MAT2613 EXAM REVISION PACK 2026

MAT2613
EXAM REVISION
PACK




2026

,This examination question paper consists of 4 pages.

Answer All Questions.

, 2 MAT1613
January/February 2024


QUESTION 1

Let f be a function defined by
x
f (x) =
(x + 1)2

(a) Determine the horizontal and vertical asymptotes. (4)

(b) Use the sign pattern for f 0 (x) to determine the interval(s) over which f rises and where it falls. (5)

(c) Determine the coordinates of the local extreme point(s). (2)

(d) Use the sign pattern for f 00 (x) to determine the interval(s) over which the graph of f is concave up and (6)
concave down.

(e) Determine the coordinates of the inflection point. (2)
[19]



QUESTION 2

At what rate is the surface area of a square increasing when the perimeter is 64 cm and the perimeter is increasing
at 4 cm/sec?
[7]



QUESTION 3

−4
Find the exact value of sin π + cos−1



5 .
[7]



QUESTION 4

Use L’Hôspital’s rule to determine

cos x − 1 + 2x2
(a) lim (5)
x→0 2x2
 
1 1
(b) lim+ − (6)
x→1 ex − 1 x

(c) lim (1 + 4x)cot x (8)
x→0+
[19]




[TURN OVER]

, 3 MAT1613
January/February 2024


QUESTION 5

Evaluate the following integrals:

(a) (6)
Z 9
dx
√ √
4 2 x(1 + x)


(b) (7)
Z  − 45
2
x +1 x dx


(c) (7)
Z 4
p √
1+ x
√ dx
0 x

[20]



QUESTION 6

Consider the following integral
Z
dx
I= √
x2 − 4x + 20

(a) First complete the square of (2)

f (x) = x2 − 4x + 20


(b) Then use trigonometric substitution to determine the integral. (8)
Z
Hint: sec θ dθ = ln | sec θ + tan θ + c|

[10]



QUESTION 7

Use the partial fractions to evaluate the integral
Z
x+4
dx
2x2 + x − 1
[8]