DSE Maths Core · Past Paper Questions

2013 · Paper 2 Q32 Exponential and logarithmic functions

The figure above shows the graph of

y = ab^{x}

, where

a

and

b

are constants. Which of the following graphs may represent the relation between

x

and

\log_{7} y

?

A

B

C

D

2013 · Paper 2 Q33 More about polynomials

A

10 \times 16^{11} + 14 \times 16^{5} + 17

B

11 \times 16^{11} + 15 \times 16^{5} + 17

C

10 \times 16^{12} + 14 \times 16^{6} + 272

D

11 \times 16^{12} + 15 \times 16^{6} + 272

2013 · Paper 2 Q34 Exponential and logarithmic functions

If

x - \log y = x^2 - \log y^2 - 10 = 2

, then

y =

A

100

.

B

2

or

-4

.

C

\frac{1}{100}

or

10\,000

.

D

\frac{1}{10\,000}

or

100

.

2013 · Paper 2 Q35 Quadratic equations in one unknown

If

\alpha \neq \beta

and

\begin{cases} 3\alpha = \alpha^2 - 5 \\ 3\beta = \beta^2 - 5 \end{cases}

, then

\alpha\beta =

A

3

.

B

-3

.

C

5

.

D

-5

.

2013 · Paper 2 Q36 More about polynomials

The real part of

i + 2i^{2} + 3i^{3} + 4i^{4}

is

A

2

.

B

-2

.

C

6

.

D

-6

.

2013 · Paper 2 Q37 Inequalities and linear programming

Consider the following system of inequalities:

\begin{cases} x \geq 2 \\ y \geq 0 \\ x + 4y \leq 22 \\ 4x - y \leq 20 \end{cases}

Let

D

be the region which represents the solution of the above system of inequalities. If

(x,y)

is a point lying in

D

, then the greatest value of

3y-4x+15

is

A

3

.

B

17

.

C

22

.

D

30

.

2013 · Paper 2 Q38 Arithmetic and geometric sequences and their summations

The

n

th term of a sequence is

2n-19

. Which of the following is/are true?

I.

25

is a term of the sequence.

II. The sequence has

10

negative terms.

III. The sum of the first

n

terms of the sequence is

n^{2}-18n

.

A I only

B II only

C I and III only

D II and III only

2013 · Paper 2 Q39 More about trigonometry

Let

h

and

k

be constants. The figure shows the graph of

y = h + k \tan 2x^\circ

, where

0 \leq x \leq \alpha

. Which of the following are true?

A I and II only

B I and III only

C II and III only

D I, II and III

2013 · Paper 2 Q40 Mensuration

If the height of a regular tetrahedron is

2\text{ cm}

, then the volume of the tetrahedron is

A

2\text{ cm}^{3}

B

\sqrt{3}\text{ cm}^{3}

C

\sqrt{6}\text{ cm}^{3}

D

3\sqrt{3}\text{ cm}^{3}

2013 · Paper 2 Q41 Basic properties of circles

In the figure,

O

is the centre of the circle

ABC

.

DE

is the tangent to the circle at

A

. If

AB

is the angle bisector of

\angle CAE

, then

\angle ACO =

A

26^{\circ}

B

28^{\circ}

C

31^{\circ}

D

34^{\circ}

2013 · Paper 2 Q42 Equations of circles

Find the range of values of

k

such that the circle

x^2 + y^2 + 2x - 2y - 7 = 0

and the straight line

3x - 4y + k = 0

intersect.

A

-8 < k < 22

B

-8 \leq k \leq 22

C

k < -22

or

k > 8

D

k \leq -22

or

k \geq 8

2013 · Paper 2 Q43 Rectangular coordinate system

Let O be the origin. If the coordinates of the points A and B are

(0, 12)

and

(30, 12)

respectively, then the y-coordinate of the circumcentre of

\Delta OAB

is

A

6

B

8

C

12

D

15

2013 · Paper 2 Q44 Permutations and combinations

If the first three digits and the last five digits of an eight-digit phone number are formed by a permutation of 5, 6, 9 and a permutation of 2, 3, 4, 7, 8 respectively, how many different eight-digit phone numbers can be formed?

A

15

B

126

C

720

D

40

320

2013 · Paper 2 Q45 Measures of dispersion

If the variance of the five numbers

x_{1}

,

x_{2}

,

x_{3}

,

x_{4}

and

x_{5}

is 13, then the variance of the five numbers

3x_{1}+4

,

3x_{2}+4

,

3x_{3}+4

,

3x_{4}+4

and

3x_{5}+4

is

A

39

B

43

C

117

D

121