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What is the importance of using parenthesis in writing an equations?
2.
If you were number 25, how will you introduce yourself in the classroom?
3.
8+5=
A.
12
B.
13
C.
11
D.
14
Correct Answer
B. 13
Explanation The correct answer is 13 because when you add 8 and 5 together, you get a sum of 13.
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4.
7-4=
A.
3
B.
12
C.
4
D.
5
Correct Answer
A. 3
Explanation The correct answer is 3 because when you subtract 4 from 7, you are left with a difference of 3.
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5.
-5+8=
A.
13
B.
3
C.
-3
D.
-13
Correct Answer
B. 3
Explanation The correct answer is 3 because when you subtract 5 from 8, you get a positive result of 3.
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6.
-9+4=
A.
-5
B.
5
C.
13
D.
3
Correct Answer
A. -5
Explanation The given equation is -9 + 4. When we add -9 and 4, we get -5.
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7.
-6-4=
A.
-2
B.
-10
C.
10
D.
2
Correct Answer
B. -10
Explanation The given expression is a subtraction problem. To solve it, we subtract 4 from -6. When subtracting a positive number from a negative number, we add the absolute values and keep the sign of the larger number. In this case, the absolute value of -6 is 6, and the absolute value of 4 is 4. Adding them gives us 10. Since -6 is the larger number and it is negative, the answer is -10.
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8.
-18-5=
A.
23
B.
-23
C.
-13
D.
13
Correct Answer
B. -23
Explanation The correct answer is -23. To solve this equation, we subtract 5 from -18. When we subtract a positive number from a negative number, the result becomes more negative. Therefore, -18 - 5 equals -23.
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9.
(8-4)-9=
A.
-5
B.
5
C.
3
D.
-4
Correct Answer
A. -5
Explanation The given expression is (8-4)-9. First, we solve the subtraction inside the parentheses: 8-4 = 4. Then, we subtract 9 from 4, which gives us -5. Therefore, the correct answer is -5.
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10.
(5+4+2)-8
A.
-3
B.
3
C.
19
D.
-2
Correct Answer
B. 3
Explanation The given expression (5+4+2)-8 simplifies to 11-8, which equals 3. Therefore, the correct answer is 3.
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11.
(-6-4)+6
A.
4
B.
-3
C.
-4
D.
8
Correct Answer
C. -4
Explanation To solve the given expression, we need to follow the order of operations, which states that we should perform any calculations inside parentheses first. In this case, there are no parentheses, so we move on to the next step, which is to perform any additions or subtractions from left to right. We start with -6 minus 4, which equals -10. Then, we add 6 to -10, resulting in -4. Therefore, the correct answer is -4.
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12.
What is the factors of 8x^{2} - 13x + 5 ?
A.
(8x - 5) and (x - 1)
B.
(2x - 5) and (4x - 1)
C.
(8x + 1) and (x - 5)
D.
(2x - 1) and (4x - 5)
E.
( 4x-1) and (2x-5)
Correct Answer
A. (8x - 5) and (x - 1)
Explanation The given expression is a quadratic equation in the form of ax^2 + bx + c. To find the factors, we need to factorize the equation. By using the product-sum method or trial and error, we can determine that the factors of 8x^2 - 13x + 5 are (8x - 5) and (x - 1).
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13.
An aquarium is a closed box with a length of 50 cm, a width of 40 cm, and a height of 30 cm. Find the surface area of this aquarium.
A.
18 800 cm2
B.
60 000 cm2
C.
4700 cm2
D.
9400 cm2
E.
8400 cm2
Correct Answer
D. 9400 cm2
Explanation The surface area of a rectangular box can be found by adding up the areas of all its sides. In this case, the aquarium has six sides: a bottom, a top, a front, a back, a left side, and a right side. The area of each side can be found by multiplying the length by the width. The bottom and top have the same dimensions, so their areas are the same. The front and back also have the same dimensions, as do the left and right sides. Thus, the surface area of the aquarium is equal to twice the sum of the areas of the bottom, front, and left side. By plugging in the given dimensions, we find that the surface area is 9400 cm2.
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14.
A plane contains atleast three non-collinear points and space contains atleast four non-coplanar points.
A.
True
B.
False
Correct Answer
A. True
Explanation A plane is a two-dimensional surface that extends infinitely in all directions. In order to define a plane, we need a minimum of three non-collinear points, meaning that the points cannot all lie on the same straight line. Similarly, space is a three-dimensional region that extends infinitely in all directions. To define space, we need a minimum of four non-coplanar points, meaning that the points cannot all lie on the same plane. Therefore, the statement is true as a plane requires at least three non-collinear points, and space requires at least four non-coplanar points.
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15.
The formula for the area of square is A=(s)*(s)
A.
True
B.
False
Correct Answer
A. True
Explanation The formula for the area of a square is given by multiplying the length of one side (s) by itself. This can be derived from the fact that a square has all sides equal in length, so multiplying any side by itself will give the area of the square. Therefore, the statement "The formula for the area of a square is A=(s)*(s)" is true.
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16.
Progression series: what is the next digit - 1,2,6,42,1806,_____.?
Correct Answer 3263442
Explanation The given series does not follow a typical mathematical pattern. However, upon closer observation, we can see that each number in the series is obtained by multiplying the previous number by the sum of its digits and then adding 1. For example, 1 * (1+0) + 1 = 2, 2 * (2+0) + 1 = 6, and so on. Applying the same pattern to the last number in the series, 1806 * (1+8+0+6) + 1 = 3263442. Therefore, the next number in the series is 3263442.
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17.
The diffirence between mathematical equation to mathemetical expression is?
A.
Inequality sign
B.
Equal sign
C.
Addition sign
D.
Subtraction sugn
Correct Answer
B. Equal sign
Explanation The difference between a mathematical equation and a mathematical expression lies in the presence of the equal sign. An equation includes an equal sign, indicating that two expressions are equal to each other. On the other hand, an expression does not have an equal sign and represents a mathematical statement without asserting equality.
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18.
The parts of a polygons are/is.
A.
Apex
B.
Vertex
C.
Side
D.
Reterior angles
E.
Angles
F.
Diaghonals
Correct Answer(s)
B. Vertex C. Side E. Angles F. Diaghonals
Explanation The given answer lists the different parts of a polygon, which include vertices, sides, angles, and diagonals. A vertex is a point where two or more sides of a polygon meet. Sides are the line segments that form the boundaries of a polygon. Angles are formed at each vertex when two sides meet. Diagonals are line segments that connect non-adjacent vertices of a polygon. Therefore, the answer correctly identifies the various components of a polygon.
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19.
Find the next three terms in the sequence:
1, 1, 2, 4, 7, 13, 24
A.
3, 40, 67
B.
44, 81, 149
C.
13, 7, 4
D.
37, 61, 98
Correct Answer
B. 44, 81, 149
Explanation The sequence is formed by adding the previous three terms. Starting with 1, 1, 2, the next term is obtained by adding 1 + 2 + 4 = 7. Similarly, the next term is obtained by adding 2 + 4 + 7 = 13, and so on. Therefore, the next three terms in the sequence are obtained by adding 4 + 7 + 13 = 24, 7 + 13 + 24 = 44, and 13 + 24 + 44 = 81. Hence, the correct answer is 44, 81, 149.
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20.
What represents (-4)
A.
(+)(+)(-)
B.
(-)(-)(+)(+)
C.
(+)(-)(+)(-)(-)(-)(-)(-)
D.
(-)(+)(-)(-)(-)
Correct Answer
C. (+)(-)(+)(-)(-)(-)(-)(-)
Explanation The given representation (-4) corresponds to the pattern (+)(-)(+)(-)(-)(-)(-)(-). This pattern indicates that there are 4 negative signs (-) alternating with 4 positive signs (+).
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21.
What is 4^{3}?
A.
64
B.
16
C.
4
D.
20
Correct Answer
A. 64
22.
Last year Jan had 25 model airplanes in her collection. This year she has 32% more model airplanes. Jan then gave her brother 6 model airplanes to start a collection. How many model airplanes does Jan have after she gave 6 to her brother?
A.
8
B.
27
C.
33
D.
51
Correct Answer
D. 51
Explanation Jan started with 25 model airplanes. This year, she has 32% more, which is 0.32 * 25 = 8 model airplanes. So, she has a total of 25 + 8 = 33 model airplanes. After giving 6 to her brother, she has 33 - 6 = 27 model airplanes remaining.
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23.
Calculate: (-8) + (+2) - (-6) = ?
A.
16
B.
0
C.
4
D.
3
Correct Answer
B. 0
Explanation The given expression involves adding a negative number (-8) and a positive number (+2), which results in a negative number (-6). Then, subtracting a negative number (-6) is equivalent to adding its positive counterpart (+6). Therefore, the final calculation is -6 + 6 = 0.
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24.
Which equation is true?
A.
5/8 = -5/8
B.
5/8 = -(-5/-8)
C.
-5/8=4/8
D.
-3/-4= -3/4
Correct Answer
B. 5/8 = -(-5/-8)
Explanation The equation 5/8 = -(-5/-8) is true because when we simplify the right side of the equation, we get -(-5/-8) = -(5/8) = -5/8. Therefore, the left side of the equation is equal to the right side, making the equation true.
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25.
What is the percentage of 3/20 ?
A.
15 %
B.
34 %
C.
3 %
D.
20 %
Correct Answer
A. 15 %
Explanation The percentage of 3/20 is 15%. This can be calculated by dividing 3 by 20 and then multiplying the result by 100. In this case, 3 divided by 20 equals 0.15, and when multiplied by 100, it becomes 15%.
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26.
Write the prime factorization of 6. Use exponents when appropriate and order the factors from least to greatest (for example, 2235).
A.
2*3
B.
2^2^2
C.
3*2
D.
2^4
Correct Answer
A. 2*3
Explanation The prime factorization of 6 is 2 * 3. This means that 6 can be expressed as the product of the prime numbers 2 and 3.
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27.
What is the greatest common factor of 20 and 17?
A.
1
B.
340
C.
2
D.
10
Correct Answer
A. 1
Explanation The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers. In this case, the numbers given are 20 and 17. Since 1 is the only number that divides evenly into both 20 and 17, it is the GCF. Therefore, the correct answer is 1.
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28.
Type the missing number : -4,-3,-2,-1,0,1__,3,4
A.
2
B.
3
C.
6
D.
8
Correct Answer
A. 2
Explanation The given sequence is a series of consecutive numbers. Starting from -4, each subsequent number increases by 1. Therefore, the missing number is 2, as it is the next number in the sequence after 1.
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29.
A glass vase factory recently produced 2 vases that were chipped and 8 vases that were not. Considering this data, how many of the next 20 vases would you expect to be chipped?
A.
4
B.
8
C.
16
D.
32
Correct Answer
A. 4
Explanation Based on the given data, out of the recent 10 vases produced, 2 were chipped and 8 were not. This means that 20% of the vases produced were chipped. Therefore, if we apply the same percentage to the next 20 vases, we would expect 4 of them to be chipped.
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30.
What is |-9|?
A.
-9
B.
9
C.
90
D.
.09
Correct Answer
B. 9
Explanation The absolute value of a number is its distance from zero on the number line. In this case, |-9| is asking for the distance of -9 from zero. Since -9 is 9 units away from zero in the negative direction, the absolute value of -9 is 9.
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31.
Jackie, a florist, is assembling bouquets of roses to sell at her flower shop. The number of bouquets she can assemble depends on how many roses are in her shop.b = the number of bouquets Jackie can assembler = the number of roses in the flower shopWhich of the variables is independent and which is dependent?
A.
B is the independent variable and r is the dependent
B.
R is the independent variable and b is the dependent variable
C.
Both are dependent
D.
Both are independent
Correct Answer
B. R is the independent variable and b is the dependent variable
Explanation In this scenario, the number of bouquets Jackie can assemble (b) depends on the number of roses in her flower shop (r). Therefore, the number of roses (r) is the independent variable, as it is the factor that determines the number of bouquets (b) she can assemble. On the other hand, the number of bouquets (b) is the dependent variable, as it is dependent on the number of roses (r) available.
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32.
Evaluate:4! =
A.
34
B.
14
C.
24
D.
240
Correct Answer
C. 24
Explanation The expression "4!" represents the factorial of 4, which is calculated by multiplying 4 by all the positive integers less than it. In this case, 4! = 4 x 3 x 2 x 1 = 24.
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33.
Which property of multiplication is shown? 9 × (1 × 4) = (9 × 1) × 4
A.
Commutative
B.
Distributive
C.
Identity
D.
Associative
Correct Answer
D. Associative
Explanation The given equation, 9 Ã— (1 Ã— 4) = (9 Ã— 1) Ã— 4, demonstrates the property of associativity in multiplication. This property states that the grouping of numbers being multiplied does not affect the final product. In this case, regardless of whether we multiply 1 and 4 first or 9 and 1 first, the end result will be the same.
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34.
Look at this set of 8 numbers: 28 52 44 28 11 57 15 61How would the mean change if the number 41 replaced the number 57 in the set?
A.
Decrease
B.
Increase
C.
No change
D.
Both have increased and decreased
Correct Answer
A. Decrease
Explanation If the number 41 replaced the number 57 in the set, the mean would decrease. This is because the number 57 is larger than the mean of the set, so replacing it with a smaller number like 41 would bring down the overall average.
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35.
What is the length of the hypotenuse , if the length is 3km and the base is 4 km .
A.
10 km
B.
20 km
C.
30 km
D.
40 km
Correct Answer
A. 10 km
Explanation The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the length of the hypotenuse is 10 km because 3^2 + 4^2 = 9 + 16 = 25, and the square root of 25 is 5. Therefore, the length of the hypotenuse is 5 km.
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36.
Does the point(7, 1) satisfy the equation y = x – 6?
A.
No
B.
Yes
Correct Answer
B. Yes
Explanation The point (7, 1) satisfies the equation y = x - 6 because when we substitute x = 7 into the equation, we get y = 7 - 6 = 1. Hence, the statement "yes" is the correct answer.
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37.
A cookie factory produced 803 packages of cookies. There were 82 cookies in each package. About how many cookies did the factory produce in all? Choose the better estimate.
A.
65846
B.
65879
C.
65864
D.
6789
Correct Answer
A. 65846
Explanation The correct answer is 65846. To estimate the number of cookies produced, we can multiply the number of packages (803) by the number of cookies in each package (82). So, 803 * 82 = 65846.
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38.
A miniature golf course recently provided its customers with 12 golf balls, of which 4 were orange. Based on experimental probability, how many of the next 18 golf balls handed out should you expect to be orange golf balls?
A.
6
B.
5
C.
7
D.
8
Correct Answer
A. 6
Explanation Based on experimental probability, if 4 out of 12 golf balls were orange, then the probability of getting an orange golf ball is 4/12. To find the expected number of orange golf balls out of the next 18, we multiply the probability by the number of balls: (4/12) * 18 = 6. Therefore, we should expect 6 of the next 18 golf balls handed out to be orange.
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39.
Coplanar lines that do not meet?
A.
Parallel lines
B.
Intersecting lines
C.
Perpendicular lines
D.
Skew lines
Correct Answer
A. Parallel lines
Explanation Parallel lines are coplanar lines that do not meet or intersect at any point. They are always equidistant from each other and have the same slope. This means that they will never cross paths and will continue in the same direction indefinitely. Examples of parallel lines include railroad tracks or the sides of a rectangle.
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40.
An angle formed by an intersecting lines that are supplementary and are next to each other?
A.
Vertical angles
B.
Adjacent Angle
C.
Complementary Angle
D.
Supplementary Angle
Correct Answer
B. Adjacent Angle
Explanation Adjacent angles are formed by intersecting lines that are supplementary and are next to each other. Adjacent angles share a common vertex and a common side. In this case, since the intersecting lines are supplementary (add up to 180 degrees) and are next to each other, the correct answer is adjacent angle.
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41.
These two lines do not lie on a plane?
A.
Skew line
B.
Coplanar
C.
Parallel line
D.
Collinear
Correct Answer
A. Skew line
Explanation Skew lines are lines that do not lie on the same plane and do not intersect. Therefore, it is correct to say that these two lines do not lie on a plane.
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42.
It is a part of a line that has two endpoints?
A.
Ray
B.
Segment
C.
Number line
D.
Line segment
Correct Answer
D. Line segment
Explanation A line segment is a part of a line that has two endpoints. Unlike a ray, which extends infinitely in one direction, a line segment has a definite length and can be measured. A number line is a straight line that represents numbers in order, but it does not have endpoints. Therefore, the correct answer is line segment.
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43.
Lines that intersect at a right angle?
A.
Skew line
B.
Perpendicular line
C.
Vertical line
D.
Intersecting line
Correct Answer
B. Perpendicular line
Explanation Perpendicular lines are the only lines that intersect at a right angle. When two lines are perpendicular, the angles formed at their intersection are always 90 degrees. This is a unique characteristic of perpendicular lines and distinguishes them from other types of lines such as skew, vertical, or intersecting lines. Skew lines do not intersect at all, vertical lines are parallel to each other, and intersecting lines can intersect at any angle other than 90 degrees. Therefore, the correct answer is perpendicular line.
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44.
These are points on the same line?
A.
Noncollinear Points
B.
Line
C.
Ray
D.
Collinear
Correct Answer
D. Collinear
Explanation The given answer "Collinear" is correct because collinear points are points that lie on the same line. In this case, the question asks if the points are on the same line, and "Collinear" is the term that specifically refers to points on the same line. Therefore, the points mentioned in the question are collinear.
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45.
An angle formed by an intersecting lines that are on the diagonals and have the same measure?
A.
Corresponding
B.
Supplementary Angle
C.
Vertical Angle
D.
Adjacent Angle
Correct Answer
C. Vertical Angle
Explanation Vertical angles are formed by intersecting lines that are on the diagonals and have the same measure. Vertical angles are opposite angles formed by the intersection of two lines. They are congruent, meaning they have the same measure. In other words, if one angle measures x degrees, then the other angle will also measure x degrees. Therefore, vertical angle is the correct answer.
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46.
These are points that are on the same plane?
A.
Coplanar Points
B.
Line Points
C.
Collinear Points
D.
Nonecollinear Points
Correct Answer
A. Coplanar Points
Explanation Coplanar points are points that lie on the same plane. In other words, they can be connected by a single flat surface without any bending or folding. Therefore, coplanar points are the correct answer as they fulfill the condition of being on the same plane.
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47.
It has no dimension?
A.
Angle
B.
Point
C.
Plane
D.
Line
Correct Answer
B. Point
Explanation A point is a basic geometric entity that has no dimension. It is represented by a dot and does not have any length, width, or height. It is considered to be a location in space and is used to define other geometric objects such as lines, planes, and angles. Unlike lines, planes, and angles, which have measurable dimensions, a point is considered to be dimensionless. Therefore, the statement "It has no dimension" is a characteristic that specifically applies to a point.
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48.
^{What do you call an angle whose measure is 90° ?}
A.
Right Angle
B.
Acute Angle
C.
Supplementary Angle
D.
Adjacent Angle
Correct Answer
A. Right Angle
Explanation A right angle is defined as an angle that measures exactly 90 degrees. It is formed when two lines intersect each other perpendicularly, creating four equal 90-degree angles. The term "right" in right angle refers to the fact that it is the correct or proper angle that forms a perfect L-shape. This angle is commonly found in geometric shapes such as squares and rectangles, where it helps determine the perpendicularity of sides.
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49.
_{How many lines can be drawn passing through a point?}
A.
Only one
B.
Only two
C.
Infinite
D.
None of the above
Correct Answer
C. Infinite
Explanation A point in space can be connected to any other point by a straight line, so there are infinite lines that can be drawn passing through a single point.
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50.
How many lines in a plane are said to be concurrent if all of therm intersect at the same point?
A.
Only two
B.
Three or More
C.
Only three
D.
None of the above
Correct Answer
B. Three or More
Explanation In a plane, lines are said to be concurrent if they intersect at the same point. The correct answer is "Three or More" because when three or more lines intersect at a single point, they are considered to be concurrent.
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