1. SAMS Standardized Test Prep Day 2
Math: The Easy Stuff
SAMS Standardized Test Prep
Day 2

2. What’s in this presentation?
Overview of math test formats
A few basic “cheats”
Math skills inventory
Question categories and types
Sample questions

3. Comparison SAT Math ACT Math SAT Math Level 1 & 2
2 sections:
No calc use: 25 min, 20 questions
Calc use: 55 min, 38 questions
Multiple-choice (4 choices) and grid-ins
No wrong answer penalty
In order of difficulty per section
Covers:
Heart of Algebra
Problem Solving and Data Analysis
Passport to Advanced Math
Additional Topics in Math
1 section (60 min, 60 qs)
Multiple-choice (5 choices)
No wrong answer penalty
In order of difficulty
Covers:
Arithmetic
Algebra 1
Geometry
Algebra 2
Data Analysis
Trigonometry (4 problems)
1 section (60 min, 50 qs)
Multiple-choice (5 choices)
Wrong answer penalty
In order of difficulty
Covers:
Arithmetic
Algebra 1
Geometry
Algebra 2
Data Analysis
Trigonometry

4. Cheat 1: Make a target
When faced with difficult or abstract problems, use your math common sense in order to find an answer.
Pick a reasonable number and plug it in where appropriate.
You now have a “target answer” that you can use to find the right answer choice.
This is especially useful in problems with variables in the answer choices.
NOTE: If you get more than one right answer, start over with a new number!

5. Now try it on your own:

6. Cheat 2: Plug-n-chug
When you have numbers in the answer choices, it is sometimes easier to try each of them until you find the right answer.
Starting with choice C can help. If it’s right, you’re done. If it’s wrong, you can usually tell if you need to go up or down.
If a question ask for the greatest or least possible value, start with the greatest or least value given

7. Now try it on your own:

8. A few mini-cheats Let the answer choices be your guide:
Variables? Try making a target.
Numbers? Try plugging-n-chugging.
If you’re given answers in radical or rational notation, then work the problem in the same notation.
Watch for “hidden” information:
For example: if the problem says, “The ratio of men to women is 2 to 3,” then it has already told you that the total number of people must be a multiple of 5.
Another example: if the problem says, “A line passes through the origin and contains the point (2, 3),” then it has already given you the slope.

9. Math Skills Inventory Do these problems for homework.
Answer as many as you can without looking anything up!

11. What is the formula for percent change?
What is the average formula?

12. What is a median?
What is a mode?

13. Define each of the terms in:
y=mx+b
What is the midpoint formula?
What is the distance formula?
Describe each of these slopes:
How does a quadratic formula graph?
What is FOIL?

14. Describe each of these transformations:
What is the formula for finding the area of a parallelogram?
Describe the relationships of the lines and angles in this figure:
What is the formula for finding the area of a trapezoid?
Describe the relationship between the central angle of a circle and the corresponding arc length and sector area.
What is the triangle inequality theorem?
What is a Pythagorean triplet?
Give two examples.
What is the formula for finding the sum of the interior angles of a polygon?

15. What is the formula for finding a simple probability?
How do you find the probability of two independent events both occurring?
What is the formula for finding the nth term of an arithmetic sequence?
What is the formula for finding the nth term of an geometric sequence?
What is the formula for finding the permutation of r choices out of n items?
What is the formula for finding the combination of r choices out of n items?
What is a union of sets?
What is an intersection of sets?

16. Fill in the denominators:

17. How’d you do?

18. Heart of algebra
SAT Category

19. Heart of Algebra makes up 33% of the math section, which works out to 19 questions. 
There will be eight in section 3 (the non-calculator math test) and 11 in section 4 (the calculator math test).
What’s covered?

20. Create, solve, or interpret a linear expression or equation in one variable that represents a context.
Create, solve, or interpret linear inequalities in one variable that represent a context.
Build a linear function that models a linear relationship between two quantities.
Create, solve, and interpret systems of linear inequalities in two variables.
Create, solve, and interpret systems of two linear equations in two variables. 
Algebraically solve linear equations (or inequalities) in one variable.
Algebraically solve systems of two linear equations in two variables. 
Interpret the variables and constants in expressions for linear functions within the context presented. 
Understand connections between algebraic and graphical representations. 
What’s covered?

21. Passport to Advanced Math
SAT Category

22. Passport To Advanced Math makes up 27% of the math section, which works out to 16 questions. 
There will be nine in section 3 (the non-calculator math test) and seven in section 4 (the calculator math test).
What’s covered?

23. Create a quadratic or exponential function or equation that models a context.
Determine the most suitable form of an expression or equation to reveal a particular trait, given a context.
Create equivalent expressions involving rational exponents and radicals, including simplifying or rewriting in other forms.
Create an equivalent form of an algebraic expression by using structure and fluency with operations.
Solve a quadratic equation having rational coefficients.
Add, subtract, and multiply polynomial expressions and simplify the result
Solve an equation in one variable that contains radicals or contains the variable in the denominator of a fraction.
Solve a system of one linear equation and one quadratic equation.
Rewrite simple rational expressions. Students will add, subtract, multiply, or divide two rational expressions or divide two polynomial expressions and simplify the result.
What’s covered?

24. Interpret parts of nonlinear expressions in terms of their context
Interpret parts of nonlinear expressions in terms of their context. Students will make connections between a context and the nonlinear equation that models the context to identify or describe the real-life meaning of a constant term, a variable, or a feature of the given equation.
Understand the relationship between zeros and factors of polynomials, and use that knowledge to sketch graphs. Students will use properties of factorable polynomials to solve conceptual problems relating to zeros, such as determining whether an expression is a factor of a polynomial based on other information provided.
Understand a nonlinear relationship between two variables by making connections between their algebraic and graphical representations. The student will select a graph corresponding to a given nonlinear equation; interpret graphs in the context of solving systems of equations; select a nonlinear equation corresponding to a given graph; determine the equation of a curve given a verbal description of a graph; determine key features of the graph of a linear function from its equation; or determine the impact on a graph of a change in the defining equation.
Use function notation, and interpret statements using function notation. The student will use function notation to solve conceptual problems related to transformations and compositions of functions.
Use structure to isolate or identify a quantity of interest in an expression or isolate a quantity of interest in an equation. The student will rearrange an equation or formula to isolate a single variable or a quantity of interest.
What’s covered?

25. Problem Solving and data Analysis
SAT Category

26. What’s covered?: problem solving and data analysis
Problem Solving and Data Analysis makes up 29% of the math section, which works out to 17 questions. 
All 17 are in section 4 (the calculator math test).
What’s covered?: problem solving and data analysis

27. What’s covered?: problem solving and data analysis
Use ratios, rates, proportional relationships, and scale drawings to solve single- and multistep problems. 
Solve single- and multistep problems involving percentages. 
Solve single- and multistep problems involving measurement quantities, units, and unit conversion. 
Given a scatterplot, use linear, quadratic, or exponential models to describe how the variables are related. 
Use the relationship between two variables to investigate key features of the graph. 
Compare linear growth with exponential growth. 
Use two-way tables to summarize categorical data and relative frequencies, and calculate conditional probability. 
Make inferences about population parameters based on sample data. 
Use statistics to investigate measures of center of data and analyze shape, center, and spread. 
Evaluate reports to make inferences, justify conclusions, and determine appropriateness of data collection methods. 
What’s covered?: problem solving and data analysis

28. Additional Topics in Math
SAT Category

29. What’s covered?: problem solving and data analysis
Additional Topics in Math makes up 10% of the math section, which works out to 6 questions. 
There will be three in section 3 (the non-calculator math test) and three in section 4 (the calculator math test).
What’s covered?: problem solving and data analysis

30. What’s covered?: Additional Topics in Math
Solve problems using volume formulas. 
Use trigonometric ratios and the Pythagorean theorem 
Add, subtract, multiply, divide, and simplify complex numbers.
Convert between degrees and radians and use radians to determine arc lengths; use trigonometric functions of radian measure. 
Apply theorems about circles to find arc lengths, angle measures, chord lengths, and areas of sectors. 
Use concepts and theorems about congruence and similarity to solve problems about lines, angles, and triangles. 
Use the relationship between similarity, right triangles, and trigonometric ratios; use the relationship between sine and cosine of complementary angles. 
Create or use an equation in two variables to solve a problem about a circle in the coordinate plane. 
What’s covered?: Additional Topics in Math

31. What about the ACT and the Subject Test?
The subscore categories recently devised by the College Board for the SAT are not very useful to students.
Both the ACT and the SAT Math Subject Tests use more task-specific language.
There are, in addition, other “unofficial” categories that can help understand all of the tests better.

32. ACT Math Number and Quantity (7-10%) Algebra (12-15%)
Functions (12-15%)
Geometry (12-15%)
Stats and Probability (8-12%)
Integrating Essential Skills (40-43%)
Basically combinations of the above
Modeling (>25%)
i.e. Data Analysis with graphs

33. SAT Subject Test: Math 1 & 2

34. A more useful “unofficial” taxonomy (note: questions often combine categories)
Number Properties
Functions
Arithmetic and Algebra
Probability
Variable Manipulation
Stats
Coordinate Geometry
Trigonometry
Plane Geometry
Trig Functions
Solid Geometry
Logarithms
Systems of Equations
Complex Numbers
Systems of Inequalities
English-to-Math Translation
Problem Solving
Beyond the Numbers
Data Analysis

35. Example 1

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39. A B C D.
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44. Example 10

45. Hint: Round your answer to the nearest tenth
Example 11

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75. Example 41