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MTEL General Curriculum Mathematics Practice

 Question 1

Let p represent the regular price of these t-shirt. Which of the following equations is correct?

 A $$\large 0.8p=\8.73$$Hint: 80% of the regular price = $8.73. B $$\large \8.73+0.2*\8.73=p$$Hint: The 20% off was off of the ORIGINAL price, not off the$8.73 (a lot of people make this mistake). Plus this is the same equation as in choice c. C $$\large 1.2*\8.73=p$$Hint: The 20% off was off of the ORIGINAL price, not off the \$8.73 (a lot of people make this mistake). Plus this is the same equation as in choice b. D $$\large p-0.2*\8.73=p$$Hint: Subtract p from both sides of this equation, and you have -.2 x 8.73 =0.
Question 1 Explanation:
Topics: Use algebra to solve word problems involving percents and identify variables, and derive algebraic expressions that represent real-world situations (Objective 0020).
 Question 2

Which of the following values of x satisfies the inequality $$\large \left| {{(x+2)}^{3}} \right|<3?$$

 A $$\large x=-3$$Hint: $$\left| {{(-3+2)}^{3}} \right|$$=$$\left | {(-1)}^3 \right |$$=$$\left | -1 \right |=1$$ . B $$\large x=0$$Hint: $$\left| {{(0+2)}^{3}} \right|$$=$$\left | {2}^3 \right |$$=$$\left | 8 \right |$$ =$$8$$ C $$\large x=-4$$Hint: $$\left| {{(-4+2)}^{3}} \right|$$=$$\left | {(-2)}^3 \right |$$=$$\left | -8 \right |$$ =$$8$$ D $$\large x=1$$Hint: $$\left| {{(1+2)}^{3}} \right|$$=$$\left | {3}^3 \right |$$=$$\left | 27 \right |$$ = $$27$$
Question 2 Explanation:
Topics: Laws of exponents, order of operations, interpret absolute value (Objective 0019).
 Question 3

Some children explored the diagonals in 2 x 2 squares on pages of a calendar (where all four squares have numbers in them).  They conjectured that the sum of the diagonals is always equal; in the example below, 8+16=9+15. Which of the equations below could best be used to explain why the children's conjecture is correct?

 A $$\large 8x+16x=9x+15x$$Hint: What would x represent in this case? Make sure you can describe in words what x represents. B $$\large x+(x+2)=(x+1)+(x+1)$$Hint: What would x represent in this case? Make sure you can describe in words what x represents. C $$\large x+(x+8)=(x+1)+(x+7)$$Hint: x is the number in the top left square, x+8 is one below and to the right, x+1 is to the right of x, and x+7 is below x. D $$\large x+8+16=x+9+15$$Hint: What would x represent in this case? Make sure you can describe in words what x represents.
Question 3 Explanation:
Topic: Recognize and apply the concepts of variable, equality, and equation to express relationships algebraically (Objective 0020).
 Question 4

Which of the lists below is in order from least to greatest value?

 A $$\large -0.044,\quad -0.04,\quad 0.04,\quad 0.044$$Hint: These are easier to compare if you add trailing zeroes (this is finding a common denominator) -- all in thousandths, -0.044, -0.040,0 .040, 0.044. The middle two numbers, -0.040 and 0.040 can be modeled as owing 4 cents and having 4 cents. The outer two numbers are owing or having a bit more. B $$\large -0.04,\quad -0.044,\quad 0.044,\quad 0.04$$Hint: 0.04=0.040, which is less than 0.044. C $$\large -0.04,\quad -0.044,\quad 0.04,\quad 0.044$$Hint: -0.04=-0.040, which is greater than $$-0.044$$. D $$\large -0.044,\quad -0.04,\quad 0.044,\quad 0.04$$Hint: 0.04=0.040, which is less than 0.044.
Question 4 Explanation:
Topic: Ordering decimals and integers (Objective 0017).
 Question 5

What is the perimeter of a right triangle with legs of lengths x and 2x?

 A $$\large 6x$$Hint: Use the Pythagorean Theorem. B $$\large 3x+5{{x}^{2}}$$Hint: Don't forget to take square roots when you use the Pythagorean Theorem. C $$\large 3x+\sqrt{5}{{x}^{2}}$$Hint: $$\sqrt {5 x^2}$$ is not $$\sqrt {5}x^2$$. D $$\large 3x+\sqrt{5}{{x}^{{}}}$$Hint: To find the hypotenuse, h, use the Pythagorean Theorem: $$x^2+(2x)^2=h^2.$$ $$5x^2=h^2,h=\sqrt{5}x$$. The perimeter is this plus x plus 2x.
Question 5 Explanation:
Topic: Recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem) (Objective 0024).
There are 5 questions to complete.

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