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.

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**INTERIM JOINT MATRICULATION BOARD EXAMINATION 2022**

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

**DATE SCHEDULED:**** **** ****MONDAY 20**^{TH}** 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 are indicated at the end
- Do not spend more than HALF (1/2) HOUR on section A
- 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%)**

- Differentiate 1+sinx1+cos x [04 marks]
- Find the direction cosines of vector 2i+2j-k [04 marks]
- Evaluate lim x→ 0 x-sinx12x3-x4 [04 marks]
- If y=ex sin x , show that y”-2y’+2y=0 [04 marks]
- 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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