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.

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**INTERIM JOINT MATRICULATION BOARD EXAMINATION 2022.**

**SUBJECT:**** **** ****‘A’ LEVEL MATHEMATICS PAPER III**

**DATE SCHEDULED:**** **** ****WEDNESDAY 22ND JUNE, 2022**

**TIME ALLOWED:**** **** ****TWO HOURS (2HRS)**

Instruction:

- Unless otherwise restricted, the use of mathematical tables is PERMITTED
- Use of SCIENTIFIC calculator is ALLOWED
- Mark for each question is indicated at the end
- Do not spend more than HALF (1/2) HOUR on section A
- 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%)**

- 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]
- Show that fx=5e-5x,0≤x≤∞ is a probability density function, hence finding the probability for x≤3. [04 marks]
- 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]
- Find the equation of the circle whose centre is the midpoint of (-1,2) and (2,3) and radius 5. [04 marks]
- 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]

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