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The Modulus Function · CAPE Pure Mathematics Unit 1

39 past-paper questions on The Modulus Function, part of Basic Algebra and Functions, from every CAPE Pure Mathematics Unit 1 paper on Quelpr.

Practise The Modulus Function
  1. Q41 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (Rest of Region) · Paper 1The basic wage W_b and the overtime wage W_o of a shop attendant never differ by more than \100$. An inequality representing this statement is
  2. Q51 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (Rest of Region) · Paper 1If |x + b| = |x|; x, b \in \mathbb{N}, then the value of x in terms of b is
  3. Q111 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (T&T) · Paper 1If |x - 1|^2 + 2|x - 1| = 3, then x is
  4. Q151 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (T&T) · Paper 1The solution set of 5 + |2m - 9| \le 6 is
  5. 1(c)5 marks· CAPE Pure Mathematics Unit 1 · 2022 · Paper 2Solve the inequality |3x + 2| \ge 4.
  6. 2(a)4 marks· CAPE Pure Mathematics Unit 1 · May/June 2005 · Paper 1Find the range of values of the real number x < 0 such that x^2 - 2|x| - 3 < 0.
  7. 2(a)6 marks· CAPE Pure Mathematics Unit 1 · May/June 2006 · Paper 1Let A = {x : 2 <= x <= 7} and B = {x : |x - 4| <= h}, h in R. Find the LARGEST value of h for which B subset of A.
  8. 3(a)(ii)4 marks· CAPE Pure Mathematics Unit 1 · May/June 2006 · Paper 1Hence, find the range of values of x in R for which (3x)/(x + 1) > 2.
  9. Q51 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 1The range of values of x that satisfies the inequality |x - b| < a is
  10. Q121 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2009 · Paper 1The values of x that satisfy the inequality |2x - a| > |x|, a > 0, are
  11. Q41 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2011 · Paper 1The range of values of x that satisfies the inequality |x - b| < a is
  12. Q61 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 1The range of values of x that satisfies the inequality |x - b| < a is
  13. Q81 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 1The graph of f(x) = |x - 2| + 1 is BEST illustrated by
  14. Q131 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 1The values of x that satisfy the inequality |2x - a| > |x|, a > 0, are
  15. Q81 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 1The graph of f(x) = |x - 2| + 1 is BEST illustrated by
  16. Q131 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 1The values of x that satisfy the inequality |2x - a| > |x|, a > 0, are
  17. 1(b)4 marks· CAPE Pure Mathematics Unit 1 · May/June 2024 · Paper 2Solve the inequality -3|2x - 5| + 2 >= -4.
  18. 1(a)4 marks· Pure Mathematics · Unit 1 Q1 1(a)Show that the inequality |x-3| ≥ |x-3| holds for any x ∈ R.
  19. 1(a)(i)2 marks· Pure Mathematics · Unit 1 Q1 1(a)(i)Complete the table below for the function |f(x)|, where f(x) = x(2-x).
  20. 1(a)(ii)4 marks· Pure Mathematics · Unit 1 Q1 1(a)(ii)Sketch the graph of |f(x)| for -2 ≤ x ≤ 4.
  21. 1(b)(i)4 marks· Pure Mathematics · Unit 1 Q1 1(b)(i)Copy the table below and complete by inserting the values for the functions f(x) = |x + 2 | and g(x) = 2 |x − 1 |.
  22. 1(b)(ii)4 marks· Pure Mathematics · Unit 1 Q1 1(b)(ii)Using a scale of 1 cm to 1 unit on both axes, draw on the same graph f(x) and g(x) for −3 ≤ x ≤ 5.
  23. 1(b)(iii)2 marks· Pure Mathematics · Unit 1 Q1 1(b)(iii)Using the graphs, find the values of x for which f(x) = g(x).
  24. 1(c)5 marks· Pure Mathematics · Unit 1 Q1 1(c)Solve, for x ∈ R, the inequality 2x-3 / x+1 > 5.
  25. 1(c)(i)5 marks· Pure Mathematics · Unit 1 Q1 1(c)(i)Find the range of values of x ∈ R for which |2x-3|≤5.
  26. 1(c)(i)5 marks· Pure Mathematics · Unit 1 Q1 1(c)(i)Solve, for real values of x, the inequality |3x-7|≤5.
  27. 1(c)(ii)1 mark· Pure Mathematics · Unit 1 Q1 1(c)(ii)Hence, determine the LEAST possible value of x + 1.
  28. 1(c)(ii)2 marks· Pure Mathematics · Unit 1 Q1 1(c)(ii)Show that no real solution, x, exists for the inequality |3x-7|+5≤0.
  29. 1(c)(ii)5 marks· Pure Mathematics · Unit 1 Q1 1(c)(ii)Solve, for real values of x, the inequality x² - |x| - 12 < 0.
  30. 1(c)(iii)1 mark· Pure Mathematics · Unit 1 Q1 1(c)(iii)Hence, determine the GREATEST possible value of x + 1.
  31. 2(b)6 marks· Pure Mathematics · Unit 1 Q2 2(b)Solve the equation |x² - 4| = 3x - 2.
  32. 2(b)(i)4 marks· Pure Mathematics · Unit 1 Q2 2(b)(i)On the same axes, sketch the graphs |f(x)| and |g(x)|.
  33. 2(b)(i)4 marks· Pure Mathematics · Unit 1 Q2 2(b)(i)Prove that |x - y| ≤ |x - z| + |z - y| for all x, y, z ∈ R.
  34. 2(b)(ii)6 marks· Pure Mathematics · Unit 1 Q2 2(b)(ii)Hence, or otherwise, solve the equation |x² – 4x + 3| = |2 – 3x|.
  35. 2(b)(ii)5 marks· Pure Mathematics · Unit 1 Q2 2(b)(ii)Solve |5x - 6| = x + 5.
  36. 2(b)(ii)8 marks· Pure Mathematics · Unit 1 Q2 2(b)(ii)Solve the inequality |6x - 2| + x² ≤ 5.
  37. 2(b)(iii)3 marks· Pure Mathematics · Unit 1 Q2 2(b)(iii)By comparing the diagrams in (b)(i) and (ii) above, determine the solution set of the equation sin x = | sin x |, 0≤ x ≤ 2π.
  38. 2(c)5 marks· Pure Mathematics · Unit 1 Q2 2(c)Find the set of real values of x for which (x+4)/(x-2) > 5.
  39. 2(c)(ii)4 marks· Pure Mathematics · Unit 1 Q2 2(c)(ii)|x + 2| = 3x + 5

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