Revision question for quiz

1. a.) For a given spring, F has the value 35 when the spring has stretched 8 inches. What is the constant of proportionality for that spring?
b) What is the value of F when the spring has stretched 11 inches?

2. The distance d that an automobile travels varies directly as the time ta) that it travels. After 2 hours, the car has traveled 115 miles.
b) Write the equation that relates d and t.b) The units on the right must be same as those of d on the left, that is, a) distance. What are the units, then, of 57.5?c) How far has the car traveled after 7 hours?

3. In a microwave receiver circuit, the resistance R of a wire 1m long is given by R = k/d2, where d is the diameter of the wire. Find R if k = 0.000 000 021 96 Ω m2 and d = 0.000 079 98m.

4. A computer can do an addition in 7.5 x 10^-15 s. How long does it take to perform 5.6 x 10^6 additions?

5. Show by first principle that the differential of y = 4x^2 -3x is 8x.

6. Water leaked into a gasoline storage tank at an oil refinery. Finding the pressure in the tank leads to the expression -4(b – c) – 3(a – b). Simplify this expression.

7. A shipment contain x film cartridges for 15 exposures each and x + 10 cartridges for 25 exposures each. What is the total number of photographs that can be taken with the film from the shipment?

8. In determining the size of a V belt to be used with an engine, the expression 3D – (D – d) is used. Simplify this expression.

9. When finding the current in a transistor circuit, the expression i1 – (2 – 3 i2) + i2 is used. Simplify this expression.

10. Each of two stores has 2n + 1 mouse pads costing $3 each and n – 2 mouse pads costing $2 each. How much more is the total value of the $3 mouse pads than te $2 mouse pads in the two stores?

11. In designing a certain machine part, it is necessary to perform the following simplification
16(8 – x) – 2(8x – x^2) – (64 – 16x + x^2)
What will be result be?

12. When analyzing the potential energy associated with gravitational forces, the expression
(GMm[(R + r) – (R – r)]) /2rR
arises. Preform the indicated division.

13. In the optical theory dealing with lasers, the following expression arises:
(8A^5 + 4A^3µ^4E^4)/8A^4
Perform the indicated division.

14. In finding the total resistance of the resistors, the expression
(6R1 + 6R2 + R1R2)/ 6R1R2
is used. Perform the indicated division.

15. The ratio of electric current I (in A) to the voltage V across a resistor is constant. If I = 1.52A for V= 60.0V, find I for V = 82.0V.

16.In order to find the distance such that weights are balanced on a lever, the equation
210(3x) = 55.3x + 38.5(8.25 – 3x)
must be solved. Find x.

17. In the study of the forces on a certain beam, the equation
W = L(wL + 2P)/8
is used. Solve for P.

18. A medical researcher finds that a given sample of an experimental drug can be divided into 4 more slides with 5mg each than with 6mg each. How many slides with 5mg each can be made up?

Variation

When a varies directly as b, we often say, "a is proportional to b." In that case, the relationship between a and b takes this algebraic form:
a = kb.
k is called the constant of proportionality.
The circumference of a circle, for example, varies directly as the diameter. The constant of proportionality is called π.
C = πD.

Example
a.) For a given spring, F has the value 35 when the spring has stretched 8 inches. What is the constant of proportionality for that spring?
b) What is the value of F when the spring has stretched 11 inches?

a) The distance d that an automobile travels varies directly as the time ta) that it travels. After 2 hours, the car has traveled 115 miles. Writea) the equation that relates d and t.
b) The units on the right must be same as those of d on the left, that is, a) distance. What are the units, then, of 57.5?
c) How far has the car traveled after 7 hours?

3.) If the side of a square doubles, how will the perimeter change?

4) a varies as the square of b. When b = 7, a = 4. What is the value of a when b = 35?
a varies as the square of b. When b = 20, a = 32. What is the value of a when b = 15?

5) The area A of a circle varies directly as the area of the circumscribed square. That is, as the area of the square changes, the area
of the circle changes proportionally.
a) Show that this implies that the area A of the circle varies as the square of the radius r.
b) If the radius of a circle changes from 6 cm to 12 cm, how will the area change?
c) What is the constant of proportionality that relates the area A to r²?

Simultaneous Equations

Why is 2 variables connected?
Why is 2 equations with the same 2 variables required to solve for the variables?

1. 1000 tickets were sold. Adult tickets cost $8.50, children's cost $4.50, and a total of $7300 was collected. How many tickets of each kind were sold?
2. Mrs. B. invested $30,000; part at 5%, and part at 8%. The total interest on the investment was $2,100. How much did she invest at each rate?
3. Samantha has 30 coins, quarters and dimes, which total $5.70. How many of each does she have?
4. "36 gallons of a 25% alcohol solution"
   means: 25%, or one quarter, of the solution is pure alcohol.
   One quarter of 36 is 9. That solution contains 9 gallons of pure alcohol.
   Here is the problem:
   How many gallons of 30% alcohol solution and how many of 60% alcohol solution must be mixed to produce 18 gallons of 50% solution?
   "18 gallons of 50% solution" means: 50%, or half, is pure alcohol. The final solution, then, will have 9 gallons of pure alcohol.
5. A saline solution is 20% salt. How much water must you add to how much saline solution, in order to dilute it to 8 gallons of 15% solution?
6. It takes 3 hours for a boat to travel 27 miles upstream. The same boat can travel 30 miles downstream in 2 hours. Find the speeds of the boat and the current.
7. A total of 925 tickets were sold for $5,925. If adult tickets cost $7.50, and children's tickets cost $3.00, how many tickets of each kind were sold?
8. Mr. B. has $20,000 to invest. He invests part at 6%, the rest at 7%, and he earns $1,280 interest. How much did he invest at each rate?
9. How many gallons of 20% alcohol solution and how many of 50% alcohol solution must be mixed to produce 9 gallons of 30% alcohol solution?
10. 15 gallons of 16% disenfectant solution is to be made from 20% and 14% solutions. How much of those solutions should be used?
11. It takes a boat 2 hours to travel 24 miles downstream and 3 hours to travel 18 miles upstream. What is the speed of the boat in still water, and how fast is the current?
12. An airplane covers a distance of 1500 miles in 3 hours
    when it flies with the wind, and in 3 1/3 hours when it flies against the wind. What is the speed of the plane in still air?

Exponent teaser

1. Solve for x and y

2^(x - 1) * 3(y + 1) = 72 * 6^(y - x + 2)

3^(x - 1) * 2^(y + 1) = 3 * 6^(x - y - 2)

2. Find the error in this proof. Prove: 5 = 7

Let a = b

Multiply both sides by a and add a^2 - 2ab to both sides:

2a^2 - 2ab = a^2 - ab

Take 2 as a common factor:

2(a^2 - ab) = a^2 - ab

Divide by a^2 - ab:

2 = 1

Multiply by 2:

4 = 2

Add 3 to both sides:

7 = 5

3. A rectangle with sides of lengths x and y has perimeter P. Prove that the largest area of this rectangle is given when the rectangle is a square.

4. Two pipes fill a swimming pool in 11 1/9 hours (eleven hours and one ninth of an hour) together. One pipe can fill the pool in 5 hours less than the other pipe. Find out how much times it takes each pipe to fill up the swimming pool separately.

5. A pharmacist has two iodine solutions: one with a concentration of 30% and one with a concentration of 80%. How much of each solution the pharmacist needs to create 8 liters of a 50% solution?

6. Mary needs to refuel her car with 60 liters of gasoline and get back home. She has two choices: drive to a gas station 20 km away from her house which charges $1.16/liter or drive to a gas station adjacent to her house which charges $1.24/liter. Mary's car's mileage is 10 km/liter. Which is cheaper for Mary?

7. A brother and a sister are mowing the lawn on their backyard. It takes the brother 15 minutes longer to mow the lawn than it takes his sister. Together they mow the lawn in 56 minutes. How long does it take each of them to mow the lawn?

8. and say that is equal to

Exponent

What is an exponent?
What is a power?
Why is a power used?
Every topics must consider the 4 basic operations, what are these?
Evaluate and explain your approach for the following: (^ means power)

1. 5^0
2. 3^2 x 3^5
3. 8^0
4. b^1
5. k^0
6. m^5 x m^8
7. 4^7 x 2^6
8. 5^11 + 5^4

A world of no fractions

What is a fraction?
Is fraction necessary?
How will the world be without fractions?
Do you use fractions in your everyday routine?
What are the 4 basic operators?
Are these true or false? Explain.

1. 3/(7x) + 2/(7x) = 5 /(14x)
2. 3/(7x) + 2/(7x) = 5 /(7x)
3. 4/(9) = 4 x 1/9
4.

Equation

What is an equation?
What is a term?
What are connectors in an equation?
What is an expression?
Which can be solve and why an equation or an expression or both?
Can all equations be solved? Explain.
Give examples of life scenario and then someone formulate the equation or expression for it.

Curve

What is a curve?
What is a line?
How is a line different from a curve?
Give examples of something that has constant change in life?
Give examples of something that has varying changes in life?
Why and How are graphs connected to equations?
In a graph what is the most important things to observe?

Trigs

What is trigs about?
Why is trigs important to life?
Give examples of trigs used in life?
What is the difference between 3D trigs and 2D trigs?
Which trigs do you enjoy or used more 2D or 3D?
Give examples of how you use 3D trigs?