UC Davis ; Math Placement Test Questions and Answers

UC Davis ; Math Placement Test
Questions and Answers

properties of exponents - correct Answer-- whole number exponents: b^n = b • b • b... (n
times)
- zero exponent: b^0 = 1; b ≠ 0
- negative exponents: b^-n = 1/(b^n); b ≠ 0
- rational exponents (nth root): ^n√(b) = 1/(b^n); n ≠ 0, and if n is even, then b ≥ 0
- rational exponents: ^n√(b^m) = ^n√(b)^m = (b^(1/n))^m = b^(m/n); n ≠ 0, and if n is
even, then b ≥ 0

operations with exponents - correct Answer-- multiplying like bases: b^n • b^m = b^(n +
m) (add exponents)
- dividing like bases: (b^n)/(b^m) = n^(n-m) (subtract exponents)
- exponent of exponent: (b^n)^m = b^(n • m) (multiply exponents)
- removing parenthesis:
> (ab)^n = a^n • b^n > (a/b)^n = (a^n)/(b^n)
- special conventions:
> -b^n = -(b^n); -b^n ≠ (-b)^n
> kb^n = k(b^n); kb^n ≠ (kb)^n
b^n^m = b^(n^m) ≠ ((b^n)^m)

log basics - correct Answer-- logb(1) = 0
- logb(b) = 1

inverse properties of logs - correct Answer-- logb(b^x) = x
- b^(logb (x)) = x

laws of logarithms - correct Answer-- logb(x) + logb(y) = logb ( x • y)
- logb(x) - logb(y) = logb(x/y)
- n • logb(x) = logb (x^n)

distributive law - correct Answer-ax + ay = a(x + y)

simple trinomial - correct Answer-x^2 + (a + b)x + (a • b) = (x + a)(a + b)

difference of squares - correct Answer-- x^2 - a^2 = (x - a)(x + a)
- x^4 - a^4 = (x^2 - a^2)(x^2 + a^2) = (x - a)(x + a)(x^2 + a^2)

sum or difference of cubes - correct Answer-- x^3 + a^3 = (x + a)(x^2 - ax + a^2)
- x^3 - a^3 = (x - a)(x^2 + ax + a^2)

, factoring by grouping - correct Answer-acx^3 + adx^2 +bcx + bd = ax^2(cx + d) + b(cx +
d) = (ax^2 + b)(cx + d)

quadratic formula - correct Answer-x = (-b ± √(b² - 4ac))/2a

adding fractions - correct Answer-find a common denominator ; a/b + c/d = a/b(d/d) +
c/d(b/b) = (ad + bc)/bd

subtracting fractions - correct Answer-find a common denominator ; a/b - c/d = a/b(d/d) -
c/d(b/b) = (ad - bc)/bd

multiplying fractions - correct Answer-(a/b)(c/d) = ac/bd

dividing fractions - correct Answer-- invert and multiply ; (a/b)/(c/d) = a/b • d/c = ad/bc

canceling fractions - correct Answer-- ab/ad = b/d
- (ab + ac)ad = (a(b + c))/ad = (b + c)/d

rationalizing fractions - correct Answer-- if the numerator or denominator is √a , multiply
by √a/√a
- if the numerator or denominator is √a - √b, multiply by (√a + √b)/(√a + √b)
- if the numerator or denominator is √a + √b, multiply by (√a - √b)/(√a - √b)

first degree equations - correct Answer-solved using addition, subtraction, multiplication,
and division

second degree equations - correct Answer-solved by factoring or the quadratic formula

absolute value - correct Answer-equivalent to two equations without the absolute value
sign
> e.g. |x + 3| = 7 → +(x + 3) = 7 or -(x + 3) = 7

solving linear inequalities - correct Answer-can be treated like a linear equation,
however, when multiplying or dividing both sides of an inequality by negative numbers
requires the inequality sign to be reversed

solving absolute value inequalities - correct Answer-- with absolute value inequalities,
you will always have two problems to solve
- solve everything outside the parenthesis before the inside after splitting the equation
> e.g. 2(x - 5) > 10 → x - 5 > 5 → x > 10

solving higher order inequalities - correct Answer-- cannot be solved in the same way as
higher order equalities; must be able to account for all possible combinations of
multiplying positive and negative terms
- use a number line to solve for these