past paper · 2017

TMUA 2017 Paper 2

Mathematical Reasoning. All 20 questions from the 2017 paper, each with a full worked solution. Topics on this paper: Differentiation and integration (6), Sequences and series (2), Trigonometry (2), Proof and counterexample (2), Exponentials and logarithms (2), Inequalities and reasoning (2), Logic and arguments (2), Coordinate geometry (1), Graphs and transformations (1).

Sit it properly first

Twenty questions, seventy-five minutes, no calculator, in a replica of the real test driver. Reading the solutions before you have tried a paper spends it.

Sit 2017 Paper 2 2017 Paper 1

Questions

1 Given that y = (1-3x)²2x^(3)/(2) which one of the following is a correct expression for (dy)/(dx)? Calculus
2 PQRS is a rectangle. The coordinates of P and Q are (0,6) and (1,8) respectively. The perpendicular to PQ at… Geometry
3 The first term of a geometric progression is 23 and the fourth term is (9)/(4). What is the sum to infinity… Sequences
4 The following question appeared in an examination: Given that tan x = 3, find the possible values of sin 2x.… Trigonometry
5 Consider the following three statements: 1   10p² + 1 and 10p² - 1 are both prime when p is an odd… Proof
6 A sequence u₀, u₁, u₂, … is defined as follows: u₀ = 1 u_n = ∫₀¹ 4x,u_n-1,dx for n ≥ 1 What is the value of… Calculus
7 The graphs of two functions are shown here: y = a^x is shown with a solid line, where a is a positive real… Logarithms
8 Which one of the following numbers is smallest in value? Logarithms
9 Consider the following attempt to prove this true theorem: Theorem: a³ + b³ = c³ has no solutions with a, b… Proof
10 f(x) is a function defined for all real values of x. Which one of the following is a sufficient condition… Calculus
11 The function f(x) is increasing and f(0) = 0. The positive constants a and b are such that a The area of the… Calculus
12 The diagram shows the graphs of y = sin 2x and y = cos 2x for -(π)/(2) Which one of the following is not true? Trigonometry hard
13 The positive real numbers a × 10⁻³, b × 10⁻² and c × 10⁻¹ are each in standard form, and (a × 10⁻³) + (b ×… Inequalities
14 The diagram shows the graph of y = x² - 2bx + c, an upward parabola whose vertex P lies in the first… Graphs
15 The function f is defined on the positive integers as follows: f(1) = 5, and for n ≥ 1, f(n+1) = 3f(n) + 1… Sequences
16 Consider the following statement: (*) If f(x) is an integer for every integer x, then f'(x) is an integer… Calculus
17 A set S of whole numbers is called stapled if and only if for every whole number a which is in S there… Logic
18 Consider the following problem: Solve the inequality (14)ⁿ A student produces the following argument: (14)ⁿ… Inequalities
19 Which one of the following is a sufficient condition for the equation x³ - 3x² + a = 0, where a is a… Calculus
20 I have forgotten my 5-character computer password, but I know that it consists of the letters a, b, c, d, e… Logic hard

Answer key for TMUA 2017 Paper 2

1 A2 E3 G4 B5 B6 A7 E8 E9 D10 D11 B12 C13 B14 F15 D16 C17 F18 B19 E20 B