# Sample math placement questions

## Part A: Elementary Algebra and Logical Reasoning (Click Here for Answers)

**2. For which value of k is the expression 2k + 5 a prime number?**

**5. Simplify the expression ab(a^{2}ba^{4}b)^{5}.**

**7. What is the slope of the straight line 3 x – 9y = 44 ?**

(a) 3 | (b) 9 | (c) 1/3 | (d) 1/9 | (e) 44 |

Answers: 1(B),2(B),3(A),4(E),5(B),6(C),7(C)

## Part B: Intermediate Algebra (Click Here for Answers)

**1. The points (***x*,*y*) represented in the table below lie on a straight line. The point (25,*t*) lies on the same line. What is the value of *t* ?

*x*,

*y*) represented in the table below lie on a straight line. The point (25,

*t*) lies on the same line. What is the value of

*t*?

ANSWERS: 1(D),2(B),3(B),4(A),5(E),6(E),7(C)

## Part C: Advanced Algebra (Click Here for Answers)

**1. What is the sum of the five roots of the equation x^{5} – 4x^{3} + 5x – 11 = 0 ?**

(a) 4 | (b) -4 | (c) 5 | (d) -5 | (e) 0 |

**2. Find the remainder when the polynomial x^{5} – 2x^{4} + 3x^{3} – 2x + 4 is divided by x – 1.**

(a) 0 | (b) 1 | (c) 2 | (d) 3 | (e) 4 |

**3. Which of the following is a vertical asymptote of the following rational function? y=3(x-1)(x-2) ^{4}/((2x-3)(x+4)).**

(a) x = -4 | (b) x = -3/2 | (c) x = 1 | (d) x = 2 | (e) x = 3 |

**4. If g(x) = 1/x, what is the value of the expression g(x + h) – g(x) ?**

(a) h/(x(x+h)) | (b) -h/(x(x+h)) | (c) 2h/(x(x+h)) | (d) -2h/(x(x+h)) | (e) 1/h |

**5. Simplify the following exponential expression. 3^(2log_3 5).**

(a) 10 | (b) 6 | (c) 9 log_{3} 5 | (d) 25 | (e) log_{3} 25 |

**6. Solve for x in the following equation. (1/3)^x=(81)(9^(x-1)).**

(a) x = 2/3 | (b) x = 3/2 | (c) x = -2/3 | (d) x = -3/2 | (e) x = 8/9 |

**7. Consider the equation x^{4} + ax^{3} + bx^{2} + cx + d = 0, where a, b, c, and d are integers. If three of the roots of this equation are 3 – i, 3 + i, and 5 – 2i, then the fourth root must be what value?**

(a) 11 – 2i | (b) 5 + 2i | (c) -5 + 2i | (d) -5 – 2i | (e) cannot be determined |

ANSWERS: 1(E), 2(E),3(A),4(B),5(D),6(C),7(B)

## Part D: Precalculus (Click Here for Answers)

**1. What is the limiting behavior of the following function as x increases without bound?**

**y=(x+1)^3 (2x+5)^2 / (x-5)^5.**

(a) y tends toward 0 | (b) y tends toward 1 | (c) y tends toward 4 | (d) y increases without bound | (e) y tends toward 2 |

**2. The surface area of a sphere varies directly as the square of its radius. If the radius of a sphere is tripled, then the surface area of the sphere increases by what percentage?**

(a) 800% | (b) 100% | (c) 2,700% | (d) 2,600% | (e) 400% |

**3. According to one model of population growth, the world’s population, P, in billions, t years after 1990, can be modeled by the function**

**P(t)=40/(1+11 exp(-0.08 t))**

**Using this model, one would expect the world’s population in the year 3000 to reach how many billion people?**

(a) 40 | (b) 20 | (c) 3.3 | (d) 55 | (e) 47.4 |

**4. Simplify the following complex number by writing it in the form a + bi where a and b are real numbers.**

**100/(3-4i)**

(a) 30 + 40i | (b) 30 – 40i | (c) 300 + 400i | (d) 12 + 16i | (e) 12 – 16i |

**5. What is the behavior of the following function as x increases without bound? y=x^100 /exp(x).**

(a) y tends toward 0 | (b) y tends toward 1 | (c) y tends toward 100 | (d) y increases without bound | (e) y oscillates between 0 and 100 |

**6. What is the period of the function y = 4 + 5 sin(4t + 3) ?**

(a) 4 | (b) | (c) | (d) | (e) |

**7. Find a closed form expression for the following (finite) sum.**

**3/5 + 3/25 + 3/125 + 3/625 + ... + 3/(5^10).**

(a) 3/4 | (b) (3/4)(1 – 1/5^{10}) | (c) (3/4)(1 – 1/5^{11}) | (d) (4/5)(1 – 1/5^{10}) | (e) (4/5)(1 – 1/5^{11}) |