Math Quiz X - Of Perimeters and Areas

1. The figure shows parallelogram ABCD with BC = 4 cm, PD = 1 cm and BQ = 2 cm. If the area of ABCD is 40 sq cm, and PQ divides it into 2 parts, then the ratio of the areas of the two parts formed is :

a) 1 : 1 b) 1: 2 c) 2: 5 d) 3 : 5

2. Parallelogram ABCD has an area of 84 sq cm and DC = 12 cm. The area of the circle in sq cm is :

a) 49 b) 41.5 c) 38.5 d) 35.35

3. A wire is bent to form a perfect semicircle of radius 7 cm. It is then bent to form a square; the area of the square is :

a) 49 sq cm b) 81 sq cm c) 100 sq cm d) 121 sq cm

4. If O is the center of the semicircle, then the ratio of the areas of the shaded to the unshaded portion is :

a) 1 : 4 b) 1 : 3 c) 1 : 2 d) 1 : 1

5. A wheel of diameter 70 cm moves up a straight path inclined at 30 degs with the horizontal. The vertical height in meters attained by the wheel in 10 revolutions is :

a) 2.3 m b) 2.2 m c) 1.1 m d) 0.77 m

6. The figure shows triangle ABC, right-angled at B. If AB = 28 cm, BC = 21 cm, then the area of the circumcircle is :

a) 962.50 sq cm b) 851.49 sq cm c) 749.70 sq cm d) 700 sq cm

7. In the figure, if the circumference of each circle is 22 cm, then the area of the unshaded portion in sq cm is :

a) 63 b) 56 c) 49 d) 42

8. The ratio of the areas of the incircle to the circumcircle of a square is :

a) 1 : 4 b) 1 : 3 c) 1 : 2 d) 2 : 3

9. For the 3 circles shown, the radius of the smallest circle is half that of the medium-sized circle. The ratio of the area of the largest circle to the area of the smallest one is :

a) 14 : 1 b) 9 : 1 c) 7 : 1 d) 7 : 2

10. The figure shows a square, and its circumcircle of radius 'r'. The radius of the smaller circle, in terms of 'r' is :

a) (1 - rt2)r/8 b) (1 + rt2)r/4

c) (2 + rt2)r/8 d) (2 - rt2)r/4

---------- Answer Key ----------

1. (d) 2. (c) 3. (b) 4. (d) 5. (c)

6. (a) 7. (d) 8. (c) 9. (b) 10. (d)

Math Quiz IX - One Challenging Question!

The figure shows isosceles triangle ABC,

AB = AC, and with its incircle of radius 3 cm.
If the base is 8 cm, find the length of AB.

Hints :

1) This question can be solved using quadratic equations or better still, trigo

2) The center of the incircle is the point where the bisectors of the vertex angles meet

3) In the circle shown, the 3 sides of the triangle are tangents to the incircle

4) Tangent segments drawn from each vertex to the circle are equal, i.e. BP = BQ and AP= AR

5) The lines joining the incentre to the sides of the triangles at the points of contact are perpendicular to the sides of the triangles

Math Quiz VIII - Percentages

1. 30% of 40% of x equals :

a) 12 x b) 1.2 x c) 0.12 x d) 0.012 x

2. A salesman earns a commission of 12% on every sale

and has to pay a tax of 4% of his earnings.

On a sale of Rs.25000 his net earning will be :

a) Rs 3240 b) Rs 2960 c) Rs 2880 d) Rs 2660

3. What is 33%of 3/11?

a) 9 b) 0,9 c) 0.09 d) 0.009

4. A number increased by 36% becomes 2720.

The same number increased by 46% will be :

a) 3808 b) 3280 c) 2920 d) 2080

5. If one-third of a cake is eaten by Shayne

and one-fourth of the remaining devoured by Wayne,

what percentage of the cake does remayne?

a) 30% b) 40% c) 50% d) 60%

6. A number is increased by 40% and the result
is then decreased by 40%. The percentage change
between the final number obtained

and the original number is :

a) 4% increase b) 8% decrease c) 12 % increase d) 16% decrease

7. From a circular sheet of cardboard of radius R

a circular piece of radius R/2 is cut out.

What is the percentage of the remaining cardboard?

a) 32% b) 48% c) 60% d) 75%

8. What is 5/11% of 22/7?

a) 5/7 b) 2/25 c) 1/35 d) 22/35

9. If a number is increased by 25%, by what percentage

should it be reduced to obtain the original number?

a) 20% b) 25% c) 30% d) 40%

10. If the sides of a square are increased by 20% each,

by what percentage does the area increase?

a) 40% b) 42% c) 44% d) 48%

11. Out of two numbers, one is increased by 20%
and the other is increased by 40%.
The percentage increase in their products is :

a) 60% b) 68% c) 72% d) 80%

12. For any number 'x', the difference between
the square of the number and the number itself
as a percentage of the original number is :

a) (x^2 - x)/100 b) (x^2 - x)100
c) (x - 1)100 d) 100x

13. If 2/5 % of a number is 20, then the number is :

a) 2000 b) 3000 c) 4000 d) 5000

14. From a square of side 10 cm, the largest possible
isosceles triangle is cut off. The percentage of the remaining
part of the square is :

a) 20% b) 30% c) 40% d) 50%

15. From a square, if the largest possible circle is cut out,
what percentage of the original square remains?

a) 20(4 - pi) b) 25(4 - pi) c) 30(5 - pi) d) 40(5 - pi)

----------Answer Key----------

1. (c) 2. (c) 3. (c) 4. (c) 5. (c) 6. (d)

7. (d) 8. (c) 9. (a) 10. (c) 11. (b) 12. (c)

13. (d) 14. (d) 15. (b)

Math Quiz VII - Profit, Loss and Discount

1. If the CP of an article is Rs 500 and its SP is Rs 650, the profit percent equals :

a) 25% b) 30% c) 32% d) 40%

2. If the CP of an article is Rs 500 and its SP is Rs 350, the loss percent equals :

a) 20% b) 25% c) 30% d) 35%

3. If an article is bought for Rs 300 and sold at a profit of 30%, its SP equals :

a) Rs 330 b) Rs 360 c) Rs 390 d) Rs 420

4. A trader buys an article for Rs. 500 and adds a profit of 20%;

the selling price will be :

a) Rs 560 b) Rs 575 c) Rs 600 d) Rs 625

5. A trader buys an article for Rs. 500 and suffers a loss of 20%;

the selling price of the article was :

a) Rs 350

b) Rs 400

c) Rs 420

d) Rs 440

6. The selling price of a laptop computer is Rs 32500, which includes a profit of 30%.

The cost price of the computer was :

a) Rs 22500 b) Rs 25000 c) Rs 27500 d) Rs 30000

7. If the SP of a widget = Rs 700 and the loss

incurred was 30%, the CP was :

a) Rs 490 b) Rs 540 c) Rs 910 d) Rs 1000

8. A shopkeeper buys apples at Rs 120 per kg

and sells them for Rs 138 per kg. His profit percent is :

a) 12% b) 13% c) 15% d) 16%

9. If CP = Rs 120, and the loss incurred was 12%, the SP would be :

a) Rs 105.60 b) Rs 115.60 c) Rs. 134.40 d) Rs 140

10. An article is marked at Rs 250 and sold at a discount of 12%; its SP equals :

a) Rs 200 b) Rs 220 c) Rs 240 d) Rs 280

11. If CP = Rs 500, MP = Rs 700, the article was marked up by how much percent?

a) 20% b) 30% c) 40% d) 50%

12. If CP = Rs 500, MP = Rs 700, and discount offered is 20%, then SP equals :

a) Rs 520 b) Rs 560 c) Rs 600 d) Rs 620

13. If CP = Rs 500, MP = Rs 700, and discount offered is 20%, then P% equals :

a) 8% b) 10% c) 12% d) 14%

----------Answer Key----------

1. (b) 2. (c) 3. (c) 4. (c) 5. (b) 6. (b) 7. (d)
8. (c) 9. (a) 10. (b) 11. (c) 12. (b) 13. (c)

Math Quiz VI

Note : All the following questions pertain
to the figure on the left which shows
a square with semicircles on its opposite sides.

1. If each side of the square is 14 cm, the perimeter of the figure equals :
a) 56 cm b) 64 cm c) 72 cm d) 84 cm

2. If each side of the square is 14 cm, the area of the figure equals :
a) 308 sq cm b) 420 sq cm c) 504 sq cm d) 630 sq cm

3. If the radius of each semicircle is 'r', the perimeter of the figure equals :
a) r(pi + 4) b) 4r(pi +2) c) 2r(pi + 2) d) 2r(pi + 4)

4. If the radius of each semicircle is 'r', the area of the figure equals :
a) (r^2)[pi + 2] b) (r^2)[pi + 4] c) 2(r^2)[pi + 4] d) 4(r^2)[pi + 1]

5. If the radius of each semicircle is 3.5 cm, the perimeter of the figure equals :
a) 35 cm b) 42 cm c) 50 cm d) 56 cm

6. If the radius of each semicircle is 3.5 cm, the area of the figure equals :
a) 87.5 sq cm b) 60 sq cm c) 93.5 sq cm d) 105 sq cm

7. If the perimeter of the figure is 72 cm, the radius of each semicircle is :
a) 7 cm b) 10.5 cm c) 14 cm d) 17,5 cm

8. If the perimeter of the figure is 72 cm, the area of the figure is :
a) 560 sq cm b) 616 sq cm c) 630 sq cm d) 700 sq cm

9. If the area of the figure is 1837.50 sq cm, then the radius of the semicircle is :
a) 10.5 cm b) 14 cm c) 17.5 cm d) 21 cm

10. If the area of the figure is 1837.50 sq cm, then the perimeter of the figure is :
a) 280 cm b) 350 cm c) 420 cm d) 490 cm

11. If the diagonal of the square is 7(rt2) cm, then the perimeter of the figure is :
a) 30 cm b) 40 cm c) 50 cm d) 60 cm

12. If the diagonal of the square is 7(rt2) cm, then the area of the figure is :
a) 70 sq cm b) 73.5 sq cm c) 80.5 sq cm d) 87.5 sq cm

----------Answer Key----------

1. (c) 2. (c) 3. (d) 4. (b) 5. (c) 6. (a)
7. (c) 8. (b) 9. (a) 10. (b) 11. (c) 12. (d)

Math Quiz V

1. The product of 2 numbers is 800.
If the first number increases by 20%

and the second reduces by 20 %,
then the new product is

a) 646 b) 768 c) 800 d) 960

2. In the figure find the total area of
the 2 semicircles shown,

given that angle B is 90 deg
and hypotenuseAC = 14 cm

a) 77 sq cm b) 140 sq cm c) 210 sq cm d) 350 sq cm

3. 8 years ago a man was 24 years old.

9 years hence his age will be :

a) 33 years b) 41 years c) 45 years d) 46 years

4. If x times y equals the square of y

then state which of the following is true :

a) x < b) x > y c) x = y d) x = 2

5. A car travels 30 km at 45 kmph
and another 30 km at 60 kmph;

the total travel time 1n minutes was :

a) 50 b) 60 c) 70 d) 80

6. A total of 60 advertisemements were sold
for a school magazine. If 20% of the 1st 20 sold
were in colour, 40% of the next 30sold were in colour,

and 80% of the last 10 sold were in colour,
what percent of the 60 ads sold were in colour?

a) 30% b) 33.33% c) 40% d) 60%

7. A ball is dropped from192 m on level ground
and after the third bounce it rises to a height of 24 m.
If the height to which the ball rises after each bounce
is always the same fraction of the height

reached on its previous bounce, what is the fraction?

a) 1/8 b) 1/4 c) 1/3 d) 1/2

8. Pete is 8 years older than Sam. Four years ago

Sam was half the age Pete is now. Pete's pesent age is:

a) 20 years b) 22 years c) 24 years d) 26 years

9. In the figure, the value of x equals :

a) 25 deg b) 30 deg c) 40 deg d) 45 deg

10. The tip of a fan blade is 2 m from its axis of rotation.

If the fan completes 600 rotations per minute,

how many km does the tip of the blade travel in 1 hour?

a) 60pi km b) 120pi km c) 144 pi km d) 176pi km

----------Answer Key----------

1. (b) 2. (a) 3. (b) 4. (c) 5. (c)

6. (c) 7. (d) 8. (c) 9. (a) 10. (c)

Math Quiz IV

1. The diameter of the circle is 10 cm and AB = 6 cm;

the area of triangle OAB in sq cm equals :

a) 10 b) 12 c) 14 d) 21

2. In the figure, AB is parallel to CD; the value of x + y + z equals :

a) 90 degs b) 120 degs c) 180 degs d) 270 degs

3. One side of a rectangle is the diameter of a circle

and the other side is a tangent to the circle.

If the radius of the circle is 7 cm, the perimeter

of the rectangle is :

a) 28 cm b) 35 cm c) 42 cm d) 49 cm

4. One side of a rectangle is the diameter of a circle

and the other side is a tangent to the circle.

If the radius of the circle is 7 cm, the area

of the rectangle is :

a) 49 sq cm b) 63 sq cm c) 77 sq cm d) 98 sq cm

5. Five more than twice a number is 17;

hence, two less than half the number is :

a) 1 b) 2 c) 3 d) -1

6. In the figure the value of x + y equals :

a) 180 degs b) 190 degs c) 200 degs d) 220 degs

7. Joe scores an average of 88 in his first four math tests

and wants to raise his average to 90 in his last test.

How much must he score in the last one to raise

his average to 90?

a) 98 b) 96 c) 94 d) 92

8. Three consecutive integers are written in increasing order.

If the sum of the first and second and twice the third is 93,

the second integer is :

a) 22 b) 23 c) 24 d) 25

9. If 4x + 6y + 3z = 9.10 and 2x + 3y + z = 3.90, then z equals :

a) 1.15 b) 1.20 c) 1.25 d) 1.30

10. If x and y are positive integers and 2x + y = 7

then the value of 4x^2 - y^2 equals :

a) 7 b) 15 c) 28 d) 35

----------Answer Key----------

1. (b) 2. (c) 3. (c) 4. (d) 5. (a)

6. (b) 7. (a) 8. (b) 9. (d) 10. (d)