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# IJMB Maths 103 Past Questions 2022

IJMB Maths 103 Past Questions 2022; This is the correct IJMB maths past questions for paper 103. Students who are about to sit for the IJMB examination are advised to study this maths blog post carefully.

INTERIM JOINT MATRICULATION BOARD EXAMINATION 2022.

SUBJECT: ‘A’ LEVEL MATHEMATICS PAPER III

DATE SCHEDULED: WEDNESDAY 22ND JUNE, 2022

TIME ALLOWED: TWO HOURS (2HRS)

Instruction:

1. Unless otherwise restricted, the use of mathematical tables is PERMITTED
2. Use  of SCIENTIFIC calculator is ALLOWED
3. Mark for each question is indicated at the end
4. Do not spend more than HALF (1/2) HOUR on section A
5. Attempt ALL questions in section  A; and FOUR (4) questions from other sections, choosing at least ONE (1) question from each of sections B and C.

SECTION A (20%)

1. Find the equation of a straight line which is perpendicular to the line x-3y+2=0 and passes through the midpoint of the line joining the point (3,-2) and (-1,5)   [05 marks]
2. Show that fx=5e-5x,0≤x≤∞ is a probability density function, hence finding the probability for x≤3. [04 marks]
3. A bag contains 15 balls out of which 7 are yellow balls, 3 white balls and the rest are black. A ball is picked from the bag at random. Find the probability that the ball is black. [03 marks]
4. Find the equation of the circle whose centre is the midpoint of (-1,2) and (2,3) and radius 5. [04 marks]
5. Find the focus of the parabola y2=3(x+1) [04 marks]

SECTION B: CALCULUS

6. (a) If  y=xey, show that

(i)   1-yy’=ey

(ii)  1-yy”=2-y(y’)2 [10 marks]

(b) Evaluate 381×1+xdx  [10 marks]

7. (a). Differentiate from first principle y=7x-5                                        [10 marks]

(b). Find the first four terms of the series expansion of the function fx=13x-1 for x<1, ascending power of x. [10 marks]

(b). Describe the locus of the point P(x,y) equidistant from the points A3,-2 and B(-3,5)

[08 marks]

8. (a) Find the equation of the tangent to the ellipse(x-h)2a2+(y-k)2b2=1, at the point x1,,y1. Hence, obtain the equation of the tangent to the ellipse (x+2)216+y24=1, at the point (-2,2)

[10 marks]

(b). Sketch the curve r=2(1+sin 3 ) in polar form 0≤θ≤360°                  [10 marks]

SECTION C: STATISTICS

9. (a) Two numbers are selected at random from integers 10 to 40, inclusive, repetition being allowed. Find the probability that:

(i) Both are multiples of 5 (ii) Both are the power of 2

(iii) One is a power of 2 and the other is a multiple of 5. What are the corresponding probabilities if repetition is not allowed? [12 marks]

(b). if X≈N74.9 find:

(i) P(x≤73)       (ii) P(70≤X≤78) [08 marks]

10. (a).  For a Binomial distribution with 5 trials and P =14, find the probability that:

(i)  Exactly 3 trials are successful;   (ii) At least 2 trials are successful;

(iii) Less than 4b trials are successful; (iv) All the 5 trails are successful;

(v)  None of the trials is successful. [12 marks]

(b). If a card is randomly selected from a deck of cards, find the probability that it is

(i) A spade or a diamond; (ii) An ace or a heart [08 marks]

11. (a) Three balls are drawn at random without replacement from a bag containing 10 black, 13 white and 11 red balls. Find the probability that

(i) the balls are the same colour (ii) 2 of the balls are black and one is white. [10 marks]     (b). If P≈PO2.5, find (i) P(x=1) (ii) P(x≥2) (iii) Px≤2.           [10 marks]