2015

Question 1

An arithmetic sequence is a sequence where:

A. The ratio between terms is constant.
B. The difference between terms is constant.
C. The product of terms is constant.
D. The exponent of terms is constant.

Answer 1

B. The difference between terms is constant.

Question 2

Which expression is definitely an arithmetic sequence in k?

A. 2ᵏ
B. 3k² + 1
C. 5k − 4
D. k!

Answer 2

C. 5k − 4 (linear in k → AP)

Question 3

For an arithmetic series with first term a₁ and last term aₙ, the correct sum formula is:
A. 𝑆𝑛=𝑎1+𝑎𝑛
B. Sn​=n(a1​+an​)
C. Sn​=n/2​(a1​+an​)
D. Sn=(a1+an)/2
​​

Answer 3

C. Sn​=n/2​(a1​+an​)

Question 4

An explicit formula for a sequence means:

A. Each term depends only on the previous term.
B. Each term depends directly on n.
C. The sequence is geometric.
D. The sequence is finite.

Answer 4

B. Each term depends directly on n.

Question 5

If the explicit formula is linear in n (like an = pn + q), the sequence is:

A. Always geometric
B. Always constant
C. Always arithmetic
D. Always random

Answer 5

C. Always arithmetic

Question 6

“Plug-in method” means:

A. Solving for n first.
B. Substituting the given n directly into the formula for aₙ.
C. Differentiating the function.
D. Using trial-and-error with choices only.

Answer 6

B. Substituting the given n directly into the formula for aₙ.

Question 7

In the term 𝑇𝑘 of (𝑎+𝑏)𝑛 , which index is used in the combination?
A. C(n, k)
B. C(n, k−1)
C. C(k, n−1)
D. C(k, n)

Answer 7

B. C(n, k−1)

Question 8

What does nCr represent?

A. Number of permutations of r objects from n.
B. Number of ways to arrange n objects in r boxes.
C. Number of combinations of r objects chosen from n.
D. Number of terms in a binomial expansion.

Answer 8

C. Number of combinations of r objects chosen from n.

Question 9

For (𝑎+𝑏)𝑛 the sum of all binomial coefficients ∑𝑛𝑟=0(𝑛/𝑟) equals:
A. n
B. n²
C. 2ⁿ
D. n!

Answer 9

C. 2ⁿ

Question 10

Statement “r is a root” of f(x) means:
A. f(r) = 1 
B. f(r) = 0 
C. f(r) = r 
D. f(r) undefined

Answer 10

B. f(r) = 0

Question 11

If quadratic has roots 2 and 5, sum of roots:
A. 3 
B. 7 
C. 10 
D. 1

Answer 11

B. 7

Question 12

Sum of roots of 𝑎𝑥^2+𝑏𝑥+𝑐=0 is:
A. a/b 
B. b/a 
C. −b/a 
D. −c/a

Answer 12

C. −b/a

Question 13

Partial fractions are useful mainly for:
A. Integration of rational functions
B. Differentiation only
C. Solving linear equations
D. Matrix inversion

Answer 13

A. Integration of rational functions

Question 14

For distinct linear factors, best shortcut to get A, B is:
A. Trial and error
B. Long division only
C. Cover-up / substitution at roots
D. Laplace transforms

Answer 14

C. Cover-up / substitution at roots

Question 15

If numerator degree ≥ denominator degree, first step is:
A. Multiply by x
B. Reverse coefficients
C. Polynomial long division
D. Take derivative

Answer 15

C. Polynomial long division

Question 16

If both workers’ times are doubled, their combined time will:
A. halve 
B. double 
C. more than double 
D. less than double

Answer 16

B. double

Question 17

More people working on same job (all with same rate) means:
A. time increases linearly
B. time decreases linearly
C. time unchanged
D. job impossible

Answer 17

B. time decreases linearly

Question 18

If total work is W, rate R = W/T. For 1 unit job (W=1), rate =:
A. 1/T 
B. T/1 
C. T² 
D. 1/T²

Answer 18

A. 1/T

Question 19

If two angles are complementary, then:
A) sum = 180°
B) sum = 90°
C) product = 90°
D) difference = 90°

Answer 19

B) sum = 90°

Question 20

If 𝐴+𝐵=90∘, then tan𝐴⋅tan𝐵=
A) 0
B) 1
C) -1
D) tan 90∘

Answer 20

B) 1

Question 21

Angle of elevation is measured from:
A) vertical line
B) horizontal line
C) line of sight downwards
D) north reference

Answer 21

B) horizontal line

Question 22

In pipe problems, rates combine by:
A) adding times
B) adding rates
C) multiplying rates
D) subtracting times always

Answer 22

B) adding rates

Question 23

If net rate is negative, it means:
A) tank fills faster
B) tank empties overall
C) tank stays full
D) time becomes zero

Answer 23

B) tank empties overall

Question 24

A leak acts like:
A) extra inlet
B) extra outlet
C) no effect
D) doubles capacity

Answer 24

B) extra outlet

Question 25

In relative motion problems, “with the current/wind” means: A) subtract speed B) add speed C) multiply speed D) divide speed

Answer 25

B) add speed

Question 26

If time with wind decreases while distance is fixed, then ground speed: A) decreases B) increases C) becomes zero D) becomes negative

Answer 26

B) increases

Question 27

If 𝑣+𝑤 and 𝑣−𝑤 are known, wind speed equals: A) average B) half the difference C) difference D) product

Answer 27

B) half the difference