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TMUA Mock Tmua-maths-targ-1

3 questions3 marks75Updated August 2026

The TMUA Mock Tmua-maths-targ-1 paper in full: all 3 questions, each with its answer. TMUA is the Test of Mathematics for University Admission. Sit it cold under exam timing, mark it, then work back through anything you missed using the solutions below.

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Question 1

1 mark
Let nn be a positive integer. Consider the statement (∗)(*): If n2−1n^2 - 1 is prime, then nn is even. Three related statements are given: I The contrapositive of (∗)(*). II The converse of (∗)(*). III The statement 'If nn is odd, then n2−1n^2 - 1 is not prime.' Which of the following is true?
  • A.Only II is true
  • B.I, II and III are all true
  • C.I and III are true, but II is false
  • D.Only III is true
  • E.I and II are true, but III is false
  • F.None of I, II, III is true
  • G.II and III are true, but I is false
  • H.Only I is true

Answer: C

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Question 2

1 mark
Let xx be a real number and consider the quadratic condition QQ: x2−5x+6<0x^2 - 5x + 6 < 0. For real constants a<ba < b, define the statement S(a,b)S(a,b): 'a<x<ba < x < b'. Given that S(a,b)S(a,b) is true if and only if QQ is true, which of the following must be the pair (a,b)(a,b), and which of the listed alternative statements about necessity/sufficiency is also correct?
I x=2x=2 is sufficient for QQ to be true.
II x=2.5x=2.5 is necessary for QQ to be true.
III QQ being true is sufficient for x<3x < 3.
  • A.(a,b)=(2,3)(a,b)=(2,3); only III is true
  • B.(a,b)=(−2,−3)(a,b)=(-2,-3); only III is true
  • C.(a,b)=(3,2)(a,b)=(3,2); only III is true
  • D.(a,b)=(2,3)(a,b)=(2,3); I and III are true
  • E.(a,b)=(2,3)(a,b)=(2,3); only II is true
  • F.(a,b)=(2,3)(a,b)=(2,3); none of I, II, III is true
  • G.(a,b)=(2,3)(a,b)=(2,3); only I is true
  • H.(a,b)=(2,3)(a,b)=(2,3); I, II and III are all true

Answer: A

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Question 3

1 mark
A quadrilateral QQ has interior angles w,x,y,zw, x, y, z (in order around the quadrilateral), each measured in degrees, and it is known that w+x+y+z=360w+x+y+z=360. Consider the statement (†)(\dagger): If w=x=y=zw=x=y=z, then QQ is a rectangle. A student is asked to classify the following three related statements as true or false:
I The contrapositive of (†)(\dagger).
II The converse of (†)(\dagger).
III If QQ is a rectangle, then w=x=y=zw=x=y=z.
Which one of the following correctly gives the truth values of I, II, III (in that order)?
  • A.False, True, False
  • B.True, True, False
  • C.False, True, True
  • D.False, False, False
  • E.True, False, False
  • F.False, False, True
  • G.True, False, True
  • H.True, True, True

Answer: G

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