Point to point

1. Mrs. Rodger got a weekly raise of $145. If she gets paid
every other week, write an integer describing how the raise
will affect her paycheck.
Solution:
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x +
145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by
$ 145.
2. The value of x + x(x x ) when x = 2 is:
(a) 10, (b) 16, (c) 18, (d) 36, (e) 64
Solution:
x + x(x x )
Put the value of x = 2 in the above expression we get,
2 + 2(2 2)
= 2 + 2(2 × 2)
= 2 + 2(4)
= 2 + 8
= 10
Answer: (a)
3. Mr. Jones sold two pipes at $1.20 each. Based on the
cost, his profit one was 20% and his loss on the other was
20%. On the sale of the pipes, he:
(a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost
10 cents, (e) gained 10 cents
Solution:
20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other
pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke
even.
Answer: (a)
4. The distance light travels in one year is approximately
5,870,000,000,000 miles. The distance light travels in 100
years is:
(a) 587 × 10 8 miles, (b) 587 × 10 10 miles, (c) 587 × 10 -10
miles, (d) 587 × 10 12 miles, (e) 587 × 10 -12 miles
Solution:
The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 10 12 miles.
Answer: (d)
5. A man has $ 10,000 to invest. He invests $ 4000 at 5 %
and $ 3500 at 4 %. In order to have a yearly income of $
500, he must invest the remainder at:
(a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 %
Solution:
Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $
140 = $ 340.
Remaining income amount in order to have a yearly income
of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right
two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4
% in order to get $ 500 income every year.
Answer: (e)
6. Jones covered a distance of 50 miles on his first trip. On
a later trip he traveled 300 miles while going three times as
fast. His new time compared with the old time was:
(a) three times as much, (b) twice as much, (c) the same,
(d) half as much, (e) a third as much
Solution:
Let speed of the 1st trip x miles / hr. and speed of the 2nd
trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his
first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his
later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the
old time was: twice as much.
Answer: (b)
7. If (0.2) x = 2 and log 2 = 0.3010, then the value of x to
the nearest tenth is:
(a) -10.0, (b) -0.5, (c) -0.4, (d) -0.2, (e) 10.0
Solution:
(0.2) x = 2.
Taking log on both sides
log (0.2) x = log 2.
x log (0.2) = 0.3010, [since log 2 = 0.3010].
x log (2 / 10 ) = 0.3010.
x [log 2 - log 10] = 0.3010.
x [log 2 - 1] = 0.3010,[since log 10=1].
x [0.3010 -1] = 0.3010, [since log 2 = 0.3010].
x[-0.699] = 0.3010.
x = 0.3010 /-0.699 .
x = -0.4306….
x = -0.4 (nearest tenth)
Answer: (c)
8. If 10 2y = 25, then 10 -y equals:
(a) -1 / 5, (b) 1 / 625, (c) 1/ 50 , (d) 1 / 25 , (e) 1 / 5
Solution:
10 2y = 25
(10 y ) 2 = 5 2
10 y = 5
1 /10 y = 1/ 5
10 -y = 1/ 5
Answer: (e)
9. The fraction (5x-11) / (2x 2 + x - 6) was obtained by
adding the two fractions A/ (x + 2) and B / (2x - 3) . The
values of A and B must be, respectively:
(a) 5x, -11, (b) -11, 5x, (c) -1, 3, (d) 3, -1, (e) 5, -11
Solution:
Answer: (d)
10. The sum of three numbers is 98. The ratio of the first to
the second is 2/ 3, and the ratio of the second to the third is
5 / 8 . The second number is:
(a) 15, (b) 20, (c) 30, (d) 32, (e) 33
Solution:
Let the three numbers be x, y and z.
Sum of the numbers is 98.
x + y + z = 98………………(i)
The ratio of the first to the second is 2 /3 .
x/y = 2 /3 .
x = 2 /3 × y.
x = 2y / 3 .
The ratio of the second to the third is 5 /8 .
y /z = 5 /8 .
z /y = 8 /5 .
z = 8 /5 × y.
z = 8y / 5 .
Put the value of x = 2y / 3 and z = 8y / 5 in (i).
2y / 3 + y + 8y / 5 = 98
49y / 15 = 98.
49y = 98 × 15.
49y = 1470.
y = 1470 /49 .
y = 30 .
Therefore, the second number is 30.
Answer: (c)
Unsolved Questions:
1. Fahrenheit temperature F is a linear function of Celsius
temperature C. The ordered pair (0, 32) is an ordered pair of
this function because 0°C is equivalent to 32°F, the freezing
point of water. The ordered pair (100, 212) is also an
ordered pair of this function because 100°C is equivalent to
212° F, the boiling point of water.
2. A sports field is 300 feet long. Write a formula that gives
the length of x sports fields in feet. Then use this formula to
determine the number of sports fields in 720 feet.
3. A recipe calls for 2 1/2 cups and I want to make 1 1/2
recipes. How many cups do I need?
4. Mario answered 30% of the questions correctly. The test
contained a total of 80 questions. How many questions did
Mario answer correctly?

Come back to basic

1) Explain what different classes of maths are and what
maths you prefer?
Different types of field for maths are Calculus, Algebra and
Fractions. I use all types of maths, but Calculus is major.
2) Explain what is algebra?
Algebra is one of the fields of maths, which uses symbols
and letters to represent numbers, point and objects, as well
as relationship between them. It is used to know the
unknown variables.
For example, you have lost 5 pens, and you are left with 10
pens now, to know the total number of pens you had it. You
will use algebraic equation.
X -5 = 10
X= 10+5 = 15 which is the total number of pens you had.
3) How much space would a 30 Cup shelf require if a 12
shell cupboard requires 18 ft. of wall space?
A 30 Cup shell requires 45 ft. of wall
4) In a staff room, there are four racks with 10 boxes of
chalk-stick. In a given day, 10 boxes of chalk stick is in
use. What is the fraction remains in the rack?
If each rack consist of 10 box of chalk stick, then total
number of box on 4 racks will be
4X 10 = 40
Now, the second part is 10 of the boxes are in use which
means that total amount of box left is= 40 – 10 = 30.
Now the fraction will be
Remained/ total = 30/ 40 = 3 / 4 is the fraction remain in the
rack
5) Explain what is the formula for calculating interest rate?
There are two types of interest which can be calculated
using a different formula
Simple Interest
Compound Interest
To calculate simple interest, formula used is (PX RX T)/ 100
Where P is the principal amount, R is for the rate of interest
and t is for time
Formula for calculating compound interest is P X (1 + r/100)
^t

6) Explain what is Commutative, Associative and
Distributive laws in maths?
Commutative laws say we can swap numbers, and you
still get the same number when you add, for example, a+b
= b+a and same for multiplication.
Associative laws say it does not matter how we group the
number final value will remain the same, for example, (a
+b)+c = (a+b)+c , and same for multiplication
Distributive laws say that we can have the same answer
while multiplying a number by a group of numbers added
together or multiplying them separately and then add
them, For example, a x ( b+c) = axb + bxc
7) In a small company average salary of three employees is
$1000 per week. If one employee earns $1100 and other
earns $500, how much will the third employee earn?
Formula to calculate this,
(e1+e2+e3) /3 = $ 1000
1100+500+e3 = 1000 x 3
1600+e3 = 3000
e3 = 3000-1600
= 1400
The third employee will earn $1400
8) Explain in a complicated calculation like 8 + (9 x 5 2 +8)
from where you will start calculation?
To avoid confusion from where to start the calculation from,
you have to follow the BODMAS
B = Bracket first
O = Orders ( Powers and Square roots )
DM = Division and Multiplication
AS = Addition and Subtraction
Once you have done with B or O, then proceed from left to
right doing any “D” or “M” as it is given in the problem, and
then proceed from left to right doing any “A” or “S” as given
in the problem.
9) Mention what is Geometry is about?
Geometry can be classified into two classes
Plane Geometry: It is about flat shapes like triangles, lines
and circles that can be drawn on a piece of paper
Solid Geometry: It is about three-dimensional objects like
cylinders, cubes, prism and spheres
10) Explain what is the difference between Line, Point,
Plane and Solid?
Point has no dimensions
Line is one-dimensional
Plane is two dimensional
Solid is three dimensional
11) Explain what is Exterior Angle in polygons?
In polygons, angle between any side of the shape and a line
extended from the next side is referred as Exterior Angles.
All the exterior angles of the polygon add up to 360°. Each
exterior angle must be 360°
12) Explain how you can convert a fraction to a percentage?
To convert a fraction to a percentage, we look into an
example for 4/9
First divide 4/9 = 0.44
Then multiply by 100 = 0.44 x 100 = 44.44
Add the “ % “ sign to the answer = 44.44%
Percentage of 4/9 = 44.4 %
13) Explain how you can convert a percentage to a fraction?
To convert a percentage into fraction let say 70% to a
fraction
Convert 70 % into decimal = 70/ 100 = 0.7
Write down the decimal “over” the number 1 = 0.7/1
Then multiply top and bottom by 10 = 0.7x 10 = 7/10
For each number after the decimal point 1 x 10
(10 for 1, 100 for 2)
Which will give = 7/10
7/10 it the fraction form
14) Explain what is Cubic Meter?
Cubic Meter is the standard unit used to measure the
volume of an object length by length. The unit is written in
m 3.
1 m 3 (Cubic Meter) = 1000 liters
15) Explain how much is a hectare and how much is square
millimetre?
1 hectare = 100 meters on each side , so a hectare has
100 m x 100 m = 10,000 m 2
A square millimetre is millimetres x millilitres; a
millimetre is a thousand part of a meter, so a square
millimetre is one millionth of a square meter
1 X 1 = 1 of a square meter
1000 1000 1,000, 000
16) If bus conductor issues 50 tickets in 30 minute how
many tickets can he be able to issues in 8 hrs.?
If bus conductor issues 50 tickets in 30 minutes, so the
number of ticket issues in 8 hr. will
(480 x50) / 30 = 800 tickets
So the conductor can issue 800 tickets during 8 hrs.
17) Explain what is Permutation?
An ordered arrangement of a group of object is known as
Permutation, for example, the permutation of arrangement
of 9 balls different in colours in 3 different rows can be
done in 9 P 3= 504 ways.
18) Explain what is a linear equation what is it used for?
To calculate or solve problems involving distance, speed
and time we used linear equation, it is also used to find
solutions that involve weight, mass and density. Linear
equation can be expressed as Ax +By+ Cz+…= D.
19) Give an example where you can use a linear equation in
your daily life?
For example, if you are the office is 20 miles from your
office, and you have reach 8 am, and you know that the
traffic is moving at 40 miles per hour.
To know what time you should leave from home, use this
equation
Time taken = distance/ rate of travel
t= 20/40 = ½ or half an hour. To reach the office at 8 a.m.,
you should leave home at 7: 30 am
20) Explain what is tangent?
A line that touches a curve at one point, without passing or
cutting across it is referred as tangent.
21) Explain what is a standard deviation?
Standard deviation is the measure of the spreadout of the
data about the mean value. It is referred as sigma and
represented as symbol σ.

Today question

1. An article is sold at 25% profit. If the CP and the SP
of the article are increased by Rs 60 and Rs 30
respectively, the profit% decreases by 15%. Find the
cost price of the article.
A) Rs 190
B) Rs 240
C) Rs 285
D) Rs 305
E) None of these

2. 5 kg of an article is bought at Rs 480, 1/3rd of it is
sold at a profit of 20%. At what loss% should the
remaining article be sold so that there is an overall
profit of 3 1/3%?
A) 8.5%
B) 7%
C) 6.5%
D) 6%
E) 8%

3. A shopkeeper bought an article at 20% discount on
the marked price, and he sold it at a profit of 40% on
the marked price. What is the actual profit% made by
the shopkeeper?
A) 55%
B) 45%
C) 75%
D) 72%
E) 66%