Stepwise
Start practisingPractise

WAEC 2015 · Paper 2 · Q7

  1. (a)

    The table is for the relation y=px2−5x+qy = px^2 - 5x + q.

    xx −3-3 −2-2 −1-1 00 11 22 33 44 55
    yy 2121 66 −12-12 00 1313

    (i) Use the table to find the values of pp and qq. (ii) Copy and complete the table.

    Separate values with commas, e.g. 3, −2

  2. (b)

    Using scales of 2 cm to 1 unit on the xx-axis and 2 cm to 5 units on the yy-axis, draw the graph of the relation for −3≤x≤5-3 \le x \le 5.

    Model answer
    −3−2−112345−15−10−55101520xyy = 2x2 − 5x − 12y = −8

    Plot every point from the table, then join them with one smooth curve (not straight lines between points). The lowest point is about (1.25,−15.1)(1.25, -15.1).

    For (c): (i) at x=1.8x = 1.8, y≈−14.5y \approx −14.5; (ii) the line y=−8y = -8 meets the curve at x≈−0.6x \approx −0.6 and 3.13.1.

  3. (c)

    Use the graph to find: (i) yy when x=1.8x = 1.8; (ii) xx when y=−8y = -8.

    Separate values with commas, e.g. 3, −2

Try it on a graph

y = 2x² − 5x − 12 with the line y = −8.

Worked solution (try it first)

(a)(i)

  1. Use the table entries that make the working easiest.
  2. When x=0x = 0, y=−12y = -12: 0−0+q=−120 - 0 + q = -12, so q=−12q = -12.
  3. When x=4x = 4, y=0y = 0: 16p−20−12=016p - 20 - 12 = 0, so 16p=3216p = 32 and p=2p = 2.
  4. The relation is y=2x2−5x−12y = 2x^2 - 5x - 12.

(ii)

  1. Substitute each missing xx: x=−1x = -1 gives 2+5−12=−52 + 5 - 12 = -5.
  2. x=1x = 1 gives 2−5−12=−152 - 5 - 12 = -15.
  3. x=2x = 2 gives 8−10−12=−148 - 10 - 12 = -14.
  4. x=3x = 3 gives 18−15−12=−918 - 15 - 12 = -9.
  5. The full row is 21,6,−5,−12,−15,−14,−9,0,1321, 6, -5, -12, -15, -14, -9, 0, 13.

(b)

  1. Plot the points with the scales given and join them with one smooth curve.

(c)(i)

  1. Read up from x=1.8x = 1.8 to the curve and across: y≈−14.5y \approx -14.5.
  2. (By calculation, 2(1.8)2−9−12=−14.522(1.8)^2 - 9 - 12 = -14.52.) (ii) Draw the line y=−8y = -8 and read down from where it meets the curve: x≈−0.6x \approx -0.6 and x≈3.1x \approx 3.1.

Report a problem with this question