MAT 2020 MCQb

10 questions40 marks60Updated July 2026

The MAT 2020 MCQb paper in full: all 10 questions, each with its answer. Sit it cold under exam timing, mark it, then work back through anything you missed using the solutions below.

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Question 1

4 marks

The distance between opposite corners of a cube is

2

. The surface area of the cube equals

A.4,
B.6,
C.8,
D.12,
E.24.

Answer: C

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Question 2

4 marks

x

is a very large positive real number, then the product

2^x \times 3^{-x} \times 4^x \times 5^{-x} \times \dots \times 18^x \times 19^{-x} \times 20^x \times 21^{-x}

A.very close to zero,
B.slightly larger than 1,
C.equal to 1,
D.very close to 2,
E.very large.

Answer: C

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Question 3

4 marks

Using degrees, the number of real solutions

x

to the equation

\cos \left( \frac{240x}{x^2 + 4} \right) = \frac{1}{2}

A.0,
B.1,
C.2,
D.3,
E.infinite.

Answer: E

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Question 4

4 marks

Let

y = 2x + 3x^2 + 5x^3 + \dots

so that the coefficient of

x^n

is the

n^{th}

prime number. Then the value of

\frac{d^5y}{dx^5}

x = 0

A.0,
B.120,
C.840,
D.1080,
E.1320.

Answer: C

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Question 5

4 marks

The curve

x^{20} - y^{20} = 1

is sketched in

A.(a)
B.(b)
C.(c)
D.(d)
E.(e)

Answer: B

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Question 6

4 marks

The following are statements about a real number

x

P : \frac{x^2 - 1}{x + 2} < 0, \quad Q : \frac{1 + x}{1 - x} > 0.

Then it follows that

A.P implies Q but Q does not imply P.
B.Q implies P but P does not imply Q.
C.P and Q are equivalent.
D.If P is true then Q is false.
E.If Q is true then P is false.

Answer: A

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Question 7

4 marks

The functions

S

and

T

are defined by

S(x) = x + 1, \quad T(x) = \frac{1}{2}x - 1.

Beginning with

x = 0

the functions

S

and

T

are repeatedly applied in some order. For example,

SSTS(0) = \frac{3}{2}

. The set of possible outputs is

A.all positive rational numbers.
B.all rational numbers greater than $-1$ with denominator a power of 2 when written in lowest terms.
C.all rational numbers with denominator a power of 2 when written in lowest terms.
D.all positive rational numbers with denominator a power of 2 when written in lowest terms.
E.all rational numbers greater than $-2$ with denominator a power of 2 when written in lowest terms.

Answer: E

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Question 8

4 marks

A sequence

a_n

is defined by

a_0 = A

and

a_k = (a_{k-1})^2

for

k > 0

, where

A > 1

. The sequence

b_n

is defined by

b_n = \log_2 a_n

. The sequence

b_n

A.constant
B.an arithmetic progression
C.a geometric progression
D.all of the above
E.none of the above

Answer: D

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Question 9

4 marks

An equilateral triangle is drawn in the

xy

-plane. Two of its vertices are at

(0, 0)

and

(1000, 0)

. The number of points

(x, y)

inside the triangle, where

x

and

y

are both whole numbers, equals

(a) 866,025, (b) 866,026, (c) 866,027, (d) 432,512, (e) 432,513.

[Note that

\sqrt{3} = 1.7321

to 4 decimal places.]

A.866,025,
B.866,026,
C.866,027,
D.432,512,
E.432,513.

Answer: D

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Question 10

4 marks

Let

R

be the region where all four of the following inequalities hold

x^2 < 2 + y, \quad x^2 < 2 - y, \quad y^2 < 2 + x, \quad y^2 < 2 - x.

What is the area of

R

A.0,
B. $\frac{28}{3}$ ,
C.4 + 2 $\pi$ ,
D. $\frac{4}{3}$ \left( 8 $\sqrt{2}$ - 7 \right),
E.infinite.

Answer: D

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