January Review - Honors

Exponents

100

Simplify: (6x^-2y³z⁴)^-2

What is x⁴ / 36y⁶z⁸ ?

200

Simplify: (2x³y⁴z⁷)(-4x^-1y³z⁶)

What is -8x²y⁷z¹³ ?

300

Simplify: (3x^-2y³z⁸ / 6x^-9y²z^-4)⁰

What is 1?

400

Simplify: (3x^-2y³z⁵ / 9xy^-6z⁴)⁵

What is (y⁴⁵z⁵/ 243x¹⁵) ?

500

Simplify: (2x⁷yz^-2)³ (2x³y²z^-1 / xy³z⁴)^-4

What is (x¹³y⁷z¹⁴ / 2) ?

Dividing Polynomials

100

Simplify: (-4x^-2y³z⁴+6x³y^-4z) / 3x⁵y²z

What is (-4yz³ / 3x⁷)+(2 / x²y⁶) ?

200

Simplify: (4x³yz⁷ - 5xy⁷z² + 10x⁴y⁷z¹¹) / 2x³y²z⁶

What is 2z/y - 5y⁵/2x²z⁴ +5xy⁵z⁵ ?

300

Divide: (2x²+5x+8) / (2x+1)

Write the answer with the quotient and the remainder.

What is x + 2 + 6/2x+1 ?

400

Divide: (3x³+8x²+7x-4) / (3x+2)

What is x²+2x+1 -6/3x+2 ?

500

Divide: 4x⁴+7x²-4x-20 / 2x-3

What is 2x³+3x²+8x+10+ 10/2x-3 ?

Synthetic Division

100

The remainder of:

(4x³+3x²-6x+7) / x+1

What is 12?

200

The remainder of:

6x⁵+x⁴-50x³-100x²-1 / x-4

What is 1,599?

300

The remainder of:

5x³+3 / x+6

What is -1,077 ?

400

The remainder of:

6x⁵+3x⁴-9x³+11 / x-2

What is 179?

500

The quotient and remainder of:

(4x⁴-3x³+2x-1) / x-5

What is 4x³+17x²+85x+427+ 2134/(x-5) ?

Evaluating Functions

100

Evaluate:

4x²y³-3x if x=2 and y=4

What is 1,018?

200

If f(x)=3x +1 evaluate f(-2) + f(1).

What is -1?

300

If f(x) = -x-3x-7x²evaluate x=-3

What is -51?

400

If f(x) = 4x² - 3 and g(x) = 2x, evaluate f(2) + g(1).

What is 15?

500

Evaluate:

-3x³(y+z)³ / 4(m+n)²  if x=-1, y=-5, z=3, m=-5, and n=2

What is -2/3?

Calculator Usage

100

Use your calculator to find the vertex of:

y=3x²-7x-4.

Round answers to 2 decimal places.

What is (1.17, -8.08) ?

200

Use your calculator to find the real solutions of:

y=(-1/3)x²+2x+3.

Round answers to 2 decimal places.

What is (-1.24,0) and (7.24,0) ?

300

Use your calculator to find the real solutions of:

y=7x²+x+6.

Round answers to 2 decimal places.

What is "there are no real solutions."

400

Use your calculator to find the vertex of:

f(x)=-4x²+9x + 8.

Round answers to 2 decimal places.

What is (1.13, 13.06) ?

500

Use your calculator to find the solutions of:

f(x)=(-1/2)x²+5x+8.

Round answers to 2 decimal places.

What is (-1.40,0) and (11.40,0) ?