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MTEL General Curriculum Mathematics Practice

Question 1

In March of 2012, 1 dollar was worth the same as 0.761 Euros, and 1 dollar was also worth the same as 83.03 Japanese Yen.  Which of the expressions below gives the number of Yen that are worth 1 Euro?

A
\( \large {83}.0{3}\cdot 0.{761}\)
Hint:
This equation gives less than the number of yen per dollar, but 1 Euro is worth more than 1 dollar.
B
\( \large \dfrac{0.{761}}{{83}.0{3}}\)
Hint:
Number is way too small.
C
\( \large \dfrac{{83}.0{3}}{0.{761}}\)
Hint:
One strategy here is to use easier numbers, say 1 dollar = .5 Euros and 100 yen, then 1 Euro would be 200 Yen (change the numbers in the equations and see what works). Another is to use dimensional analysis: we want # yen per Euro, or yen/Euro = yen/dollar \(\times\) dollar/Euro = \(83.03 \times \dfrac {1}{0.761}\)
D
\( \large \dfrac{1}{0.{761}}\cdot \dfrac{1}{{83}.0{3}}\)
Hint:
Number is way too small.
Question 1 Explanation: 
Topic: Analyze the relationships among proportions, constant rates, and linear functions (Objective 0022).
Question 2

The letters A, B, and C represent digits (possibly equal) in the twelve digit number x=111,111,111,ABC.  For which values of A, B, and C is x divisible by 40?

A
\( \large A = 3, B = 2, C=0\)
Hint:
Note that it doesn't matter what the first 9 digits are, since 1000 is divisible by 40, so DEF,GHI,JKL,000 is divisible by 40 - we need to check the last 3.
B
\( \large A = 0, B = 0, C=4\)
Hint:
Not divisible by 10, since it doesn't end in 0.
C
\( \large A = 4, B = 2, C=0\)
Hint:
Divisible by 10 and by 4, but not by 40, as it's not divisible by 8. Look at 40 as the product of powers of primes -- 8 x 5, and check each. To check 8, either check whether 420 is divisible by 8, or take ones place + twice tens place + 4 * hundreds place = 18, which is not divisible by 8.
D
\( \large A =1, B=0, C=0\)
Hint:
Divisible by 10 and by 4, but not by 40, as it's not divisible by 8. Look at 40 as the product of powers of primes -- 8 x 5, and check each. To check 8, either check whether 100 is divisible by 8, or take ones place + twice tens place + 4 * hundreds place = 4, which is not divisible by 8.
Question 2 Explanation: 
Topic: Understand divisibility rules and why they work (Objective 018).
Question 3

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
\( \large 28 \dfrac{4}{7}\) ml
Hint:
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
\( \large 28 \dfrac{1}{4}\) ml
Hint:
49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
C
\( \large 28 \dfrac{1}{7}\) ml
Hint:
49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
D
\( \large 87.5\) ml
Hint:
49 ml of medicine requires 28 ml of saline. How much saline does the extra ml require?
Question 3 Explanation: 
Topic: Apply proportional thinking to estimate quantities in real world situations (Objective 0019).
Question 4

At a school fundraising event, people can buy a ticket to spin a spinner like the one below.  The region that the spinner lands in tells which, if any, prize the person wins.

If 240 people buy tickets to spin the spinner, what is the best estimate of the number of keychains that will be given away?

A

40

Hint:
"Keychain" appears on the spinner twice.
B

80

Hint:
The probability of getting a keychain is 1/3, and so about 1/3 of the time the spinner will win.
C

100

Hint:
What is the probability of winning a keychain?
D

120

Hint:
That would be the answer for getting any prize, not a keychain specifically.
Question 4 Explanation: 
Topic: I would call this topic expected value, which is not listed on the objectives. This question is very similar to one on the sample test. It's not a good question in that it's oversimplified (a more difficult and interesting question would be something like, "The school bought 100 keychains for prizes, what is the probability that they will run out before 240 people play?"). In any case, I believe the objective this is meant for is, "Recognize the difference between experimentally and theoretically determined probabilities in real-world situations. (Objective 0026)." This is not something easily assessed with multiple choice .
Question 5

A family went on a long car trip.  Below is a graph of how far they had driven at each hour.

Which of the following is closest to their average speed driving on the trip?

 
A
\( \large d=20t\)
Hint:
Try plugging t=7 into the equation, and see how it matches the graph.
B
\( \large d=30t\)
Hint:
Try plugging t=7 into the equation, and see how it matches the graph.
C
\( \large d=40t\)
D
\( \large d=50t\)
Hint:
Try plugging t=7 into the equation, and see how it matches the graph.
Question 5 Explanation: 
Topic: Select the linear equation that best models a real-world situation (Objective 0022).
There are 5 questions to complete.

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