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## MTEL General Curriculum Mathematics Practice

 Question 1

#### What is the length of side $$\overline{BD}$$ in the triangle below, where $$\angle DBA$$ is a right angle?

 A $$\large 1$$Hint: Use the Pythagorean Theorem. B $$\large \sqrt{5}$$Hint: $$2^2+e^2=3^2$$ or $$4+e^2=9;e^2=5; e=\sqrt{5}$$. C $$\large \sqrt{13}$$Hint: e is not the hypotenuse. D $$\large 5$$Hint: Use the Pythagorean Theorem.
Question 1 Explanation:
Topic: Derive and use formulas for calculating the lengths, perimeters, areas, volumes, and surface areas of geometric shapes and figures (Objective 0023), and recognize and apply connections between algebra and geometry (e.g., the use of coordinate systems, the Pythagorean theorem) (Objective 0024).
 Question 2

#### Tetrahedron

Hint:
All the faces of a tetrahedron are triangles.

#### Triangular Prism

Hint:
A prism has two congruent, parallel bases, connected by parallelograms (since this is a right prism, the parallelograms are rectangles).

#### Triangular Pyramid

Hint:
A pyramid has one base, not two.

#### Trigon

Hint:
A trigon is a triangle (this is not a common term).
Question 2 Explanation:
Topic: Classify and analyze three-dimensional figures using attributes of faces, edges, and vertices (Objective 0024).
 Question 3

#### The quotient is $$3\dfrac{1}{2}$$. There are 3 whole blocks each representing $$\dfrac{2}{3}$$ and a partial block composed of 3 small rectangles. The 3 small rectangles represent $$\dfrac{3}{6}$$ of a whole, or $$\dfrac{1}{2}$$.

Hint:
We are counting how many 2/3's are in
2 1/2: the unit becomes 2/3, not 1.

#### The quotient is $$\dfrac{4}{15}$$. There are four whole blocks separated into a total of 15 small rectangles.

Hint:
This explanation doesn't make much sense. Probably you are doing "invert and multiply," but inverting the wrong thing.

#### This picture cannot be used to find the quotient because it does not show how to separate $$2\dfrac{1}{2}$$ into equal sized groups.

Hint:
Study the measurement/quotative model of division. It's often very useful with fractions.
Question 3 Explanation:
Topic: Recognize and analyze pictorial representations of number operations. (Objective 0019).
 Question 4

#### P divides 30

Hint:
2, 3, and 5 are the prime factors of 240, and all divide 30.

#### P divides 48

Hint:
P=5 doesn't work.

#### P divides 75

Hint:
P=2 doesn't work.

#### P divides 80

Hint:
P=3 doesn't work.
Question 4 Explanation:
Topic: Find the prime factorization of a number and recognize its uses (Objective 0018).
 Question 5

#### 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 5 Explanation:
Topic: Ordering decimals and integers (Objective 0017).
 Question 6

#### 4 congruent sides

Hint:
The most common definition of a rhombus is a quadrilateral with 4 congruent sides.

#### A center of rotational symmetry

Hint:
The diagonal of a rhombus separates it into two congruent isosceles triangles. The center of this line is a center of 180 degree rotational symmetry that switches the triangles.

#### 4 congruent angles

Hint:
Unless the rhombus is a square, it does not have 4 congruent angles.

#### 2 sets of parallel sides

Hint:
All rhombi are parallelograms.
Question 6 Explanation:
Topic: Classify and analyze polygons using attributes of sides and angles, and symmetry (Objective 0024).
 Question 7

#### How many of the figures pictured above have at least one line of reflective symmetry?

 A $$\large 1$$ B $$\large 2$$Hint: The ellipse has 2 lines of reflective symmetry (horizontal and vertical, through the center) and the triangle has 3. The other two figures have rotational symmetry, but not reflective symmetry. C $$\large 3$$ D $$\large 4$$Hint: All four have rotational symmetry, but not reflective symmetry.
Question 7 Explanation:
Topic: Analyze and apply geometric transformations (e.g., translations, rotations, reflections, dilations); relate them to concepts of symmetry, similarity, and congruence; and use these concepts to solve problems (Objective 0024).
 Question 8

#### a

Hint:
The slope of line a is negative.

#### b

Hint:
Wrong slope and wrong intercept.

#### c

Hint:
The intercept of line c is positive.

#### d

Hint:
Slope is 2 -- for every increase of 1 in x, y increases by 2. Intercept is -5 -- the point (0,-5) is on the line.
Question 8 Explanation:
Topic: Find a linear equation that represents a graph (Objective 0022).
 Question 9

#### 1.5°

Hint:
Celsius and Fahrenheit don't increase at the same rate.

#### 1.8°

Hint:
That's how much the Fahrenheit temp increases when the Celsius temp goes up by 1 degree.

#### 2.7°

Hint:
Each degree increase in Celsius corresponds to a $$\dfrac{9}{5}=1.8$$ degree increase in Fahrenheit. Thus the increase is 1.8+0.9=2.7.

#### Not enough information.

Hint:
A linear equation has constant slope, which means that every increase of the same amount in one variable, gives a constant increase in the other variable. It doesn't matter what temperature the patient started out at.
Question 9 Explanation:
Topic: Interpret the meaning of the slope and the intercepts of a linear equation that models a real-world situation (Objective 0022).
 Question 10

#### Store A

Hint:
This would save about \$2.50. You can quickly see that D saves more.

#### Store B

Hint:
This saves 15% and C saves 25%.

#### Store D

Hint:
This is about 20% off, which is less of a discount than C.
Question 19 Explanation:
Topic: Understand the meanings and models of integers, fractions, decimals,percents, and mixed numbers and apply them to the solution of word problems (Objective 0017).
 Question 20

#### Which of the following inequalities describes all values of x  with $$\large \dfrac{x}{2}\le \dfrac{x}{3}$$?

 A $$\large x < 0$$Hint: If x =0, then x/2 = x/3, so this answer can't be correct. B $$\large x \le 0$$ C $$\large x > 0$$Hint: If x =0, then x/2 = x/3, so this answer can't be correct. D $$\large x \ge 0$$Hint: Try plugging in x = 6.
Question 20 Explanation:
Topics: Inequalities, operations (Objective 0019) (not exactly sure how to classify, but this is like one of the problems on the official sample test).
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