Arithmetic:

You must be able to do addition, subtraction, multiplication, and division without a calculator, particularly if the products are integers. You must be able to express any rational number as a fraction with the lowest common denominator. You must know how to move from decimal notation to fractions, and express a decimal in percentage terms. When dividing one number into another, you must be able to keep track of the correct decimal places. You must know how to calculate a simple growth rate and express it as a percentage of the base.

You must be able to use symbolic notation, and know the difference between constants and variables. Know that endogenous (or dependent) variables depend on other variables, and if a variable is not endogenous it is exogenous (or independent). An endogenous variable is a function of other variables if there is only one possible solution for a given set of variables; if there is more than one possible solution, then it is only a relationship, not a function. You must be able to solve for a single equation through rearrangement. For example: if a/b=c+(d/e), then e=d/((a/b)-c). A linear equation has a constant slope. If there are n unique linear equations that are not parallel, and n variables, then the system is fully identified and there is only one solution. You must be able to solve identified systems of equations through substitution. For example: if X=a+bY and Y=c-dX, then X=(a+bc)/(1+bd) and Y=(c-ad)/(1+bd). Finally, you should be able to solve equations with exponents in them (at least in symbolic equation form).

A linear surface is a point along one dimension, a line along two dimensions, a plane along three dimensions, and a hyperplane along more. Any two-dimensional equation, linear or otherwise, can be drawn as a geometric figure. For a line, you must know how to calculate a slope, and how to express it in slope-intercept form (if Y=a+bX, then a is the Y-intercept and b is the slope Y/X; since X=Y/b-(a/b), -a/b is the X-intercept and X/Y=1/b). Unique parallel lines never cross, and perpendicular ones cross at 90 to each other. Any two unique lines in two dimensions that are not parallel must cross at only one point.

If your answers are not clearly marked or exactly right, they are wrong. There is no partial credit. Use a piece of scratch paper if necessary. 15 questions, 20 minutes.

1. What is the sum of these numbers? 17.305, 4, 98.7, 12.01

2. Rank these numbers or fractions in ascending order: 100%, 1/3, 2/5, .25, 7/20, 4/3

3. If national income in Canada is $500 billion, and Consumption Spending accounts for 60%, how much is Consumption Spending?

4. If national income in Canada is $500 billion, and their population is 25 million people, what is the amount of national income per person?

5. If Canadian national income grew from $500 billion to $525 billion, what is the amount of growth as a percent of $500 billion?

6. If Canadian national income is $500 billion (in U.S. Dollars), and the U.S. Dollar is worth $1.20 in Canadian Dollars, what is Canadian national income in Canadian Dollars?

7. If a/b = c/d, then rearrange to solve for d.

8. In fractions, what is 5/4 times 2/3?

9. In fractions, what is 5/4 minus 2/3?

10. In fractions, what is 5/4 divided by 2/3?

11. What is the slope of a 45-degree ray from the origin?

12. What is the slope Y/X of the equation Y=10+9X?

13. Solve for X and Y at the intersection of Y=10+9X and Y=100-9X.

14. Graph the equations Y=10+9X and Y=100-9X for positive values of X and Y, clearly labeling the X and Y axes, their intercepts, and the intersection.

15. If a test has 15 questions and you must answer 80% of them correctly to pass, how many questions can you miss without failing?

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