End of Year Review (Part 1)

Solving Linear Equations Part 1

100

Solve:

4x+4x-3=6x+9

8x-3=6x+9

2x=12

x=6

200

Solve:

3x+7=-x-1

4x=-8

x=-2

300

Solve:

1+2x+5=4x-3

-2x+6=4x-3

9=6x

3/2=x

400

Solve:

4x-2+x=-2+2x

5x-2=2x-2

3x=0

x=0

500

Solve:

3x-4+1=-2x-5+5x

3x-3=3x-5

-3=-5

not solution

Evaluating Expressions and Order of Operations

100

Evaluate: 2x²-3x+2 for x=-5

2(-5)²-3(-5)+2

2(25)-3(-5)+2

50-(-15)+2

50+15+2

=67

200

Evaluate x-y for x=-2 and y=-3

-2-(-3)

-2+3

=1

300

Evaluate 2x+3y+z for x=-2 y=-3 and z=5

2(-2)+3(-3)+5

-4+-9+5

-13+5=-8

400

Evaluate 2(x+y)/(z) for x=-2 y=-3 and z=5

2(-2+-3)/(5)

2(-5)/(5)

-10/5

=-2

500

Evaluate: 5(x+2y)/(x-y)  for x=-3 and y=2

5(-3+2*2)/(-3-2)

5(-3+4)/(-3-2)

5(1)/(-5)

5/(-5)

=-1

Operations with Rational Numbers

100

Compute

(1/3) + (-9/20)

20/60  + -27/60

= -7/60

200

Compute:

-1 1/4 - (-3 9/10)

-1 5/20+ 3 18/20

=2 13/20

300

-1 1/4  divided by 7 1/2

-5/4 divided by 15/2

-5/4 * 2/15

-10/60

=-1/6

400

(3 1/3) * (-2/5)

(10/3)*(-2/5)

-20/15

-4/3 or (-1 1/3)

500

(-2 1/4) *(2/3)

(-9/4)*(2/3)

-18/12

-3/2 or (-1 1/2)

Solving Linear Equations Part 2

100

Solve:

1/2x+x-3=(1/3)x+4

Multiply everything by 6

3x+6x-18=2x+24

9x-18=2x+24

7x=42

x=6

200

Solve:

(y/2)+(y/3)-3=y

Multiply by 6

3y+2y-18=6y

-18=y

300

Solve:

(1/6)m-3=-5

Multiply by 6.

m-18=-30

m=-12

400

Solve:

(2/3)x-3=(1/2)x-7

Multiply by 6.

4x-18=3x-42

x=-24

500

Solve:

x+(x/2)-4=(x/4)

Multiply by 4.

4x+2x-16=x

5x=16

x=16/5

Law of Exponents and Scientific Notation

100

Simplify

4²*4⁵

4⁷

200

Multiply and give the answer in scientific notation.

(8*10⁴) *(4.5*10^-2)

8*4.5=36

10⁴*10^-2=10²

36*10²

3.6*10³

300

Simplify:

4² * 4^-4

4^-2

(1/4²)

=(1/16)

400

(5⁰)³​​​​

5^0*3=5⁰

=1

500

Simplify:

((x²)³*y⁴)/(x^-2 *y)

(x⁶ *y⁴)/(x^-2 *y)

(x⁶)/(x^-2) * (y⁴/y)

(x⁶ *x²) * (y⁴/y)

(x⁸)*(y³)

=x⁸y³