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MTEL General Curriculum Mathematics Practice

Question 1

Which of the following points is closest to \( \dfrac{34}{135} \times \dfrac{53}{86}\)?

A

A

Hint:
\(\frac{34}{135} \approx \frac{1}{4}\) and \( \frac{53}{86} \approx \frac {2}{3}\). \(\frac {1}{4}\) of \(\frac {2}{3}\) is small and closest to A.
B

B

Hint:
Estimate with simpler fractions.
C

C

Hint:
Estimate with simpler fractions.
D

D

Hint:
Estimate with simpler fractions.
Question 1 Explanation: 
Topic: Understand meaning and models of operations on fractions (Objective 0019).
Question 2

Which of the lists below contains only irrational numbers?

A
\( \large\pi , \quad \sqrt{6},\quad \sqrt{\dfrac{1}{2}}\)
B
\( \large\pi , \quad \sqrt{9}, \quad \pi +1\)
Hint:
\( \sqrt{9}=3\)
C
\( \large\dfrac{1}{3},\quad \dfrac{5}{4},\quad \dfrac{2}{9}\)
Hint:
These are all rational.
D
\( \large-3,\quad 14,\quad 0\)
Hint:
These are all rational.
Question 2 Explanation: 
Topic: Identifying rational and irrational numbers (Objective 0016).
Question 3

Which of the following is an irrational number?

A
\( \large \sqrt[3]{8}\)
Hint:
This answer is the cube root of 8. Since 2 x 2 x 2 =8, this is equal to 2, which is rational because 2 = 2/1.
B
\( \large \sqrt{8}\)
Hint:
It is not trivial to prove that this is irrational, but you can get this answer by eliminating the other choices.
C
\( \large \dfrac{1}{8}\)
Hint:
1/8 is the RATIO of two integers, so it is rational.
D
\( \large -8\)
Hint:
Negative integers are also rational, -8 = -8/1, a ratio of integers.
Question 3 Explanation: 
Topic: Identifying rational and irrational numbers (Objective 0016).
Question 4

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 4 Explanation: 
Topic: Integers (Objective 0016)
Question 5

The histogram below shows the frequency of a class's scores on a 4 question quiz.

What was the mean score on the quiz?

A
\( \large 2.75\)
Hint:
There were 20 students who took the quiz. Total points earned: \(2 \times 1+6 \times 2+ 7\times 3+5 \times 4=55\), and 55/20 = 2.75.
B
\( \large 2\)
Hint:
How many students are there total? Did you count them all?
C
\( \large 3\)
Hint:
How many students are there total? Did you count them all? Be sure you're finding the mean, not the median or the mode.
D
\( \large 2.5\)
Hint:
How many students are there total? Did you count them all? Don't just take the mean of 1, 2, 3, 4 -- you have to weight them properly.
Question 5 Explanation: 
Topics: Analyze and interpret various graphic representations, and use measures of central tendency (e.g., mean, median, mode) and spread to describe and interpret real-world data (Objective 0025).
There are 5 questions to complete.

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