Category Archives: Algebra 1

09.10.14
by

Algebra 1, 2 – systems of equations

Q: Red pens cost twice as much as blue pens. Two blue pens and three red pens cost a total of $2.32. How much does a blue pen cost?

 Answer:  $0.29

 Explanation:  Let r be the cost of a red pen, and let b be the cost of a blue pen. 

Then, r = 2b and 2b + 3r = 2.32. Solve this system of equations. 

By substitution,

r + 3r = 2.32

4r = 2.32

r = 0.58

Plug r= 0.58 into the first equation (or second, but I like the first better):

0.58 = 2b

0.29 = b

 You can also use other algebraic methods such as elimination, Cramer’s Rule, etc.  Or use my TI-84 Plus program CRAMER once you rearrange the system to say: 2b – r = 0 and 2b + 3r = 2.32.

 

Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

09.09.14
by

SAT, Algebra 1 – percent change

Q: Last year, Emmy was 40 inches tall.  This year, she is 42 inches tall.  By what percent has her height increased?

 Answer: 5%

 Explanation:  Percent change is calculated by the following formula:

 (New – Original)/Original  x 100%

 (42 – 40)/40 = 2/40 = .05

 .05 x 100% = 5%

 Since it is positive, this is a percent increase.

My TI-84 Plus program PRCNTCHG will calculate this, too.

 

Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

09.07.14
by

Algebra 2 – linear functions

Q:  f(x) is a linear function with a y-intercept of 6. If f(-2) = 9, what is f(2)?

Answer:   3

Click ‘Like’ if you got it right!

Explanation:

f(x) = mx + b              (because it is linear)

m is the slope of the line passing through (0,6) and (-2,9).

m = (9-6) / (-2-0)

m = – 3/2

b is the y-intercept.  b = 6.

So, f(x) = – 3/2 x + 6

Now, find f(2):

f(2) = (- 3/2)(2) + 6 = 3

Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

09.04.14
by

Algebra 1, 2 – solving quadratic equations

Q: The square of a positive number is equal to 5 more than the product of 4 and the same number. What is the number?

Answer: 5

Explanation:

2014-09-04_231259

Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

09.01.14
by

Algebra 1 – Find the equation of a line

Q:  Find the equation of the line that has the following intercepts:

x-intercept: 5,   y-intercept: -3

Answer:  y = 3/5 x – 3

Explanation:  The x-intercept is the point (5, 0).  The y-intercept is the point (0, -3).  Calculate the slope of the line passing through these points:

m= (0- -3)/(5 – 0) = 3/5

Using slope intercept form (y = mx + b), the equation is y = 3/5 x + b.  We just need to find b.  Or do we?  We could plug in an ordered pair and solve for b, but it’s not necessary.  We already have b, because in slope-intercept form, b always stands for the y-intercept.  So, b = -3.

The equation is: y = 3/5 x – 3

My TI-84 Plus program ‘LINES’ will find this equation for you, given the two intercepts.

Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

09.01.14
by

SAT / Algebra 1: Ratios

Q:  In my box of cereal, the ratio of flakes to raisins is 9:2. If there are a total of 220 flakes and raisins in the box, how many of these are flakes?
 
Answer:  180
Explanation:  Solve the equation: 9x + 2x = 220 to get x = 20.  ‘Flakes’ are the 9x part of the equation.  9(20) = 180.  Or, use my TI-84 Plus program ‘RATIO’.
Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

09.01.14
by

Algebra 1, 2 – functions

Q: Which of the following represents a function?  (Choose all correct answers.)
 
a. {(4,2), (6,2), (-1,5), (3,-2), (-4,-7)}
b. {(4,2), (5,1), (-1,5), (5,-2), (4,-2)}
c. {(-1,-1), (1,1), (4,4), (3,3), (6,6)}
d. {(1,2), (3,2), (5,2), (7,2), (9,2)}
 
Answer: a, c, and d
Explanation:  A function must have only one y-value for each x-value.  Choice b has two points with the same x:  (4,2) and (4, -2) (and also two others).  All of the other choices have no repeated values for x, so they are functions.
 
Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

08.25.14
by

SAT – systems of equations

Q: A phone call costs c cents for the first 10 minutes and n cents per minute for additional minutes. A 20-minute phone call costs 50 cents, and a 40-minute phone call costs 90 cents. What is the value of c?
 
Answer: 30
Explanation:  A 20-minute call costs c cents for the first 10 minutes and n cents per minute for each of the next 10 minutes.  So, c+10n=50.  A 40-minute call costs c cents for the first 10 minutes and n cents per minute for each of the next 30 minutes: c+30n=90.  Solve this system of equations.  Use my TI-84 Plus program CRAMER or an algebraic method such as substitution, elimination, Cramer’s Rule, etc.  c=30.
Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

08.11.14
by

Algebra 1, 2 – systems of equations

Q: 100 people are to be seated at 22 tables. Some tables seat 4 people and some seat 6 people. If no seats are empty, how many tables seating 4 people are there?
 
Answer: 16
Explanation:  Solve the system: x + y = 22; 4x + 6y = 100.  My ‘CRAMER’ program will solve this for you! The number of 4-person tables is the x-value of the solution.
Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

08.09.14
by

Algebra 1 – distance

Q: To the nearest tenth, what is the distance between the points (-6,2) and (6,5)?
 
Answer:  12.4 
(Use the distance formula, and round to the nearest tenth.)
My TI-84 Plus program DISTANCE will find this value.
Highly Effective Headline!
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.