1. What is
Mathematics
for?

2. Kevin is two years older than his wife Angela. In 15 years, the sum of their ages will be
one more than thrice Kevin’s age now. What are their present ages?
A bank teller has some P50 bills and some P200 bills. The teller has five more P200 bills
than P50 bills. The total value of the money is P7250. Find the number of P50 bills.
A gardener has 26 kg of a mixture of a fertilizer and weed killer. If one kilo of the mixture is
replaced by weed killer the result is a mixture that is 5% weed killer.
What percent of the original mixture was weed killer?
A ladder is to be constructed with 16 rungs whose lengths decrease uniformly from 20
inches at the base to 16 inches at the top. Find the total length of material needed for
the rungs.
The angle of elevation from the ground to the top of a cliff is 320 at point A. Point B is
exactly 100 feet nearer the cliff, and the angle of elevation from that point is 420. Find
the height of the cliff.

3. Our future lawyers, clergy, and
statesmen are expected at the
University to learn a good deal about
curves, and angles, and number
and proportions; not because these
subjects have the smallest relation
to the needs of their lives, but
because in the very act of learn­
ing them they are likely to acquire
that habit of steadfast and accurate
thinking, which is indispensible in
all the pursuits of life.
• JD Fitch, 1906

4. Mathematics and natural philosophy
are so peculiarly engaging and
delightful as would induce every­
one to wish an acquaintance with
them. Besides this, the faculties
of the mind, like the members
of a body, are strengthened and
improved by exercise. Mathematical
reasoning and deductions are,
therefore, a fine preparation for
investigating the abstruse speculations
of the law.
• Thomas Jefferson

5. Mathematics is the study which
forms the foundation of the course
[at West Point]. This is necessary,
both to impart to the mind that
combined strength and versatility,
the peculiar vigor and rapidity of
comparison necessary for military
action, and to pave the way for
progress in the higher military
Sciences.
• Congressional Committee on Military
Affairs, 1834

6. Give 100 loaves to five men so
that the shares are in arithmetic
progression and the sum of the
two smallest is 1/7 of the three
greatest.
- a problem found in the Rhind
Papyrus, Egyptian textbook of
mathematics c. 1650 BC

7. Simplify:
1 1 1 1
2
 2 2
− 2
x y x y
−
1 1 1 1
2
− 2 2
 2
x y x y
 
8
 
2 2
x y x− y x y
  −2
x− y x y y
2
x
2

8. What mathematics education is for is
not for jobs. It is to teach the race to
reason. It does not, heaven knows,
always succeed, but it is the best
method that we have. It is not the only
road to the goal, but there is none
better. Furthermore, it is worth
teaching.
­ Underwood Dudley, American
Mathematics Society