Practice Math Placement Exam
Part I Arithmetic
1. Evaluate: 16 × 32 × 53.
2. If 5 articles cost 75 cents, find the cost of 6 articles.
3. Find the quotient and remainder when 133 is divided by 85.
4. Find the sum of two-fifths and one-tenth.
5. Find the product : 
.
6. Find the difference between one-fourth and one-sixth.
7. 10% of what number is 5?
8. Find the quotient when 0.24 is divided by 0.8.
9. Evaluate 53 × 62
10. .0716 × 48.2
11. Give the prime factorization of 180 in exponential form.
12. Convert 3.3% to a decimal.
13. Change 2.03 to a percent.
14. Change 18% to a fraction in lowest terms.
15. Compute the area of the circle with diameter 6 ft. to the nearest tenth. ( use 3.14 for pi )
Part II Elementary Algebra I
1. Evaluate the following: - 5 + 4 - 3 - 6 + 9 - 3
2. If a = -2 and b = 4, 3a2 - 5b + 6ab2 = ________ .
3. Write an expression for 4 less than twice a number n.
4. Solve for w: 3w - 10 = 4w + 5.
5. Solve for t: 4 - t > t.
6. John can jog 4 miles in 56 minutes. At the same pace how far could he jog in 84 minutes?
7. Solve for x: 
8. Factor completely: 4x - 8x2.
9. Factor completely: x2 - 2x - 15.
10. Factor completely: 3r2 - 3.
11. Solve for x: x2 + 3x = 10.
12. Multiply: ( x + 5 )( x - 7 ).
13. Combine and simplify: 3x2 - 2x - ( x2 - 5x ).
14. Simplify: 
15. Simplify: ( x2yz3)2.
Part III Elementary Algebra II
1. Factor completely: 6x2 - 7x - 3
2. Simplify: 
.
3. Solve the following for W: P = 2L + 2W
4. Divide and simplify: 
.
5. Find the slope of the line containing the points ( -1, 3 ) and ( 2, 4 ).
6. Remove negative exponents and combine: x-2 + y-1.
7. Find the y - intercept of the line y + 2x - 1 = 0.
8. The difference between two numbers is 3. If four times the smaller is divided by the larger, the quotient is 5. Find the numbers.
9. Solve the system: x + 3y = 13 and 2x - y = -2.
10. Find the equation of the line parallel to y = 8 containing the point ( -2, 4 ).
11. Solve for x: 
12. Simplify : 
.
13. Find the vertex to the parabola defined by y = x2 - 6.
14. Put in standard form. Find b. x2 - 9 = 4x.
15. Solve for x: x2 - 4x + 2 = 0.
Part IV Intermediate Algebra and Trigonometry
For Problems 1 - 4 use the triangle below with C = 90o, a = 5 cm and b = 12 cm.
1. Find c.
2. Find sin( A ).
3. Find tan( B ).
4. Find cos( C ).
5. If sin( x ) = -.5 and x is in the third quadrant, find x.
6. If tan( x ) = 1 and x is in the second quadrant, find x.
7. Simplify and reduce to lowest terms 
.
8. The expression in #7 is not defined for which values of x?
9. Factor completely: 2x3 + 16.
10. Find the remainder when x2 + 6x + 3 is divided by x - 1.
11. Given y = x2 + 3x - 4, find the x-intercepts.
12. If f( x ) = 4x - 1, find f( 2x ).
13. If g(x) = x2 - x find g(x + h) - g (x).
14. In which quadrants does the solution to x + y > 6 lie?
15. How many quarts of 30% salt solution should be added to 20 quarts of 50% salt solution in order to produce a 38% salt solution?
Part V Intermediate Algebra and Trigonometry II
1. Find the amplitude of the graph of y = 3 sin( 2x ).
2. Find the period of the above function.
3. Without using tables evaluate: log2 4 - 2log3 27 + log2 1.
4. Find the domain of the function y = log10x.
5.Solve for x: log10 (x - 3) + log10 x = 1.
6. Perform the indicated operations and simplify to the form a + bi: ( 1 + 3i )2.
7. Find the conjugate to 1 + 3i.
8. Identify the following conic section: x2 - 4y2 = 4 .
9. Find the domain to the function f(x) = 2 - x2.
10. Find the range of the above function.
11. Find the inverse function to y = 3x + 4.
12. Evaluate f( f-1( x ) ).
13. Find the sum of the first 20 terms of 126, 117, 108, ...
14. Find the sum of an infinite number of terms 9, 3, 1, ...
15. Find the second term of (2x - 5)5 using the Binomial Theorem.
Answers
Part I
1. 27136 2. 90¢ 3. 1 r 48 4. 1/2 5. 2 6. 1/12 7. 50 8. 0.3 9. 4500 10. 3.45112 11. 22 32 5 12. 0.033 13. 203% 14. 9/50 15. 28.3 ft.
Part II
1. -4 2. -200 3. 2n - 4 4. -15 5. t < 2 6. 6 miles 7. 2 8. 4x( 1 - 2x ) 9. ( x - 5 )( x + 3 ) 10. 3( r + 1 )( r - 1 ) 11. -5, 2 12. x2 - 2x - 35 13. 2x2 + 3x 14. b/a 15. x4y2z6
Part III
1. ( 3x + 1 )( 2x - 3 ) 2. ( x + 2 )/( x - 4 ) 3. W = ( P - 2L )/2 4. ( x + 1 )( x + 4 )/(( x - 4 )( x + 5 )) 5. 1/3 6. ( y + x2 )/( x2y ) 7. ( 0, 1 ) 8. -12, -15 9. ( 1, 4 ) 10. y = 4 11. 33 12. 
13. ( 0, -6 ) 14. -4 15.
Part IV
1. 13 cm 2. 5/13 3. 12/5 4. 0 5. 210o 6. 135o 7. x2 + 1 8. ±1 9. 2( x + 2 )( x2 - 2x + 4 ) 10. 10 11. ( -4, 0 ) and ( 1, 0 ) 12. 8x - 1 13. 2xh + h2 - h 14. I, II and IV 15. 30 qts.
Part V
1. 3 2. pi rad. or 180o 3. -4 4. x > 0 5. 5 6. -8 + 6i 7. 1 - 3i 8. hyperbola 9. all reals 10. y < 2 or y = 2 11. ( x - 4 )/3 12. x 13. 810 14. 27/2 15. -400x4