Q. What is the y-intercept of the line represented by the equation y = -3x + 6?
Solution
The y-intercept is the constant term when x = 0, which is 6.
Correct Answer:
A
— 6
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Q. What is the y-intercept of the line represented by the equation y = -3x + 7?
Solution
The y-intercept is the constant term when x = 0, which is 7.
Correct Answer:
A
— 7
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Q. What type of angles are formed when a transversal intersects two parallel lines?
-
A.
Complementary angles
-
B.
Supplementary angles
-
C.
Equal angles
-
D.
All of the above
Solution
When a transversal intersects two parallel lines, it forms complementary, supplementary, and equal angles.
Correct Answer:
D
— All of the above
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Q. What type of polygon has all sides and angles equal?
-
A.
Scalene triangle
-
B.
Isosceles triangle
-
C.
Regular polygon
-
D.
Irregular polygon
Solution
A regular polygon is defined as a polygon with all sides and angles equal.
Correct Answer:
C
— Regular polygon
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Q. What type of polygon is a shape with 5 sides?
-
A.
Triangle
-
B.
Quadrilateral
-
C.
Pentagon
-
D.
Hexagon
Solution
A polygon with 5 sides is called a pentagon.
Correct Answer:
C
— Pentagon
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Q. What type of quadrilateral has all sides equal and all angles equal?
-
A.
Square
-
B.
Rectangle
-
C.
Rhombus
-
D.
Trapezoid
Solution
A square is a type of quadrilateral that has all sides equal and all angles equal (90 degrees).
Correct Answer:
A
— Square
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Q. What type of quadrilateral has one pair of parallel sides?
-
A.
Rectangle
-
B.
Square
-
C.
Trapezoid
-
D.
Rhombus
Solution
A trapezoid is defined as a quadrilateral that has at least one pair of parallel sides.
Correct Answer:
C
— Trapezoid
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Q. What type of quadrilateral has opposite sides that are equal and all angles are right angles?
-
A.
Rectangle
-
B.
Rhombus
-
C.
Trapezoid
-
D.
Parallelogram
Solution
A rectangle is defined as a quadrilateral with opposite sides equal and all angles measuring 90 degrees.
Correct Answer:
A
— Rectangle
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Q. What type of triangle has all sides of different lengths?
-
A.
Equilateral
-
B.
Isosceles
-
C.
Scalene
-
D.
Right
Solution
A triangle with all sides of different lengths is called a scalene triangle.
Correct Answer:
C
— Scalene
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Q. What type of triangle is formed by the vertices (0,0), (4,0), and (2,3)?
-
A.
Equilateral
-
B.
Isosceles
-
C.
Scalene
-
D.
Right
Solution
The triangle has two sides of equal length (the distances from (0,0) to (2,3) and from (4,0) to (2,3)), making it an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. When two parallel lines are intersected by a transversal, which angles are always equal?
-
A.
Same-side interior angles
-
B.
Alternate interior angles
-
C.
Vertical angles
-
D.
Same-side exterior angles
Solution
Alternate interior angles are equal when two parallel lines are cut by a transversal.
Correct Answer:
B
— Alternate interior angles
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Q. Which equation represents the double angle identity for sine?
-
A.
sin(2x) = 2sin(x)cos(x)
-
B.
sin(2x) = sin²(x) + cos²(x)
-
C.
sin(2x) = sin(x) + cos(x)
-
D.
sin(2x) = 2sin²(x)
Solution
The double angle identity for sine is sin(2x) = 2sin(x)cos(x).
Correct Answer:
A
— sin(2x) = 2sin(x)cos(x)
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Q. Which expression represents the difference of squares for a^2 - b^2?
-
A.
(a + b)(a - b)
-
B.
(a - b)(a + b)
-
C.
(a + b)^2
-
D.
(a - b)^2
Solution
The difference of squares is factored as (a + b)(a - b).
Correct Answer:
A
— (a + b)(a - b)
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Q. Which expression represents the difference of squares for x^2 - 16?
-
A.
(x - 4)(x + 4)
-
B.
(x - 8)(x + 8)
-
C.
(x - 2)(x + 2)
-
D.
(x - 16)(x + 16)
Solution
The expression can be factored as (x - 4)(x + 4) since 16 is 4^2.
Correct Answer:
A
— (x - 4)(x + 4)
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Q. Which expression represents the expansion of (x + 2)(x - 3)?
-
A.
x^2 - x - 6
-
B.
x^2 - x + 6
-
C.
x^2 + x - 6
-
D.
x^2 + x + 6
Solution
Use the distributive property: x^2 - 3x + 2x - 6 = x^2 - x - 6.
Correct Answer:
A
— x^2 - x - 6
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Q. Which expression represents the expansion of (x + 2)^2?
-
A.
x^2 + 4
-
B.
x^2 + 4x + 4
-
C.
x^2 + 2x + 2
-
D.
x^2 + 2x + 4
Solution
Use the formula (a + b)^2 = a^2 + 2ab + b^2: (x + 2)^2 = x^2 + 4x + 4.
Correct Answer:
B
— x^2 + 4x + 4
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Q. Which expression represents the factored form of x^2 + 5x + 6?
-
A.
(x + 2)(x + 3)
-
B.
(x - 2)(x - 3)
-
C.
(x + 1)(x + 6)
-
D.
(x - 1)(x - 6)
Solution
The expression factors to (x + 2)(x + 3) since 2 and 3 add to 5 and multiply to 6.
Correct Answer:
A
— (x + 2)(x + 3)
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Q. Which expression represents the factored form of x^2 + 7x + 10?
-
A.
(x + 5)(x + 2)
-
B.
(x - 5)(x - 2)
-
C.
(x + 10)(x - 1)
-
D.
(x - 10)(x + 1)
Solution
The expression factors to (x + 5)(x + 2) since 5 and 2 add to 7 and multiply to 10.
Correct Answer:
A
— (x + 5)(x + 2)
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Q. Which expression represents the factored form of x^2 - 16?
-
A.
(x - 4)(x + 4)
-
B.
(x - 8)(x + 2)
-
C.
(x - 2)(x + 2)
-
D.
(x + 4)(x + 4)
Solution
This is a difference of squares: x^2 - 4^2 = (x - 4)(x + 4).
Correct Answer:
A
— (x - 4)(x + 4)
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Q. Which expression represents the factored form of x^2 - 9?
-
A.
(x - 3)(x + 3)
-
B.
(x - 1)(x + 1)
-
C.
(x - 2)(x + 2)
-
D.
(x - 4)(x + 4)
Solution
Step 1: Recognize it as a difference of squares: x^2 - 3^2. Step 2: Factor: (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. Which expression represents the polynomial 3x^2 + 5x - 2 factored?
-
A.
(3x - 1)(x + 2)
-
B.
(3x + 2)(x - 1)
-
C.
(x + 2)(3x - 1)
-
D.
(x - 2)(3x + 1)
Solution
To factor, find two numbers that multiply to -6 and add to 5: (3x - 1)(x + 2).
Correct Answer:
A
— (3x - 1)(x + 2)
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Q. Which expression represents the sum of the first n terms of an arithmetic series with first term a and common difference d?
-
A.
n/2 * (2a + (n-1)d)
-
B.
n * (a + d)
-
C.
n * a + d
-
D.
n/2 * (a + d)
Solution
The formula for the sum of the first n terms is S_n = n/2 * (2a + (n-1)d).
Correct Answer:
A
— n/2 * (2a + (n-1)d)
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Q. Which expression represents the sum of the polynomials (2x^2 + 3x) and (4x^2 - x)?
-
A.
6x^2 + 2x
-
B.
2x^2 + 4x
-
C.
6x^2 + 4x
-
D.
2x^2 + 2x
Solution
Step 1: Combine like terms: (2x^2 + 4x^2) + (3x - x) = 6x^2 + 2x.
Correct Answer:
A
— 6x^2 + 2x
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Q. Which expression represents the sum of the polynomials (3x^2 + 2x) and (4x^2 - 5x)?
-
A.
7x^2 - 3x
-
B.
7x^2 + 3x
-
C.
x^2 - 3x
-
D.
x^2 + 3x
Solution
Step 1: Combine like terms: (3x^2 + 4x^2) + (2x - 5x) = 7x^2 - 3x.
Correct Answer:
A
— 7x^2 - 3x
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Q. Which expression represents the sum of the roots of the equation x^2 - 6x + 8 = 0?
Solution
Step 1: The sum of the roots is given by -b/a: 6/1 = 6.
Correct Answer:
A
— 6
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Q. Which expression represents the sum of the roots of the quadratic equation x^2 + 6x + 8 = 0?
Solution
The sum of the roots is given by -b/a. Here, b = 6, so the sum is -6.
Correct Answer:
A
— -6
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Q. Which inequality represents the solution set for x + 4 < 10?
-
A.
x < 6
-
B.
x > 6
-
C.
x ≤ 6
-
D.
x ≥ 6
Solution
To solve the inequality, subtract 4 from both sides: x < 6.
Correct Answer:
A
— x < 6
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Q. Which inequality represents the solution set for x^2 - 4 < 0?
-
A.
x < -2 or x > 2
-
B.
-2 < x < 2
-
C.
x > -2 and x < 2
-
D.
x < 2
Solution
The inequality x^2 - 4 < 0 can be factored as (x - 2)(x + 2) < 0. The solution set is -2 < x < 2.
Correct Answer:
B
— -2 < x < 2
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Q. Which inequality represents the solution to the equation 4x - 8 = 0?
-
A.
x < 2
-
B.
x > 2
-
C.
x = 2
-
D.
x ≤ 2
Solution
To solve the equation, add 8 to both sides: 4x = 8. Then divide by 4: x = 2. The solution is x = 2.
Correct Answer:
C
— x = 2
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Q. Which measure of central tendency is most affected by extreme values?
-
A.
Mean
-
B.
Median
-
C.
Mode
-
D.
Range
Solution
The mean is most affected by extreme values, as it takes all values into account.
Correct Answer:
A
— Mean
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