Download MTA 001 Test #2 Sample Questions

MTA 001
Oct 25, 2011
Test #2 Sample Questions
The following questions are a guide to help you study for Test #2. This is not to be considered
the actual test.
Algebra:
Introduction to Equations
Equations (One equation with one unknown)
Translate into equivalent algebraic expressions, only if needed. Solve if specified.
1. What is the role of the variable, x, in the two following statements:
2. Use binomial multiplication to calculate
, without using a calculator. Show all your work.
3. Provide a counter-example that would disprove the following incorrect statement:
Is the equation above dimensionally correct?
4. In the formula
, what are the dimensions of A if M is [M],
is [ ],
is
, and W is
?
5. The sum of three consecutive integers is 366. Find the integers.
6. The sum of three consecutive odd integers is 281. Find the three integers, if possible.
7. The sum of four consecutive even integers is 636. Find the four integers.
8. A rectangle’s length is two times its width. If the perimeter of the rectangle is 168 cm, find the
length of the rectangle.
9. A rectangle’s length is 7 inches longer than its width. If the perimeter of the rectangle is 110
inches, find its length and width.
10. A right triangle has a height that is 4 times longer than its base. If the area of the triangle is 392
square metres, find the height of the triangle.
11. (n+1) + (n+2) + (n+3) = 10 + 2(n+1). Translate this equation into a word statement, and find the
value of n algebraically.
12. The mass of ¾ of a bag of cement is equivalent to half a bag of cement plus 20 kg. Find the
weight of the bag.
13. The sum of three consecutive even numbers is 7 more than two times the second number.
What are the three numbers?
14. A pole is standing in a small lake. If one-sixth of the length of the pole is in the sand at the
bottom of the lake, 25 ft are in the water, and two-thirds of the total length is in the air above
the water, what is the length of the pole? [Hint: let x be the total length of the pole]
15. Find an abstract algebraic expression for the following sequence of numbers:
(a) 1 + 2 + 3 + ... + N = _________ (i.e. sum of consecutive numbers)
(b) 1 + 3 + ... + (2N-1) = ________ (i.e. sum of consecutive odd numbers)
16. Calculate each value, and arrange from smallest to largest.
a.
b.
c.
d.
17. Expand and simplify. Leave your answer in positive exponents.
18. If both the radius and the height of a cylinder are doubled, by what factor will the volume of the
cylinder increase?
Volume of cylinder: V = πr2h
19. The dimensions of a rectangular solar panel are:
Length = (2x + 3) metres
Width = (x + 1) metres
(a)Write an algebraic expression for the area of the solar panel.
(b) What is the area of the solar panel if x= 2.2 metres (i.e. evaluate the area when x=2.2 m)
Algebra Study Guide #2
You are responsible for completing the assigned work in the following sections: A, B, C, and D.
For additional practice, I would encourage students to attempt questions in the following
sections:
Quick Test, Readiness Test, and some questions from past tests
NOTES:
GOOD LUCK!!