1. The Kaplan Method for Math & Linear Equations
PSAT: Heart of Algebra

2. The Kaplan Method for Math
Have a method to approach all questions…
Read the question, identifying and organizing important information as you go.
Choose the best strategy to answer the question.
Check that you answered the right question.

3. 1.
Read the question, identifying & organizing important information as you go.
What information am I given?
Separate the question from the context.
How are the answer choices different?
Should I label or draw a diagram?

4. 2. Choose the best strategy to answer the question. Look for patterns.
Pick numbers or use straightforward math.

5. 3. Check that you answered the right question.
Review the question stem.
Check units of measurement.
Double-check your work.

6. Linear Equations Common elements on the PSAT
Model relationships and changes Ex: time, temperature, population
Graphs

7. Example #1
Which value of x satisfies the equation?
-61
-55
-42
-35

8. Example #2
Which value of x satisfies the equation?
5/2
7/2
9/2
11/2

9. Example #3 Which approximate value of x satisfies the equation? 4.29
4.65
6.6
6.8

10. Linear Word Problems + - x ÷ =
x, n, etc.

11. C = 3 2* J Linear Word Problems
Define any variables, choosing letters that make sense
Break sentences into short phrases
Translate each phrase into a mathematical expression
Put the expressions together to form an equation
Ex. Colin’s age is three less than twice Jim’s age. C = 3 2* J
subtract
switch the order

12. Example #4
The number k can be determined in the following way: Multiply m by 2, add 3n to the result, and subtract (4m – 5n) from this sum. What is the value of k in terms of m and n?
-2m – 3n
-2m + 2n
-2m + 8n
6m – 2n

13. Linear Graphs Slope from two points Slope-Intercept Form
Point-Slope Form

14. Example #5
Which of the following answer choices shows the graph of the line ?

15. Example #6
Jacques Charles was a French scientist who discovered the relationship between the temperature and volume of a gas. Specifically, Charles found that gases expand when heated. This relationship was formalized in Charles’s Law, which illustrates a linear relationship between temperature and volume in gasses. The graph here shows the volume of a sample of gas as it is cooled. If T is the temperature of the gas and V is the volume, which of the following gives a line that, when plotted, could produce the graph shown?
V = T + 100
V = T
V = T + 1
V = T – 0.25

16. Example #7 Before: m = -1, After: m = 0 Before: m = 1, After: m = - ½
A university admissions department compiled data that ere collected on students over a 25-year period. The department was particularly interested in how many students admitted in a given year graduated four years later with a degree. It noted that the number of students admitted showed a regular and consistent increase over the 25-year period. These data are plotted in the graph shown. Halfway through the data collection period, the general college enacted a policy that would allow students to take a year-long break during their studies. The college wants to model the relationship between the number of students admitted and the number of degrees attained in four years with a line of best fit before and after the policy change. Which of the following describes the best estimate for m, the slope of this line, before the change and after the change?
Before: m = -1, After: m = 0
Before: m = 1, After: m = - ½
Before: m = -1, After: m = ¾
Before: m = ¾, After: m = 0

17. Example #8
Ms. Walser’s class had 18 students. She used three equally weighted tests to determine their final grades. The class average for the first test was 92, and the class average for the second test was 77. If the overall class average was 84, what was the average score for the third test?
74.3 77 83
84.3

18. Example #9
A box of candies contains only chocolates, licorice sticks, peppermints, and gummy bears. If ¼ of the candies are chocolates, 1/6 of the candies are gummy bears, 1/3 are peppermints, and 9 are licorice sticks, what is the product of the number of peppermints and the number of chocolates? 12 36 72
108

19. Example #10
Ibrahim has a contract for a cell phone plan that includes the following rates: The plan has a fixed cost of $50 a month, a data plan that provides 2 GB of data for free and $8 for each GB of data after that, and a text message plan that costs $0.10 per text message sent. Which of the following equations represents the amount of money in dollars that Ibrahim will spend as long as he uses at least 2 GB of data? (Assume d= dollars, g= number of GB of data used, and t= number of text messages sent.)

20. Example #11
If 3 (n – 2) = 6, then what does equal?

21. Example #12
A certain gym sells two membership packages. The first package, the die-hard package, cost $250 for 6 months of unlimited use. The second package, the personal package, costs $130 initially plus $4 each day the member visits. How many visits would a person need to use for each package to cost the same amount over a 6-month period? 2 30 96
120