Daily Digest Exam 1-1 Algebra I
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Algebra I - 1st Quarter Summative Assessment
Questions and Answers
- 1.
What is 35% of 20?
Explanation
To find 35% of 20, you can multiply 20 by 0.35. This will give you the result of 7, which represents 35% of 20. Alternatively, you can express the answer as 7.0, which is the same value but with a decimal point.Rate this question:
- 2.
Find the absolute value of x in: x = -13 + 13
Explanation
The absolute value of a number is the distance of that number from zero on the number line. In this case, x is equal to -13 + 13 which simplifies to 0. Therefore, the absolute value of x is 0, as it is exactly 0 units away from zero on the number line.Rate this question:
- 3.
A bag contains 2 orange marbles, 4 purple marbles, and 6 green marble. What is the probability of pulling out an orange marble on the first pick? Express your answer as a simplified fraction.
Explanation
The probability of pulling out an orange marble on the first pick can be found by dividing the number of orange marbles (2) by the total number of marbles (12). Simplifying this fraction gives us 1/6.Rate this question:
- 4.
A bag contains 2 orange marbles, 4 purple marbles, and 6 green marble. What is the probability of pulling out a purple marble on the first pick? Express your answer as a simplified fraction.
Explanation
The probability of pulling out a purple marble on the first pick can be calculated by dividing the number of purple marbles by the total number of marbles in the bag. In this case, there are 4 purple marbles and a total of 12 marbles in the bag. Simplifying the fraction 4/12 gives us 1/3, so the probability of pulling out a purple marble on the first pick is 1/3.Rate this question:
- 5.
A bag contains 2 orange marbles, 4 purple marbles, and 6 green marble. What is the probability of pulling out a green marble on the first pick? Express your answer as a simplified fraction.
Explanation
The probability of pulling out a green marble on the first pick can be determined by dividing the number of green marbles (6) by the total number of marbles (12). Simplifying the fraction 6/12 gives 1/2, which represents the probability of pulling out a green marble on the first pick.Rate this question:
- 6.
Find the slope (m) of the line that contains the following points. P1 = ( -1, 9) P2 = ( 1, 5)
Explanation
The slope of a line can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Plugging in the values from the given points, we get (5 - 9) / (1 - (-1)) = -4 / 2 = -2. Therefore, the slope of the line is -2.Rate this question:
- 7.
Which point on the graph represents the following coordinate: ( -1, -8) ?
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
B. BExplanation
The point on the graph that represents the coordinate (-1, -8) is point B.Rate this question:
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- 8.
Which point on the graph represents the following coordinate: ( -1, 8) ?
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
A. AExplanation
Point A represents the coordinate (-1, 8) on the graph.Rate this question:
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- 9.
Which point on the graph represents the following coordinate: ( 8, -1) ?
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
D. DExplanation
The point (8, -1) on the graph is represented by point D.Rate this question:
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- 10.
Find the absolute value of x in: x = -5 - ( -5)
Correct Answer
0Explanation
The absolute value of a number is the distance of that number from zero on the number line. In this case, the expression -5 - (-5) simplifies to -5 + 5, which equals 0. Therefore, the absolute value of 0 is 0.Rate this question:
- 11.
Find the absolute value of x in: x = - 4 - 4
Correct Answer
8Explanation
The absolute value of a number is its distance from zero on the number line. In this case, the given equation x = -4 - 4 / 8 can be simplified to x = -8 / 8, which further simplifies to x = -1. Therefore, the absolute value of x is 1.Rate this question:
- 12.
Using the figure, compute the perimeter if x = 5 and y =9.
Correct Answer
28 - 13.
Using the figure, compute the perimeter if x = 4 and y =8
Correct Answer
24Explanation
The perimeter of a shape is the sum of the lengths of all its sides. In this figure, there are two sides with length x and two sides with length y. Given that x = 4 and y = 8, we can calculate the perimeter by adding the lengths of all the sides: 4 + 4 + 8 + 8 = 24.Rate this question:
- 14.
Using the figure, compute the perimeter if x = 6, y = 8, and z =10.
Correct Answer
24Explanation
The perimeter of a shape is the sum of the lengths of all its sides. In this figure, there are four sides: two sides with length x, one side with length y, and one side with length z. Given that x = 6, y = 8, and z = 10, we can calculate the perimeter by adding the lengths of all the sides: 6 + 6 + 8 + 10 = 30. Therefore, the answer of 24 is incorrect.Rate this question:
- 15.
Using the figure, compute the perimeter if a = 5, b =12, and c =13.
Correct Answer
30 - 16.
Using the figure, compute the circumference if x = 7.
Correct Answer
14pi
14 piExplanation
The circumference of a circle can be calculated using the formula C = 2πr, where π is a constant equal to approximately 3.14 and r is the radius of the circle. In this question, the value of x is given as 7, which represents the radius of the circle. By substituting this value into the formula, we can calculate the circumference as 2π(7) = 14π. Therefore, the correct answer is 14π or 14 pi.Rate this question:
- 17.
Using the figure, compute the circumference if x = 12.
Correct Answer
12pi
12 piExplanation
The circumference of a circle is calculated using the formula C = 2πr, where r is the radius of the circle. In this case, the value of x is given as 12, which represents the radius of the circle. Therefore, substituting x = 12 into the formula, we get C = 2π(12) = 24π, which simplifies to 24π or 24 pi.Rate this question:
- 18.
Using the figure, compute the volume if x = 3 and z = 2.
Correct Answer
18 - 19.
Using the figure, compute the volume if x = 5.
Correct Answer
125 - 20.
What is 2/5 of 25?
Correct Answer
10Explanation
To find 2/5 of 25, we can multiply 25 by 2/5. This can be done by multiplying 25 by the numerator (2) and then dividing the result by the denominator (5). So, 25 multiplied by 2 equals 50, and when we divide 50 by 5, we get the answer of 10. Therefore, 2/5 of 25 is 10.Rate this question:
- 21.
Factor the following: x^2 + 11x +10
Correct Answer
(x+10)(x+1)
(x+1)(x+10)Explanation
The given expression can be factored as (x+10)(x+1) or (x+1)(x+10). Both of these expressions are equivalent and represent the factored form of x^2 + 11x + 10.Rate this question:
- 22.
Simplify: 5x - 10y + 8x + 15y
Correct Answer
13x+5y
5y+13xExplanation
The given expression involves adding and subtracting variables with coefficients. By combining like terms, we can simplify the expression to 13x + 5y. The order of the terms does not affect the result, so 5y + 13x is also a valid simplified form.Rate this question:
- 23.
Given the equation y = 3x + 4. What is the slope of the line?
Correct Answer
3
+3Explanation
The slope of a line is the coefficient of the x term in the equation of the line. In this case, the equation is y = 3x + 4, so the coefficient of the x term is 3. Therefore, the slope of the line is 3.Rate this question:
- 24.
Given the equation y = 2x + 5. At what y value does the line cross the y-axis?
Correct Answer
5
+5Explanation
The line crosses the y-axis at the point (0, 5) because the y-intercept is the value of y when x is equal to 0. In the equation y = 2x + 5, when x is 0, the equation becomes y = 2(0) + 5, which simplifies to y = 5. Therefore, the line crosses the y-axis at y = 5.Rate this question:
- 25.
Given the equation y = 2x + 4. What is the y value when x = 3?
Correct Answer
10
+10Explanation
When the equation y = 2x + 4 is given, it means that the value of y is equal to 2 times the value of x, plus 4. In this case, when x = 3, we can substitute this value into the equation to find the value of y. Therefore, y = 2(3) + 4 = 6 + 4 = 10. So, the y value when x = 3 is 10.Rate this question:
- 26.
Given the equation y = 2x + 4. What is the y value when x = -4?
Correct Answer
-4 - 27.
Given the equation y = x + 4. What is the y value when x = - 4?
Correct Answer
0Explanation
When x = -4, we can substitute this value into the equation y = x + 4. Thus, y = -4 + 4 = 0. Therefore, the y value when x = -4 is 0.Rate this question:
- 28.
Using the figure, compute the area if x = 4.
Correct Answer
4pi
4 pi - 29.
Using the figure, compute the area if x = 3.
Correct Answer
9pi
9 piExplanation
The area can be calculated using the formula A = πr^2, where r is the radius of the circle. In this case, the radius is given as x = 3. Plugging this value into the formula, we get A = π(3)^2 = 9π. Therefore, the area is 9π.Rate this question:
- 30.
Using the figure, compute the area if a = 10, b =?, and c =26.
Correct Answer
120 - 31.
Simplify: 4x + 4xy + 8xy + 4y
Correct Answer
4x+12xy+4y
4x+4y+12xy
4y+4xy+4xExplanation
The given expression is a sum of terms that contain variables x and y. To simplify the expression, we can combine like terms by adding the coefficients of the same variables. In this case, the terms 4xy and 8xy have the same variables, so we can add their coefficients to get 12xy. The terms 4x and 4y do not have any other terms with the same variables, so they remain unchanged. Therefore, the simplified expression is 4x + 12xy + 4y. The other two answer choices are just different ways of writing the same simplified expression.Rate this question:
- 32.
Using the figure, compute the area if x = 7 and y =10.
Correct Answer
70Explanation
The formula to calculate the area of a rectangle is length multiplied by width. In this case, x is the length and y is the width. Substituting the given values, x = 7 and y = 10, into the formula, we get 7 * 10 = 70. Therefore, the area of the rectangle is 70.Rate this question:
- 33.
Using the figure, compute the area if x = 3 and y =7.
Correct Answer
21 - 34.
Using the figure, compute the area if x = 9, y = ?, and z = 15.
Correct Answer
54 - 35.
Which of the following represents the equation of the graph below?
- A.
Y = -1x - 1
- B.
Y = -1x + 1
- C.
Y = 1x - 1
- D.
Y = 1x + 1
Correct Answer
C. Y = 1x - 1Explanation
The equation y = 1x - 1 represents the graph below because it has a slope of 1, meaning that for every increase of 1 in the x-coordinate, there is a corresponding increase of 1 in the y-coordinate. Additionally, the equation has a y-intercept of -1, which is where the graph intersects the y-axis.Rate this question:
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- 36.
Which point on the graph represents the following coordinate: ( 8, 1) ?
- A.
A
- B.
B
- C.
C
- D.
D
Correct Answer
C. CExplanation
Point C on the graph represents the coordinate (8, 1) because it is the only point that is located at x = 8 and y = 1.Rate this question:
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- 37.
Which of the following represents the equation of the graph below?
- A.
Y = -2x - 2
- B.
Y = -2x + 2
- C.
Y = 2x - 2
- D.
Y = 2x + 2
Correct Answer
D. Y = 2x + 2Explanation
The equation of the graph can be determined by analyzing the slope and y-intercept. In this case, the slope is positive 2 and the y-intercept is positive 2. The equation y = 2x + 2 represents a line with a slope of 2 and a y-intercept of 2, which matches the given graph.Rate this question:
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- 38.
Which of the following represents the equation of the graph below?
- A.
Y = -2x - 3
- B.
Y = -2x + 3
- C.
Y = -3x - 2
- D.
Y = 3x - 3
Correct Answer
A. Y = -2x - 3Explanation
The equation of the graph can be determined by observing the slope and y-intercept. In this case, the slope is -2 and the y-intercept is -3. Therefore, the equation that represents the graph is y = -2x - 3.Rate this question:
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- 39.
Factor the following: x^2 - 9x +20
Correct Answer
(x-5)(x-4)
(x-4)(x-5)Explanation
The given expression can be factored as (x-5)(x-4) or (x-4)(x-5). Both of these factorizations are equivalent and correct.Rate this question:
- 40.
Factor the following: x^2 - 2x - 24
Correct Answer
(x-6)(x+4)
(x+4)(x-6)Explanation
The correct answer is (x-6)(x+4) or (x+4)(x-6). This is the factored form of the given quadratic expression x^2 - 2x - 24. The factoring was done by finding two numbers that multiply to -24 and add up to -2, which are -6 and 4. Therefore, the factors are (x-6) and (x+4). The order of the factors can be reversed, resulting in (x+4)(x-6).Rate this question:
- 41.
Factor the following: x^2 + 9x - 36
Correct Answer
(x+12)(x-3)
(x-3)(x+12)Explanation
The given expression can be factored as (x+12)(x-3) or (x-3)(x+12). Both of these factorizations are correct and equivalent.Rate this question:
- 42.
If the area of a cirlce is 49pi, what is the measure of its radius?
Correct Answer
7Explanation
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the area is given as 49π. By substituting this value into the formula, we get 49π = πr^2. Simplifying the equation, we can cancel out the π on both sides, leaving us with 49 = r^2. Taking the square root of both sides, we find that the radius, r, is equal to 7.Rate this question:
- 43.
If the perimeter of a square is 28, what is the measure of its length?
Correct Answer
7Explanation
The perimeter of a square is the sum of all its sides. Since a square has all sides equal in length, we can divide the perimeter by 4 to find the length of each side. In this case, the perimeter is given as 28, so dividing it by 4 gives us a length of 7 for each side of the square.Rate this question:
- 44.
If the perimeter of a square is 28, what is the measure of its length?
Correct Answer
7Explanation
The perimeter of a square is the sum of all its sides. In this case, the perimeter is given as 28. Since all sides of a square are equal in length, we can divide the perimeter by 4 to find the length of each side. 28 divided by 4 is equal to 7, so the measure of the length of each side of the square is 7.Rate this question:
- 45.
What is the area of a triangle that has a hypoetnuse of 20 and a base of 16?
Correct Answer
96Explanation
The area of a triangle can be calculated using the formula A = 1/2 * base * height. In this case, the base of the triangle is given as 16. However, the height is not provided in the question. Without the height, it is not possible to calculate the area of the triangle accurately. Therefore, an explanation for the given answer of 96 is not available.Rate this question:
.jpg "Which point on the graph represents the following coordinate: ( -1, -8) ?")
.jpg "Using the figure, compute the circumference if x = 7.")
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