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## MTEL General Curriculum Mathematics Practice

 Question 1

#### 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 1 Explanation:
Topic: Recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem) (Objective 0024).
 Question 2

#### Which of the following is equal to one million three hundred thousand?

 A $$\large1.3\times {{10}^{6}}$$ B $$\large1.3\times {{10}^{9}}$$ Hint: That's one billion three hundred million. C $$\large1.03\times {{10}^{6}}$$ Hint: That's one million thirty thousand. D $$\large1.03\times {{10}^{9}}$$Hint: That's one billion thirty million
Question 2 Explanation:
Topic: Scientific Notation (Objective 0016)
 Question 3

#### A 90 degree clockwise rotation about (2,1) followed by a translation of two units to the right.

Hint:
Part of the figure would move below the x-axis with these transformations.

#### A translation 3 units up, followed by a reflection about the line y=x.

Hint:
See what happens to the point (5,1) under this set of transformations.

#### A 90 degree clockwise rotation about (2,1) followed by a translation of 2 units to the right.

Hint:
See what happens to the point (3,3) under this set of transformations.
Question 3 Explanation:
Topic:Analyze and apply geometric transformations (e.g., translations, rotations, reflections, dilations) (Objective 0024).
 Question 4

#### Let d represent the distance a passenger travels in miles (with $$d>\dfrac{1}{7}$$). Which of the following expressions represents the total fare?

 A $$\large \2.60+\0.40d$$Hint: It's 40 cents for 1/7 of a mile, not per mile. B $$\large \2.60+\0.40\dfrac{d}{7}$$Hint: According to this equation, going 7 miles would cost $3; does that make sense? C $$\large \2.20+\2.80d$$Hint: You can think of the fare as$2.20 to enter the cab, and then $0.40 for each 1/7 of a mile, including the first 1/7 of a mile (or$2.80 per mile). Alternatively, you pay $2.60 for the first 1/7 of a mile, and then$2.80 per mile for d-1/7 miles. The total is 2.60+2.80(d-1/7) = 2.60+ 2.80d -.40 = 2.20+2.80d. D $$\large \2.60+\2.80d$$Hint: Don't count the first 1/7 of a mile twice.
Question 4 Explanation:
Topic: Identify variables and derive algebraic expressions that represent real-world situations (Objective 0020), and select the linear equation that best models a real-world situation (Objective 0022).
 Question 5

#### 23 flats, 4 rods, 7 little cubes

Hint:
Be sure you read the question carefully: 2300+40+7=2347

#### 2 large cubes, 3 flats, 47 rods

Hint:
2000+300+470 $$\neq$$ 2347

#### 2 large cubes, 34 rods, 7 little cubes

Hint:
Be sure you read the question carefully: 2000+340+7=2347

#### 2 large cubes, 3 flats, 4 rods, 7 little cubes

Hint:
Be sure you read the question carefully: 2000+300+40+7=2347
Question 5 Explanation:
Topic: Place Value (Objective 0016)
There are 5 questions to complete.

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