Q. In the polynomial expression 4x^3 - 2x^2 + x - 5, which term is the constant term?
-
A.
4x^3
-
B.
-2x^2
-
C.
x
-
D.
-5
Solution
The constant term in a polynomial is the term that does not contain any variables, which in this case is -5.
Correct Answer:
D
— -5
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Q. In the polynomial expression 4x^3 - 3x^2 + 2x - 1, which term is the constant term?
-
A.
4x^3
-
B.
-3x^2
-
C.
2x
-
D.
-1
Solution
The constant term in a polynomial is the term that does not contain any variable, which in this case is -1.
Correct Answer:
D
— -1
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Q. In the polynomial f(x) = 2x^3 - 3x^2 + x - 5, what is the coefficient of x^2?
Solution
The coefficient of x^2 in the polynomial f(x) = 2x^3 - 3x^2 + x - 5 is -3.
Correct Answer:
B
— -3
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Q. In the polynomial f(x) = 2x^4 - 3x^3 + x - 5, what is the coefficient of x^3?
Solution
The coefficient of x^3 in the polynomial f(x) = 2x^4 - 3x^3 + x - 5 is -3.
Correct Answer:
A
— -3
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Q. In the polynomial h(x) = 4x^3 - 2x^2 + 3, what is the constant term?
Solution
The constant term in the polynomial h(x) = 4x^3 - 2x^2 + 3 is 3.
Correct Answer:
C
— 3
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Q. In the polynomial k(x) = 2x^4 - 3x^3 + 0x^2 + 5, what is the term with the highest degree?
-
A.
2x^4
-
B.
-3x^3
-
C.
0x^2
-
D.
5
Solution
The term with the highest degree in the polynomial k(x) is 2x^4, as it has the highest exponent.
Correct Answer:
A
— 2x^4
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Q. In the polynomial P(x) = 3x^4 - 2x^3 + x - 7, what is the constant term?
Solution
The constant term in the polynomial P(x) is the term that does not contain any variable, which is -7.
Correct Answer:
D
— -7
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Q. In the polynomial P(x) = 4x^3 - 2x^2 + x - 7, what is the constant term?
Solution
The constant term in the polynomial P(x) is -7.
Correct Answer:
D
— -7
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Q. In the polynomial P(x) = 5x^4 - 2x^3 + x - 7, what is the constant term?
Solution
The constant term in the polynomial P(x) is -7.
Correct Answer:
D
— -7
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Q. In the quadratic equation 3x^2 - 12x + 9 = 0, what is the nature of the roots?
-
A.
Two distinct real roots
-
B.
One real root
-
C.
Two complex roots
-
D.
No roots
Solution
The discriminant is zero (0), indicating one real root (a repeated root).
Correct Answer:
B
— One real root
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Q. In the quadratic equation x^2 + 6x + 9 = 0, what type of roots does it have?
-
A.
Real and distinct
-
B.
Real and equal
-
C.
Complex
-
D.
Imaginary
Solution
The discriminant is zero, indicating that the roots are real and equal.
Correct Answer:
B
— Real and equal
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Q. In the quadratic equation x² + 6x + 9 = 0, what is the nature of the roots?
-
A.
Real and distinct
-
B.
Real and equal
-
C.
Complex
-
D.
Imaginary
Solution
The discriminant is 0 (b² - 4ac = 0), indicating that the roots are real and equal.
Correct Answer:
B
— Real and equal
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Q. In the series 2, 4, 8, 16, what is the 5th term? (2023)
Solution
The series is a geometric series with a common ratio of 2. The 5th term is 2 * 2^4 = 32.
Correct Answer:
A
— 32
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Q. In the series 2, 4, 8, 16, what is the pattern followed? (2023)
-
A.
Addition
-
B.
Subtraction
-
C.
Multiplication
-
D.
Division
Solution
Each term is obtained by multiplying the previous term by 2, indicating a multiplication pattern.
Correct Answer:
C
— Multiplication
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Q. In the series 2, 5, 10, 17, what is the pattern in the differences between consecutive terms? (2023)
-
A.
Increasing by 1
-
B.
Increasing by 2
-
C.
Increasing by 3
-
D.
Increasing by 4
Solution
The differences are 3, 5, 7, which are increasing by 2 each time.
Correct Answer:
C
— Increasing by 3
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Q. In the series 2, 5, 10, 17, what is the pattern used to generate the next term? (2023)
-
A.
Add consecutive odd numbers
-
B.
Add consecutive even numbers
-
C.
Multiply by 2
-
D.
Subtract 1
Solution
The pattern is to add consecutive odd numbers: 2 + 3 = 5, 5 + 5 = 10, 10 + 7 = 17. The next term is 17 + 9 = 26.
Correct Answer:
A
— Add consecutive odd numbers
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Q. In triangle ABC, if angle A is 30 degrees and angle B is 60 degrees, what is the measure of angle C?
-
A.
30 degrees
-
B.
60 degrees
-
C.
90 degrees
-
D.
120 degrees
Solution
Using the property that the sum of angles in a triangle is 180 degrees, angle C can be calculated as 180 - (30 + 60) = 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. In triangle DEF, if angle D is 45 degrees and angle E is 45 degrees, what is the type of triangle?
-
A.
Scalene
-
B.
Isosceles
-
C.
Equilateral
-
D.
Right
Solution
Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if angle D is 45 degrees and angle E is 45 degrees, what type of triangle is DEF?
-
A.
Scalene
-
B.
Isosceles
-
C.
Equilateral
-
D.
Right-angled
Solution
Since two angles are equal (45 degrees each), triangle DEF is an isosceles triangle.
Correct Answer:
B
— Isosceles
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Q. In triangle DEF, if angle D is 90 degrees and the lengths of the legs are 6 cm and 8 cm, what is the length of the hypotenuse?
-
A.
10 cm
-
B.
12 cm
-
C.
14 cm
-
D.
16 cm
Solution
Using the Pythagorean theorem, hypotenuse = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.
Correct Answer:
A
— 10 cm
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Q. In triangle XYZ, if side XY = 8 cm, side YZ = 6 cm, and side XZ = 10 cm, which of the following is true?
-
A.
It is a right triangle.
-
B.
It is an obtuse triangle.
-
C.
It is an acute triangle.
-
D.
It cannot be classified.
Solution
Using the Pythagorean theorem, since 10^2 = 8^2 + 6^2 (100 = 64 + 36), triangle XYZ is a right triangle.
Correct Answer:
A
— It is a right triangle.
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Q. In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and angle X is 45 degrees, which method can be used to find the length of side XZ?
-
A.
Pythagorean theorem
-
B.
Sine rule
-
C.
Cosine rule
-
D.
Area formula
Solution
To find the length of side XZ when two sides and the included angle are known, the Cosine rule is applicable.
Correct Answer:
C
— Cosine rule
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Q. In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and side XZ is 10 cm, which of the following is true?
-
A.
It is a right triangle.
-
B.
It is an isosceles triangle.
-
C.
It is an equilateral triangle.
-
D.
It is a scalene triangle.
Solution
Since all sides are of different lengths, triangle XYZ is a scalene triangle.
Correct Answer:
D
— It is a scalene triangle.
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Q. In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, what type of triangle is it?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Using the Pythagorean theorem, since 5^2 + 12^2 = 25 + 144 = 169 = 13^2, triangle XYZ is a right triangle.
Correct Answer:
C
— Right
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Q. In triangle XYZ, if XY = 8 cm, YZ = 6 cm, and XZ = 10 cm, which of the following is true?
-
A.
It is an equilateral triangle.
-
B.
It is an isosceles triangle.
-
C.
It is a scalene triangle.
-
D.
It is a right triangle.
Solution
Since all sides are of different lengths, triangle XYZ is a scalene triangle.
Correct Answer:
C
— It is a scalene triangle.
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Q. In triangle XYZ, if XY = 8 cm, YZ = 6 cm, and XZ = 10 cm, which side is the longest?
-
A.
XY
-
B.
YZ
-
C.
XZ
-
D.
All sides are equal
Solution
The longest side in triangle XYZ is XZ, which measures 10 cm.
Correct Answer:
C
— XZ
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Q. The ages of two siblings are in the ratio 4:5. If the sum of their ages is 72, what is the age of the older sibling? (2023)
Solution
Let the ages be 4x and 5x. Then, 4x + 5x = 72, leading to 9x = 72, so x = 8. The older sibling's age is 5x = 40.
Correct Answer:
A
— 40
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Q. The area of a parallelogram is 120 square meters, and its base is 15 meters. What is the height?
-
A.
8 m
-
B.
10 m
-
C.
12 m
-
D.
15 m
Solution
Area = base × height. Thus, 120 = 15 × height, giving height = 120/15 = 8 m.
Correct Answer:
B
— 10 m
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Q. The area of a parallelogram is 120 square units, and its base is 15 units. What is the height?
-
A.
8 units
-
B.
10 units
-
C.
12 units
-
D.
15 units
Solution
Area = base × height. Thus, 120 = 15 × height, giving height = 120/15 = 8 units.
Correct Answer:
B
— 10 units
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Q. The area of a rhombus is 48 square cm and one diagonal is 8 cm. What is the length of the other diagonal?
-
A.
12 cm
-
B.
10 cm
-
C.
8 cm
-
D.
6 cm
Solution
Area = (1/2) × d1 × d2. Thus, 48 = (1/2) × 8 × d2, giving d2 = 12 cm.
Correct Answer:
A
— 12 cm
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