On the actual examination an answer sheet is provided.

Use of a calculator is permitted and recommended on the entrance examination.

The actual examination is in a multiple choice format, forty questions in length, ten in each section. The practice test problems are set at an equivalent or slightly higher level of difficulty than the actual test questions but test the same material. No warranty or guarantee of topic coverage or warranty of any other kind is implied by the publishing of this practice test. Material on the actual entrance examination can and will differ.

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Part I

1. Find the perimeter of this figure. Dimensions are in centimeters. The right side is a semicircle.
   
2. Find seventy three percent of five hundred.
3. Find the tax on a $24.00 purchase when the tax rate is 7.5%
4. Write 1.74 × 10^-3 in decimal notation
5. Find the volume of a cube with edges 7 centimeters in length.
6. Find the area of a circle that has a diameter of 60 meters. Use 3.14 for π pi
7. Calculate (-1)×(3) + (-5)×(-7) + (30)÷(-3)
   
8. Find 0.35 - 1.007
9. Put the following fractions in order from smallest to largest: $\frac{7}{11}\text{,}\frac{7}{12}\text{,}\frac{14}{23}$
10. Convert 0.875 to a fractional form.

Part II

11. Evaluate 5x - 8y + -6z if x = -2, y = 3and z = -1.
12. Solve 5.1x - 3.4 = 17
13. Solve 42x - 29 = 39x + 17
14. A canoe sails 10 km North from Oroluk, turns right and sails 5 kilometers to the East, turn right again and sails 10 kilometers South. How far from Oroluk is the canoe?
15. If a number can be expressed as the quotient of two integers, could the number also be irrational?
16. If the cost of sixteen bars of Ivory™ soap at Five Star store is $8.00, then how much would a dozen bars cost at the same price per bar?
17. Which of the following is a prime number? 141, 143, 145, 147, 149
18. 76 is what percentage of 67?
19. Find the area of the figure shown with bases of 7 cm and 9 cm and a height of 7 cm:
    
20. Find the area of a rectangle with a width 10 cm longer than the length and an area of 75 cm³

Part III

21. Find the cube root of $\frac{512x^6{y}^6}{64}$
22. Factor out the common factor: 16x⁴ - 4x² + 2x
23. Factor x² - 169
24. Multiply the following: 4x(8x³ + 24)
25. Determine the slope intercept form for a line through (3, 5) and (-4, -2).
26. Solve the following system of two equations:
    

      -x + 3y = 7
       x + 5y = 17

27. What feature of an equation makes an equation a quadratic equation as opposed to a linear or cubic equation?
28. Solve for x: x² - 20x + 51 = 0
29. Solve for x by completing the square: x² + 6x + 1 = 17
30. Solve for x using the quadratic formula: x² - 10x - 15 = 0

Part IV

31. What is the domain of $f\left(x\right)=\sqrt{5-\mathrm{x}}\text{?}$
32. Find the inverse function $f^{-1}\left(x\right)$ for $f\left(x\right)=\frac{11x}{13}-143$
33. Does the following table represent a linear function?

    x	y
    0	-15
    1	0
    2	3
    3	0
    4	-3
    5	0
    6	15

34. Factor x² - 36x + 323
35. Solve x² - 36x + 323 = 0
36. Which graph shown below represents y = x² - 36x + 323?
    
37. Does the following set of ordered pairs represent a function?
    { (9, 3) (9, -3) (16, 4) (16, -4) (36, 6) (36, -6) }
38. Graph w = | x - 4 |
39. Using the vertical line test, is the equation x² + y² = 1 a function?
40. What what are asymptotes for $f\left(x\right)=\frac{3x+2}{x^2-49}\text{?}$