Algebra Sample Quiz 1
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Welcome to the SelectiveMath Sample Question Showcase!
Each individual quiz contains less than 10 questions and takes only a few minutes to complete.
Instructions: Read the questions carefully. Feel free to use a scratch pad to work out your answers. When you think that you know the answer, click on the appropriate button. Then click the “Show Answer and Next Question” button. You will be given a detailed explanation on how you could have solved the problem. At that point you can move on to the next question.
At the end of the quiz, you’ll be given your final score out of 100 points.
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Question 1 of 7
1. Question
Points P and Q lie on a line.
If P = (-7, 3) and Q = (4, -2), what is the y-intercept of this line?a.
b. 
c. 
d. Hint: Write out the formula for a line: y = mx + b. Use the formula for calculating slope (e.g., difference between y divided by the difference between x) to find m and then plug in a point to find the y-intercept.
Correct
Your answer of d. was correct.The answer is: d.
To solve this problem, first find the slope of the line that contains points P and Q:
This yields
. Next, find the y-intercept by plugging in a given point. In this case, we are plugging in point Q: 
; multiply out to get 
; which is: 
; therefore, 
.Incorrect
Your answer was incorrect.
Correct answer is: d.The answer is: d.
To solve this problem, first find the slope of the line that contains points P and Q:
This yields
. Next, find the y-intercept by plugging in a given point. In this case, we are plugging in point Q: ; multiply out to get ; which is: ; therefore, . -
Question 2 of 7
2. Question
A triangle has vertices at (3, 7), (8, 7), and (5, 1). What is its area?
Hint: Try plotting these points.
Correct
Your answer of a. 15 was correct.The answer is: a. 15
Plot these points and you will see that the base equals 5 and the height is 6, so the area is 15.
Incorrect
Your answer was incorrect.
Correct answer is: a. 15The answer is: a. 15
Plot these points and you will see that the base equals 5 and the height is 6, so the area is 15.
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Question 3 of 7
3. Question
Which of the following are the coordinates of the midpoint of the segment that contains the points (-2, 3) and (6,-5)?
Hint: Finding a midpoint is similar to finding an average.
Correct
Your answer of d. (2, -1) was correct.
The answer is: d. (2,1)
Finding a midpoint is the same as finding an average. If a line segment has the endpoints
and 
, the midpoint is given by the following formula: 
. So to calculate the midpoint, we compute: 
, which equals 2, -1.Incorrect
Your answer was incorrect.
Correct answer is: d. (2, -1)The answer is: d. (2,1)
Finding a midpoint is the same as finding an average. If a line segment has the endpoints
and , the midpoint is given by the following formula: . So to calculate the midpoint, we compute: , which equals 2, -1. -
Question 4 of 7
4. Question
Which of the following are the coordinates of the midpoint of the segment that contains the points (-2, 3) and (6, -5)?
a. y =
x + 5 b. y = 3x – 5 c. y = 4x + 5 d. y = -3x – 5Hint: Parallel lines have the same slope.
Correct
Your answer of b. was correct.The answer is b. y = 3x – 5.
Parallel lines have the same slope by have different y-intercepts. The only line with the same slope as the given line, which has a slope of 3 is choice b, y = 3x – 5.
Incorrect
Your answer was incorrect.
Correct answer is: b.The answer is b. y = 3x – 5.
Parallel lines have the same slope by have different y-intercepts. The only line with the same slope as the given line, which has a slope of 3 is choice b, y = 3x – 5.
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Question 5 of 7
5. Question
What is a potential equation for a line perpendicular to y = –
x – 28?a. y =
x – 14 b. y = –x – 28 c. y = –
x + 14 d. y = + 18Hint: Perpendicular lines have a negative reciprocal slope relative to the original line.
Correct
Your answer of c. was correct.The answer is c. –
x + 14If line a (the original line) is perpendicular to line b (the 2nd line), then the slope of line a is the negative reciprocal of the slope of line b:
. Therefore, the slope of a line perpendicular to y =x – 28 is the negative reciprocal of which is –.Incorrect
Your answer was incorrect.
Correct answer is: c.The answer is c. –
x + 14If line a (the original line) is perpendicular to line b (the 2nd line), then the slope of line a is the negative reciprocal of the slope of line b:
. Therefore, the slope of a line perpendicular to y =x – 28 is the negative reciprocal of which is –. -
Question 6 of 7
6. Question
The function below is most likely:
Hints:
- Remember for a linear function, the numbers would be increasing by a steady amount.
- Remember for an absolute value function, the y-values of x and –x (e.g., -3 and 3) are different.
- Try plotting these points and see what it looks like.
Correct
Your answer of c. quadratic was incorrect.The answer is: c. quadratic
One way to solve this problem is to quickly sketch out its graph – it becomes apparent that the graph is of a parabola. Another method of solving this problem is to go through process of elimination. The numbers are not increasing by a steady amount, ruling out a linear function. Absolute value is ruled out due to the fact that the y-values of x and -x (e.g. -3 and 3) are different. Finally, the exponential choice can be ruled out by the decreasing and increasing movement of y as x increases.
Incorrect
Your answer was incorrect.
Correct answer is: c. quadraticThe answer is: c. quadratic
One way to solve this problem is to quickly sketch out its graph – it becomes apparent that the graph is of a parabola. Another method of solving this problem is to go through process of elimination. The numbers are not increasing by a steady amount, ruling out a linear function. Absolute value is ruled out due to the fact that the y-values of x and -x (e.g. -3 and 3) are different. Finally, the exponential choice can be ruled out by the decreasing and increasing movement of y as x increases.
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Question 7 of 7
7. Question
For the given function, which of the following is true?
Hint: Take a look at the denominator. When does the function become undefined?
Correct
Your answer of a. The domain is all real numbers with x ? 1 was incorrect.
The answer is: a.
The domain is all real numbers with x ? 1.
The domain for a function is the set of all possible x-values. For the above function to hold true, the denominator must not be equal to 0, x – 1 ? 0, so x ? 1.
Incorrect
Your answer was incorrect.
Correct answer is: a. The domain is all real numbers with x ? 1The answer is: a.
The domain is all real numbers with x ? 1.
The domain for a function is the set of all possible x-values. For the above function to hold true, the denominator must not be equal to 0, x – 1 ? 0, so x ? 1.