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## MTEL General Curriculum Mathematics Practice

 Question 1

#### 4

Hint:
The card blocks more than half of the circles, so this number is too small.

#### 5

Hint:
The card blocks more than half of the circles, so this number is too small.

#### 8

Hint:
The card blocks more than half of the circles, so this number is too small.

#### 12

Hint:
2/5 of the circles or 8 circles are showing. Thus 4 circles represent 1/5 of the circles, and $$4 \times 5=20$$ circles represent 5/5 or all the circles. Thus 12 circles are hidden.
Question 1 Explanation:
Topic: Models of Fractions (Objective 0017)
 Question 2

#### Which of the following is equal to eleven billion four hundred thousand?

 A $$\large 11,400,000$$Hint: That's eleven million four hundred thousand. B $$\large11,000,400,000$$ C $$\large11,000,000,400,000$$Hint: That's eleven trillion four hundred thousand (although with British conventions; this answer is correct, but in the US, it isn't). D $$\large 11,400,000,000$$Hint: That's eleven billion four hundred million
Question 2 Explanation:
Topic: Place Value (Objective 0016)
 Question 3

#### 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 3 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 4

#### A family has four children.  What is the probability that two children are girls and two are boys?  Assume the the probability of having a boy (or a girl) is 50%.

 A $$\large \dfrac{1}{2}$$Hint: How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls? B $$\large \dfrac{1}{4}$$Hint: How many different configurations are there from oldest to youngest, e.g. BGGG? How many of them have 2 boys and 2 girls? C $$\large \dfrac{1}{5}$$Hint: Some configurations are more probable than others -- i.e. it's more likely to have two boys and two girls than all boys. Be sure you are weighting properly. D $$\large \dfrac{3}{8}$$Hint: There are two possibilities for each child, so there are $$2 \times 2 \times 2 \times 2 =16$$ different configurations, e.g. from oldest to youngest BBBG, BGGB, GBBB, etc. Of these configurations, there are 6 with two boys and two girls (this is the combination $$_{4}C_{2}$$ or "4 choose 2"): BBGG, BGBG, BGGB, GGBB, GBGB, and GBBG. Thus the probability is 6/16=3/8.
Question 4 Explanation:
Topic: Apply knowledge of combinations and permutations to the computation of probabilities (Objective 0026).
 Question 5

#### A solution requires 4 ml of saline for every 7 ml of medicine. How much saline would be required for 50 ml of medicine?

 A $$\large 28 \dfrac{4}{7}$$ mlHint: 49 ml of medicine requires 28 ml of saline. The extra ml of saline requires 4 ml saline/ 7 ml medicine = 4/7 ml saline per 1 ml medicine. B $$\large 28 \dfrac{1}{4}$$ mlHint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? C $$\large 28 \dfrac{1}{7}$$ mlHint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require? D $$\large 87.5$$ mlHint: 49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
Question 5 Explanation:
Topic: Apply proportional thinking to estimate quantities in real world situations (Objective 0019).
 Question 6

#### How many students at the college are seniors who are not vegetarians?

 A $$\large 137$$Hint: Doesn't include the senior athletes who are not vegetarians. B $$\large 167$$ C $$\large 197$$Hint: That's all seniors, including vegetarians. D $$\large 279$$Hint: Includes all athletes who are not vegetarians, some of whom are not seniors.
Question 6 Explanation:
Topic: Venn Diagrams (Objective 0025)
 Question 7

#### $$7-4=3$$ and $$8-5=3$$, so the fractions are equal.

Hint:
Not how to compare fractions. By this logic, 1/2 and 3/4 are equal, but 1/2 and 2/4 are not.

#### $$4\times 8=32$$ and $$7\times 5=35$$. Since $$32<35$$ , $$\dfrac{5}{8}<\dfrac{4}{7}$$

Hint:
Starts out as something that works, but the conclusion is wrong. 4/7 = 32/56 and 5/8 = 35/56. The cross multiplication gives the numerators, and 35/56 is bigger.

#### $$4<5$$ and $$7<8$$, so $$\dfrac{4}{7}<\dfrac{5}{8}$$

Hint:
Conclusion is correct, logic is wrong. With this reasoning, 1/2 would be less than 2/100,000.
Question 7 Explanation:
Topics: Comparing fractions, and understanding the meaning of fractions (Objective 0017).
 Question 8

#### The student used a method that worked for this problem and can be generalized to any subtraction problem.

Hint:
Note that this algorithm is taught as the "standard" algorithm in much of Europe (it's where the term "borrowing" came from -- you borrow on top and "pay back" on the bottom).

#### The student used a method that worked for this problem and that will work for any subtraction problem that only requires one regrouping; it will not work if more regrouping is required.

Hint:
Try some more examples.

#### The student used a method that worked for this problem and will work for all three-digit subtraction problems, but will not work for larger problems.

Hint:
Try some more examples.

#### The student used a method that does not work. The student made two mistakes that cancelled each other out and was lucky to get the right answer for this problem.

Hint:
Remember, there are many ways to do subtraction; there is no one "right" algorithm.
Question 8 Explanation:
Topic: Analyze and justify standard and non-standard computational techniques (Objective 0019).
 Question 9

#### 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 9 Explanation:
Topics: Laws of exponents, order of operations, interpret absolute value (Objective 0019).
 Question 10

#### Which of the following does not represent the number of gumdrops in a row of h houses?

 A $$\large 2+3h$$Hint: Think of this as start with 2 gumdrops on the left wall, and then add 3 gumdrops for each house. B $$\large 5+3(h-1)$$Hint: Think of this as start with one house, and then add 3 gumdrops for each of the other h-1 houses. C $$\large h+(h+1)+(h+1)$$Hint: Look at the gumdrops in 3 rows: h gumdrops for the "rooftops," h+1 for the tops of the vertical walls, and h+1 for the floors. D $$\large 5+3h$$Hint: This one is not a correct equation (which makes it the correct answer!). Compare to choice A. One of them has to be wrong, as they differ by 3.
Question 10 Explanation:
Topic: Translate among different representations (e.g., tables, graphs, algebraic expressions, verbal descriptions) of functional relationships (Objective 0021).
There are 10 questions to complete.

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