Problems on Sec. 1- Sec. 4

1. Let set $ K=\{-12, -6, -9, -\sqrt{7},-\sqrt{4},0,\frac{1}{8},\frac{\pi}{4}, 6,\sqrt{11}\}$. List all elements of $ K$ that belong to each set

(a) Integers (b) Rational numbers

2. Write each algebraic identity (true statement) as a complete English sentence without using the names of the variables. For instance, $ z(x+y)=zx+zy$ can be stated as "The multiple of a sum is the sum of the multiples."

(a) $ a(b-c)=ab-ac$ (b) $ \frac{1}{xy}=\frac{1}{x}\cdot \frac{1}{y}$ (c) $ \vert st\vert=\vert s\vert\cdot \vert t\vert$

3. Identify by name each property illustrated.

(a) $ 8(5+9)=(5+9)8$ (b) $ 3\cdot (4\cdot 2)$ (c) $ (9+p)+0=9+p$

4. Simplify each expression.

(a) $ (-4-1)(-3-5)-2^3$ (b) $ \Big(-\frac{5}{9}-\frac{2}{3}\Big)-\frac{5}{6}$ (c) $ \frac{6(-4)-3^2(-2)^3}{-5[-2-(-6)]}$

5. Evaluate each expression if $ a=-1$, $ b=-2$, and $ c=4$.

(a) $ -c(2a-5b)$ (b) $ \frac{9a+2b}{a+b+c}$.

6. Write without absolute value bars.

(a) $ -\vert-6\vert+\vert 3\vert$ (b) $ \vert\sqrt{8}-8\vert$

7. Perform the indicated operations.

(a) $ (3q^3-9q^2+6)+(4q^3-8q+3)$ (b) $ (8y-7)(2y+7)$ (c) $ (3k-5m)^2$

8. Factor as completely as possible.

(a) $ 3(z-4)^2+9(z-4)^3$ (b) $ z^2-6zk-16k^2$ (c) $ 6m^2-13m-5$ (d) $ 169y^4-1$ (e) $ 15mp+9mq-10np-6nq$



Department of Mathematics
Last modified: 2005-08-30