisor of 3^2^(5^(12))+1?
- Question 2Each face of a fair cubical die is labelled with one of the numbers 1 through 6. On every face an arrow is drawn pointing to one of its…
- Question 3Let A and B be subsets of the xy-plane, and consider the following statements. P: For all real numbers x and y, (x,y) is in A if and only…
- Question 4Jenny is typing all the integers from 1 to ∞, in order. The 5 on her computer is broken however, so she just skips any number containing a…
- Question 5Let x and y be real numbers. Which of the following is a necessary and sufficient condition for |x-y|=|x|+|y|?
- Question 6What is the units digit of 8^(2023)?
- Question 7Find the sum of all real x for which 2^(3x+1)-33·2^(2x)+2^(x+3)=0.
- Question 8A triangle has altitudes of length 12, 15, and 20. Find its area.
- Question 9If p and q are positive integers and (1000)/(1001)<frac pq<(1001)/(1002), what is the minimum value of p?
- Question 10Let f(x) and g(x) be functions whose derivatives f'(x) and g'(x) exist for all real numbers. Which of the following statements is implied…
- Question 11Find the range of values of m so that the equation 3x√(x)+fracmx√(x)=m-1 has two distinct real roots.
- Question 12Consider the integral ∫_0^6√(6x-x^2) dx. The exact value of the integral is a. The value of the integral approximated using the trapezoidal…
- Question 13Let n be a positive integer and define I_n=∫_0^1x^ne^x dx. Which of the following statements is true?
- Question 14Let x and y be non-zero numbers. Which of the following must be false if |x+2|=|y|?
- Question 15Simplify the following logarithmic expression: log((45)/(28))+log((14)/(15))+log((21)/(16))-log(frac98).
- Question 16The lines ℓ_1 and ℓ_2 are parallel, with ℓ_1 above ℓ_2. A point P lies in the region between them. The segment PA meets ℓ_1 at A, and the…
- Question 17Peter the rabbit likes bounding around the infinite square grid of fields on his farm. Each hop of one field to the north, south, east, or…
- Question 18Newton has a wardrobe containing 7 hats of 3 different types: 3 Einstein hats, 2 Euler hats, and 2 Newton hats. He repeatedly takes out 2…
- Question 19Find Σ_(k=0)^∞lfloorfrac1+√((8 000 000)/(4^k))2rfloor, where lfloor xrfloor denotes the largest integer less than or equal to x.
- Question 20For each positive integer n, consider the function f_n(x)=(x-2)^n(x+2)^n. Which of the following statements is/are necessarily true? - I…