Quelpr

CSEC Mathematics

54 questions and parts from this paper. Open one to see it in full, then practise it on Quelpr and get it marked against the mark scheme.

Practise this paper
  1. 1(a)(i)2 marksEvaluate 2 1/4 - 1 3/5 / 3.
  2. 1(a)(ii)1 markEvaluate 2.14 sin 75°, giving your answer to 2 decimal places.
  3. 1(b)(i)1 markWhat is Irma's annual take-home pay? (Assume she works 52 weeks in any given year.)
  4. 1(b)(ii)3 marksDetermine the amount of money that Irma allocates for rent each month.
  5. 1(b)(iii)2 marksAll of Irma's savings is used to pay her son's university tuition cost, which is…
  6. 2(a)(i)1 markSimplify completely 3p² × 4p⁵.
  7. 2(a)(ii)2 marksSimplify completely 3x / (4y³) ÷ 21x² / (20y²).
  8. 2(b)3 marksSolve the equation 3 / (7x - 1) + 1 / x = 0.
  9. 2(c)(i)1 markExpress y in terms of x.
  10. 2(c)(ii)2 marksDetermine the two values of x that satisfy the equation y = x AND the equation derived in (c)(i).
  11. 3(a)4 marksUsing a ruler, a pencil and a pair of compasses only, construct the triangle NLM, in which LM = 12 cm, ∠MLN = 30° and ∠LMN = 90°. (Credit will be given for clearly drawn construction lines.)
  12. 3(b)(i)2 marksOn the diagram, draw and label triangle LMN.
  13. 3(b)(ii)2 marksDescribe fully a single transformation that maps triangle ABC onto triangle LMN.
  14. 3(b)(iii)1 markState the 2 × 2 matrix for the transformation that maps triangle ABC onto triangle LMN.
  15. 4(a)(i)1 markUsing the letters P, V and k, form an equation connecting the quantities P and V.
  16. 4(a)(ii)2 marksGiven that V = 3 when P = 4, determine the positive value of V when P = 1.
  17. 4(b)(i)2 marksSolve the inequality -7 < 3x + 5 ≤ 7.
  18. 4(b)(ii)1 markRepresent your answer in (b)(i) on the number line shown below.
  19. 4(c)(i)1 markDetermine the coordinates of Q.
  20. 4(c)(ii)2 marksWhat is the gradient of this line?
  21. 5(a)(i)1 markFor the class 21-30, determine the lower class boundary.
  22. 5(a)(ii)1 markFor the class 21-30, determine the class width.
  23. 5(b)1 markHow many vehicles were recorded in the class 31-40?
  24. 5(c)2 marksA vehicle is chosen at random from the 150 vehicles. What is the probability that the volume of petrol needed to fill its tank is more than 50.5 litres? Leave your answer as a fraction.
  25. 5(d)1 markByron estimates the median amount of petrol to be 43.5 litres. Explain why Byron's estimate is INCORRECT.
  26. 5(e)3 marksOn the partially labelled grid below, construct a histogram to represent the distribution of the volume of petrol needed to fill the tanks of the 150 vehicles.
  27. 6(a)(i)2 marksDetermine the actual distance, in km, represented by 0.5 cm on the map.
  28. 6(a)(ii)3 marksCalculate the actual area, in km², represented by 2.25 cm² on the map.
  29. 6(b)(i)2 marksDetermine, in terms of π and d, the volume of water in Jar X.
  30. 6(b)(ii)2 marksIf all the water from Jar X is now poured into Jar Y, calculate the height it will reach.
  31. 7(a)(i)1 markShow that the first term of the sequence is 1.
  32. 7(a)(ii)1 markWhat is the third term of the sequence?
  33. 7(a)(iii)3 marksGiven that T_n = 145, what is the value of n?
  34. 7(b)(i)2 marksWrite down the next two terms in the sequence, that is, U(9) and U(10).
  35. 7(b)(ii)1 markWhich term in the sequence is the sum of U(18) and U(19)?
  36. 7(b)(iii)2 marksShow that U(20) - U(19) = U(19) - U(17).
  37. 8(a)(i)1 markState a value of x that CANNOT be in the domain of f.
  38. 8(a)(ii)a)2 marksFind, in its simplest form, expressions for fg(x).
  39. 8(a)(ii)b)2 marksFind, in its simplest form, expressions for f⁻¹(x).
  40. 8(b)(i)3 marksBy writing an expression for the area of rectangle ABCD, show that x² + 2x - 4 = 0.
  41. 8(b)(ii)2 marksCalculate, to 3 decimal places, the value of x.
  42. 8(b)(iii)2 marksCalculate the perimeter of the UNSHADED region.
  43. 9(a)(i)2 marksCalculate the value of ∠DBA. Show detailed working where necessary and give a reason to support your answers.
  44. 9(a)(ii)2 marksCalculate the value of ∠DAC. Show detailed working where necessary and give a reason to support your answers.
  45. 9(a)(iii)2 marksCalculate the value of ∠BCE. Show detailed working where necessary and give a reason to support your answers.
  46. 9(b)(i)2 marksDetermine the length PS.
  47. 9(b)(ii)1 markDetermine the length PQ.
  48. 9(b)(iii)3 marksDetermine the area of PQRS.
  49. 10(a)(i)a)2 marksFind the matrix product [-1 3; 4 h] [k; 5].
  50. 10(a)(i)b)2 marksHence, find the values of h and k that satisfy the matrix equation [-1 3; 4 h] [k; 5] = [0; 0].
  51. 10(a)(ii)3 marksUsing a matrix method, solve the simultaneous equations 2x + 3y = 5 and -5x + y = 13.
  52. 10(b)(i)1 markExpress the vector AB in the form [a; b].
  53. 10(b)(ii)2 marksExpress the vector OD in the form [a; b].
  54. 10(b)(iii)2 marksExpress the vector BE in the form [a; b].

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