Math Practice Test Set 5 - My Career Tools

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1. Mia goes to East York Collegiate Institute. She is given the following information:

There are 150 grade 12 students at East York Collegiate Institute. 70 of the grade 12 students drive a car at the school. Half of all students with a grade average of 90 or higher have a car.

She is asked to find the probability of randomly choosing a grade 12 student with a car, given that the
student has an average grade of 90 or higher. She reasons initially that, since there are 70 grade 12 students out of 150 who have a car, it would be \(frac{7}{15}\). However, since it is a conditional probability, she needs to multiply by \(\frac{1}{2}\), since the probability that a student with a grade average of 90 or higher is \(frac{1}{2}\). This results in a probability of \(frac{7}{30}\). Is she correct or not, and why?

A.Yes, and her reasoning is correct.

B.No, she didn't need to multiply by \(\frac{1}{2}\) and the probability is \(\frac{7}{15}\). The probability that a student has a car can be assumed to be independent of their grade average, and so no multiplication is needed.

C.No, there is insufficient information to find this probability.

D.No, she needs to state that it can be assumed that half of grade 12 students have an average of 90 or higher. Therefore, half of 70 is 35, half of 150 is 75, and the probability is \(\frac{7}{15}\)

Question 1 of 10

2. An integer is randomly chosen from the following number line. Given that the number lies on A-D , what is
the probability that it also lies on C-F

A.\(\frac{8}{8}\)

B.\(\frac{1}{2}\)

C.\(\frac{8}{11}\)

D.\(\frac{5}{8}\)

Question 2 of 10

3. The graph of this data would most resemble which of the following types of graphs?

A.positive linear

B.negative linear

C.constant linear

D.none of the above

Question 3 of 10

Math-Distributive Property

4. Use the distributive property to expand the given expression.

\(−8u^{2}(−7u^{3}− 8u^{2}− 2u + 10) \)

A.\(56u^{5}+ 64u^{4} + 16u^{3}− 80u^{2} \)

B.\(-56u^{5}+ 64u^{4} + 16u^{3}− 80u^{2} \)

C.\(56u^{5} - 64u^{4} + 16u^{3}− 80u^{2} \)

D.\(56u^{5} + 64u^{4} + 16u^{3} + 80u^{2} \)

Question 4 of 10

Math-Solution of equations

5. Determine k so that the point (9, k) is a solution of y = −6x + 1.

A.k = −53

B.k = −54

C.k = 53

D.k = 54

Question 5 of 10

6. Use the substitution method to solve each of the following systems.

x + 2y = −4
6x − 4y = −56

A.(-8, 2)

B.-(-8, 2)

C.(-16, 8)

D.(-2, 8)

Question 6 of 10

Math-Evaluate expression

7. Simplify the given expression.

\((-2)^{4}\)

A.16

B.8

C.-16

D.-8

Question 7 of 10

8. Evaluate the expression at the given value of x.

\(−3x^{2}− 6x + 3\) at \(x = 7 \)

A.-186

B.186

C.-198

D.198

Question 8 of 10

Math-Slope

9. Calculate the slope of the line passing through the points P and Q. Be sure to reduce your answer to lowest terms.

P(0, 11), Q(16,−11)

A.\(-\frac{11}{8}\)

B.\(1\frac{3}{8}\)

C.\(\frac{11}{8}\)

D.\(\frac{8}{11}\)

Question 9 of 10

Math-Inequalities

10. Solve the given inequality.

2x − 9 ≥ 5 − 8x

A.\(\frac{7}{5}\)

B.\(\frac{5}{7}\)

C.\(\frac{14}{10}\)

D.\(\frac{10}{14}\)

Question 10 of 10