Mathematical Problem Solving

This video tutorial covers lesson 10.2 from the sixth-grade Go Math textbook. It includes evaluating expressions for ticket prices, calculating the area of a square and doubling it, managing savings account transactions, and identifying patterns in expressions. The tutorial also explains how to calculate kinetic energy, the area of triangles, and the volume of pyramids. Additionally, it discusses checking the equivalence of expressions and identifying common mistakes in calculations.

What is the expression for the total cost of tickets if adult tickets are $8.75, children's tickets are $6.50, and senior tickets are $6.50?

• 8.75a + 8.75c + 6.50s

• 6.50a + 8.75c + 6.50s

• 8.75a + 6.50c

• 8.75a + 6.50c + 6.50s

If the Andrews family bought 2 adult tickets, 3 children's tickets, and 1 senior ticket, what is the total cost?

• $43.50

• $48.00

• $45.00

• $50.00

How do you represent the area of a square garden that is doubled in size if the original side length is 8 feet?

• 2x^2

• x^2

• 4x^2

• 8x^2

What is the new balance in Ramon's account if he deposits $100 and withdraws half of it?

• $2340

• $2390

• $2400

• $2450

What pattern is observed when evaluating the expression 6x - x^2 for x values from 0 to 6?

• Increases to 9 and then decreases

• Decreases to 0 and then increases

• Remains constant

• Fluctuates randomly

How is kinetic energy calculated for a moving object?

• 1/2 mv^2

• mv^2

• 1/2 m^2v

• m^2v^2

What is the area of a triangle with a base of 12 and height of 7?

• 21 square units

• 84 square units

• 42 square units

• 56 square units

What is the volume of a pyramid with a square base of side 24 feet and height 30 feet?

• 5760 cubic feet

• 6000 cubic feet

• 7200 cubic feet

• 4800 cubic feet

Are the expressions 3x(x-2)+2 and 2x^2+3x-12 equivalent for x=2 and x=7?

• Equivalent only for x=7

• Equivalent only for x=2

• No, they are not equivalent

• Yes, they are equivalent

What mistake did Marjorie make when evaluating 3x+2 for x=5?

• She used the wrong value for x

• She multiplied incorrectly

• She subtracted instead of adding

• She added instead of multiplying