Mathematics

1

In a survey of 450 people, 200 liked tea, 250 liked coffee, but 50 liked neither.

[6 marks]

a.

If T and C denote the sets who like tea and coffee respectively, write n(T ∪ C).

[1 mark]

b.

Present in Venn diagram.

[1 mark]

c.

Find number who liked only tea.

[3 marks]

d.

Compare number who liked both vs. only coffee.

[1 mark]

2

Rs. 50,000 deposited for 2 years at 8% p.a. compound interest.

[5 marks]

a.

How many times per year is interest compounded?

[1 mark]

b.

Interest after 2 years?

[2 marks]

c.

How much more if compounded semi-annually?

[2 marks]

3

Bus bought for Rs. 45,00,000, earned Rs. 12,00,000 in 2 years, 10% p.a. depreciation.

[4 marks]

a.

Express V_T in terms of V₀, R, T.

[1 mark]

b.

Depreciation in first year?

[1 mark]

c.

% profit/loss after 2 years?

[2 marks]

4

Buying rate Rs. 138.23, selling Rs. 138.83 per $1.

[4 marks]

a.

Selling higher by how much?

[1 mark]

b.

Nepali rupees for $500?

[2 marks]

c.

If selling becomes Rs. 139.80, % devaluation of NPR?

[1 mark]

5

Square-based pyramid: height 12 cm, base side 10 cm.

Square-based pyramid figure for question 5

[5 marks]

a.

Number of triangular faces?

[1 mark]

b.

Volume?

[2 marks]

c.

Total surface area?

[2 marks]

6

Combined cylinder + cone, same radius. Cylinder length 28 cm, cone slant height 17 cm, cylinder vol 5632 cm³.

Combined cylinder and cone figure for question 6

[5 marks]

a.

Base shape?

[1 mark]

b.

Compare cone height & cylinder length?

[2 marks]

c.

Is cylinder vol 5× cone vol?

[2 marks]

7

Room 12 m × 8 m × 3 m, two 2×2 m windows, 1.5×1 m door.

[4 marks]

a.

Floor area

[1 mark]

b.

Cost to paint walls + ceiling @ Rs.15/m² excluding windows & door

[3 marks]

8

7 arithmetic means between 3 and 27.

[5 marks]

a.

Formula for AM between a and b

[1 mark]

b.

5th mean?

[2 marks]

c.

Which is larger — AM or GM between 3 and 27? By how much?

[2 marks]

9

Rectangular ground perimeter 44 m, area 120 m².

[5 marks]

a.

Quadratic formula

[1 mark]

b.

Length and breadth?

[2 marks]

c.

If made square by reducing length, % change in area?

[2 marks]

10

[5 marks]

a.

Simplify: a/(a−b) + b/(b−a)

[2 marks]

b.

Solve: 2^x + 1/2^x = 2.5

[3 marks]

11

Figure: EC ∥ AB, DA ∥ CB, DF ⊥ BC.

[5 marks]

a.

Relation between triangle & parallelogram on same base & between same parallels

[1 mark]

b.

If BC=6 cm, DF=8 cm, area of ΔABE

[2 marks]

c.

Prove AD ∥ BC if area ΔAOB = ΔCOD

[2 marks]

12

O centre, PQRS cyclic quadrilateral.

Cyclic quadrilateral figure for question 12

[4 marks]

a.

Relation between ∠QRS and reflex ∠QOS

[1 mark]

b.

If ∠QPS=46°, find ∠QOS

[1 mark]

c.

Experimentally verify ∠QPS + ∠QRS = 180°

[2 marks]

13

[4 marks]

a.

Construct ΔMNO (MN=8 cm, NO=7 cm, ∠MNO=60°) and rectangle NPQR equal in area.

[3 marks]

b.

Why areas equal? Reason.

[1 mark]

14

Tower AB=30 m, depression angle 30°, BD=10√3 m.

Height and distance figure for question 14

[4 marks]

a.

Define angle of elevation

[1 mark]

b.

Elevation angle from roof to tower top

[1 mark]

c.

Height of house

[1 mark]

d.

Value of ∠CAH when AE=EC? Reason

[1 mark]

15

15 students' marks (out of 50): 0-10:5, 10-20:3, 20-30:4, 30-40:2, 40-50:1

[6 marks]

a.

Q1 formula for continuous series

[1 mark]

b.

First quartile

[2 marks]

c.

Median

[2 marks]

d.

Maximum students who can score more than mean?

[1 mark]

16

7 black, 4 red balls. Two drawn without replacement.

[5 marks]

a.

Formula P(B ∩ R) if independent

[1 mark]

b.

Tree diagram of outcomes

[2 marks]

c.

P(both black)

[1 mark]

d.

Compare P(both red) vs P(both black)

[1 mark]