Curve Graph Question for E.Maths

Ahm97sic SG

A Curve Graph Practice Question for E.Maths

A typical "O" level E. Maths curve graph question will consist of 2 parts.

The first part will ask candidates to derive a curve function. The second part will ask the candidates to draw the curve followed by many small parts on the curve graph.

Actual past "O" level E. Maths on Curve Graph

Nov 2000 Paper 2 Question 9

Nov 2001 Paper 2 Question 9

Nov 2002 Paper 2 Question 10

Nov 2003 Paper 2 Question 9

Nov 2004 Paper 2 Question 10

Nov 2005 Paper 2 Question 10

Nov 2006 Paper 2 Question 10

Nov 2007 Paper 2 Question 10

Nov 2008 Paper 2 Question 9 or Question 10 ?

A Curve Graph Practice Question for E.Maths

This practice question encompasses the different types of small parts questions on the curve graph asked in the actual "O" level exams.

Question

The variables x and y are connected by the equation y = x² - x - 5. Some corresponding values of x and y are given in the table below.

x -4 -3 -2 -1 0 1 2 3 4 5

y 15 7 a -3 -5 b -3 1 7 15

(a) Calculate the values of a and b

(b) Use 2 cm to represent 1 unit on the x-axis and 1 cm to represent

1 unit on the y-axis, draw the graph of y = x² - x - 5 for

- 4 £ x £ 5.

(ii) the values of x when y = - 2

(iii) the minimum value of y

(iv) the values of x when y = 0

(v) the value of y when x = 0

(vi) the range of values of y when -2 < x < 2

(d) By drawing a suitable straight line to intersect the curve graph,

find the solutions to the equation

(i) x² - x - 5 = 0

(ii) x² - x - 5 = 2x + 1

(iii) x² - x = 8

(e)* Use your graph to solve the inequality x² - x - 5 > 2x + 1

(f) By drawing a tangent, find the gradient of the curve y = x² - x - 5

at the point (2, -3)

(g)* By drawing a suitable tangent to the curve, find the co-ordinates of

the point A at which the gradient of the tangent at A is 1

(h)* From the graph, find the values of x for which the gradient is positive.

(i) Describe fully the symmetry of the graph.

(j)* Find the cubic equation which is satisfied by the x values of the

intersecting point of the curve x² - x - 5 and the curve 1/x

Hope this will be of help for E. Maths students who will be taking their "O" level exam.

Thank you for your kind attention.

Regards,

ahm97sic

chiaz SG

so troublesome have to draw the graph to scale.

Ahm97sic SG

Hi Tamago,

I have observed that you are very good at using computer program to draw very beautiful graphs. Can you help to draw out the graphs for the answers of this question for the benefit of the "O" level E. Maths students ? Many thanks.

a) a = 1, b = -5
ci) y = 10.75
cii) x = 2.30 or -1.30
ciii) min value of y = -5.25
civ) x = 2.79 or -1.79
cv) y = -5
di) Find roots
dii) Intersection of curve and y=2x+1
diii) Intersection of curve and y=3
e) x > 4.37 or x < 1.37
h) y is increasing for x > 0.5
i) Curve is symmetrical about the line x = 0.5

Ahm97sic SG

Hi Tamago,

The graph is beautiful.

I have forgotten to type the domain - 2 < x < 2 for the part c(vi) and the curve 1/x for the part (j) and hence you have not provided the answers to parts c(vi) and (j). Please accept my apology.

Hi Tamago, perhaps you can highlight the answers for the part (d)(i), (ii) and (iii) in the graph ie the x answers and perhaps you can type "Please refer to the graph for the answer for parts (b), (f) and (g).

Thank you very much. Well Done !

Thank you very much for your kind attention.

Regards,

ahm97sic

eagle SG

tonight I will put up the questions and answers on ExamWorld as well :D

Ahm97sic, perhaps it would be good to start a thread on economics here as well. I took econs at As, and although I stopped after that, I really liked the subject... Pity during my year 1, there was no engineering and econs double degree (only when I was year 3 )

With your help, we would have additional coverage for economics students in this forum :D

Right now, we have physics (me), maths (tamago, me and you), chemistry & biology (UltimaOnline) for Os and As

It would be extremely useful to hv an economics expert like you too :D

Ahm97sic SG

Hi Eagle,

You have forgotten to ask Tamago's permission whether it is ok to post his answers in the Examworld. The answers to the whole question and the beautiful graph are the good effort of Tamago, so we must express our thanks for him.

Thank you for your kind attention.

Regards,

ahm97sic

^tamago^ SG

Can post one no problems.

eagle SG

Hi Eagle,

Thank you for your kind attention.

Regards,

ahm97sic

yup

anyway, we are all here with the common aim of helping students :D