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## MTEL General Curriculum Mathematics Practice

 Question 1

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

 A $$\large \dfrac{1}{2},\quad \dfrac{1}{3},\quad \dfrac{1}{4},\quad \dfrac{1}{5}$$Hint: This is ordered from greatest to least. B $$\large \dfrac{1}{3},\quad \dfrac{2}{7},\quad \dfrac{3}{8},\quad \dfrac{4}{11}$$Hint: 1/3 = 2/6 is bigger than 2/7. C $$\large \dfrac{1}{4},\quad \dfrac{2}{5},\quad \dfrac{2}{3},\quad \dfrac{4}{5}$$Hint: One way to look at this: 1/4 and 2/5 are both less than 1/2, and 2/3 and 4/5 are both greater than 1/2. 1/4 is 25% and 2/5 is 40%, so 2/5 is greater. The distance from 2/3 to 1 is 1/3 and from 4/5 to 1 is 1/5, and 1/5 is less than 1/3, so 4/5 is bigger. D $$\large \dfrac{7}{8},\quad \dfrac{6}{7},\quad \dfrac{5}{6},\quad \dfrac{4}{5}$$Hint: This is in order from greatest to least.
Question 1 Explanation:
Topic: Ordering Fractions (Objective 0017)
 Question 2

#### 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 2 Explanation:
Topic: Ordering decimals and integers (Objective 0017).
 Question 3

#### 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 3 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 4

#### 0.38

Hint:
If you are just writing the numerator next to the denominator then your technique is way off, but by coincidence your answer is close; try with 2/3 and 0.23 is nowhere near correct.

#### 0.125

Hint:
This is 1/8, not 3/8.

#### 0.83

Hint:
3/8 is less than a half, and 0.83 is more than a half, so they can't be equal.
Question 4 Explanation:
Topic: Converting between fractions and decimals (Objective 0017)
 Question 5

#### Which of the numbers below is a fraction equivalent to $$0.\bar{6}$$?

 A $$\large \dfrac{4}{6}$$Hint: $$0.\bar{6}=\dfrac{2}{3}=\dfrac{4}{6}$$ B $$\large \dfrac{3}{5}$$Hint: This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice c, which is another way to tell that it's wrong. C $$\large \dfrac{6}{10}$$Hint: This is equal to 0.6, without the repeating decimal. Answer is equivalent to choice b, which is another way to tell that it's wrong. D $$\large \dfrac{1}{6}$$Hint: This is less than a half, and $$0.\bar{6}$$ is greater than a half.
Question 5 Explanation:
Topic: Converting between fraction and decimal representations (Objective 0017)
 Question 6

#### Which of the numbers below is not equivalent to 4%?

 A $$\large \dfrac{1}{25}$$Hint: 1/25=4/100, so this is equal to 4% (be sure you read the question correctly). B $$\large \dfrac{4}{100}$$Hint: 4/100=4% (be sure you read the question correctly). C $$\large 0.4$$Hint: 0.4=40% so this is not equal to 4% D $$\large 0.04$$Hint: 0.04=4/100, so this is equal to 4% (be sure you read the question correctly).
Question 6 Explanation:
Converting between fractions, decimals, and percents (Objective 0017).
 Question 7

#### Given that 10 cm is approximately equal to 4 inches, which of the following expressions models a way to find out approximately how many inches are equivalent to 350 cm?

 A $$\large 350\times \left( \dfrac{10}{4} \right)$$Hint: The final result should be smaller than 350, and this answer is bigger. B $$\large 350\times \left( \dfrac{4}{10} \right)$$Hint: Dimensional analysis can help here: $$350 \text{cm} \times \dfrac{4 \text{in}}{10 \text{cm}}$$. The cm's cancel and the answer is in inches. C $$\large (10-4) \times 350$$Hint: This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense. D $$\large (350-10) \times 4$$Hint: This answer doesn't make much sense. Try with a simpler example (e.g. 20 cm not 350 cm) to make sure that your logic makes sense.
Question 7 Explanation:
Topic: Applying fractions to word problems (Objective 0017) This problem is similar to one on the official sample test for that objective, but it might fit better into unit conversion and dimensional analysis (Objective 0023: Measurement)
 Question 8

#### What fraction of the area of the picture below is shaded? A $$\large \dfrac{17}{24}$$Hint: You might try adding segments so each quadrant is divided into 6 pieces with equal area -- there will be 24 regions, not all the same shape, but all the same area, with 17 of them shaded (for the top left quarter, you could also first change the diagonal line to a horizontal or vertical line that divides the square in two equal pieces and shade one) . B $$\large \dfrac{3}{4}$$Hint: Be sure you're taking into account the different sizes of the pieces. C $$\large \dfrac{2}{3}$$Hint: The bottom half of the picture is 2/3 shaded, and the top half is more than 2/3 shaded, so this answer is too small. D $$\large \dfrac{17}{6}$$Hint: This answer is bigger than 1, so doesn't make any sense. Be sure you are using the whole picture, not one quadrant, as the unit.
Question 8 Explanation:
Topic: Models of Fractions (Objective 0017)
 Question 9

#### The picture below shows identical circles drawn on a piece of paper.  The rectangle represents an index card that is blocking your view of $$\dfrac{3}{5}$$ of the circles on the paper.  How many circles are covered by the rectangle? #### 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 9 Explanation:
Topic: Models of Fractions (Objective 0017)
 Question 10
 I. $$\large \dfrac{1}{2}+\dfrac{1}{3}$$ II. $$\large .400000$$ III. $$\large\dfrac{1}{5}+\dfrac{1}{5}$$ IV. $$\large 40\%$$ V. $$\large 0.25$$ VI. $$\large\dfrac{14}{35}$$

#### I, III, V, VI

Hint:
I and V are not at all how fractions and decimals work.

#### III, VI

Hint:
These are right, but there are more.

#### II, III, VI

Hint:
These are right, but there are more.

#### II, III, IV, VI

Question 10 Explanation:
Topic: Converting between fractions, decimals, and percents (Objective 0017)
 Question 11

#### Below is a portion of a number line. #### Point A is one-quarter of the distance from 0.26 to 0.28.  What number is represented by point A?

 A $$\large0.26$$Hint: Please reread the question. B $$\large0.2625$$Hint: This is one-quarter of the distance between 0.26 and 0.27, which is not what the question asked. C $$\large0.265$$ D $$\large0.27$$Hint: Please read the question more carefully. This answer would be correct if Point A were halfway between the tick marks, but it's not.
Question 11 Explanation:
Topic: Using number lines (Objective 0017)
 Question 12

#### Below is a portion of a number line: #### Point B is halfway between two tick marks.  What number is represented by Point B?

 A $$\large 0.645$$Hint: That point is marked on the line, to the right. B $$\large 0.6421$$Hint: That point is to the left of point B. C $$\large 0.6422$$Hint: That point is to the left of point B. D $$\large 0.6425$$
Question 12 Explanation:
Topic: Using Number Lines (Objective 0017)
 Question 13

#### $$7-4=3$$ 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 13 Explanation:
Topics: Comparing fractions, and understanding the meaning of fractions (Objective 0017).
There are 13 questions to complete.

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