IJMB Maths 102 Past Questions For 2022

IJMB Maths 102 Past Questions For 2022; Maths students who have mathematics as one of the 3 subjects they will sit for during the upcoming IJMB EXAMINATION should spend more time on this website practicing past questions available.

Recommended; See Other IJMB Past Questions Here

INTERIM JOINT MATRICULATION BOARD EXAMINATION 2022

SUBJECT: ‘A’ LEVEL MATHEMATICS

DATE SCHEDULED: MONDAY 20^TH 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 are indicated at the end
4. Do not spend more than HALF (1/2) HOUR on section A 
5. Attempt ALL question in section  A; and FOUR (4) question from other section, choosing at least ONE (1) question from each of section B and C.

SECTION A (20%)

1. Differentiate 1+sinx1+cos x [04 marks]
2. Find the direction cosines of vector 2i+2j-k [04 marks]
3. Evaluate  lim x→ 0  x-sinx12x3-x4 [04 marks]
4. If  y=ex sin x , show that y”-2y’+2y=0 [04 marks]
5. Show that 01dx1+x[2+log⁡(1+x)=loglog2e22 [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]

8. (a) Sketch the graph of the function y=x3-2×2-5x+6 and obtain the area bounded by the curve and x-axis.

      (b). Differetiate (1+x2 +x.\

SECTION C: DIFFERETIATIAL EQUATION AND VECTOR

9. (a) Solve the equation dydx-ytan x=x, y2=0                                        [10 marks]

     (b) Find the angles the vector a=3i+j-2k makes with the coordinate axes [10 marks]

10.(a) Solve the equation yxdx-1+x2dy=0, y0=1               [10 marks]

      (b) Given the vectors a=3i+j-k and b=2i-j-k, compute the projection of 3a-2b on the vector (2a+3b). [10 marks]

11.(a) Solve the differential equation for dydx=x2-3xy+4y2x2 if y1=0 [15 marks]

      (b). Determine the value of y if the vector yi-2j-k and k-i are linearly dependent.  [05 marks]

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