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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

#### 95% of 12 year old boys can do 56 sit-ups in 60 seconds.

Hint:
The 95th percentile means that 95% of scores are less than or equal to 56, and 5% are greater than or equal to 56.

#### At most 25% of 7 year old boys can do 19 or more sit-ups in 60 seconds.

Hint:
The 25th percentile means that 25% of scores are less than or equal to 19, and 75% are greater than or equal to 19.

#### Half of all 13 year old boys can do less than 41 sit-ups in 60 seconds and half can do more than 41 sit-ups in 60 seconds.

Hint:
Close, but not quite. There's no accounting for boys who can do exactly 41 sit ups. Look at these data: 10, 20, 41, 41, 41, 41, 50, 60, 90. The median is 41, but more than half can do 41 or more.

#### At least 75% of 16 year old boys can only do 51 or fewer sit-ups in 60 seconds.

Hint:
The "at least" is necessary due to duplicates. Suppose the data were 10, 20, 51, 51. The 75th percentile is 51, but 100% of the boys can only do 51 or fewer situps.
Question 2 Explanation:
Topic: Analyze and interpret various graphic and nongraphic data representations (e.g., frequency distributions, percentiles) (Objective 0025).
 Question 3

#### If  x  is an integer, which of the following must also be an integer?

 A $$\large \dfrac{x}{2}$$Hint: If x is odd, then $$\dfrac{x}{2}$$ is not an integer, e.g. 3/2 = 1.5. B $$\large \dfrac{2}{x}$$Hint: Only an integer if x = -2, -1, 1, or 2. C $$\large-x$$Hint: -1 times any integer is still an integer. D $$\large\sqrt{x}$$Hint: Usually not an integer, e.g. $$\sqrt{2} \approx 1.414$$.
Question 3 Explanation:
Topic: Integers (Objective 0016)
 Question 4

#### 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 4 Explanation:
Topic: Scientific Notation (Objective 0016)
 Question 5

#### Four children randomly line up, single file.  What is the probability that they are in height order, with the shortest child in front?   All of the children are different heights.

 A $$\large \dfrac{1}{4}$$Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children. B $$\large \dfrac{1}{256}$$Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children. C $$\large \dfrac{1}{16}$$Hint: Try a simpler question with 3 children -- call them big, medium, and small -- and list all the ways they could line up. Then see how to extend your logic to the problem with 4 children. D $$\large \dfrac{1}{24}$$Hint: The number of ways for the children to line up is $$4!=4 \times 3 \times 2 \times 1 =24$$ -- there are 4 choices for who is first in line, then 3 for who is second, etc. Only one of these lines has the children in the order specified.
Question 5 Explanation:
Topic: Apply knowledge of combinations and permutations to the computation of probabilities (Objective 0026).
There are 5 questions to complete.

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