Q. If a polynomial p(x) is expressed as p(x) = x^2 - 5x + 6, what are its roots?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
5 and 1
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Solution
The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.
Correct Answer:
A
— 2 and 3
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Q. If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are its roots?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
5 and 1
Show solution
Solution
The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.
Correct Answer:
A
— 2 and 3
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Q. If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are the roots of the polynomial?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
5 and 1
Show solution
Solution
The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.
Correct Answer:
A
— 2 and 3
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Q. If a polynomial p(x) is given by p(x) = x^3 - 6x^2 + 11x - 6, what can be inferred about its roots?
A.
It has three distinct real roots.
B.
It has one real root and two complex roots.
C.
It has no real roots.
D.
It has two distinct real roots.
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Solution
By applying the Rational Root Theorem and synthetic division, we can find that p(x) has three distinct real roots.
Correct Answer:
A
— It has three distinct real roots.
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Q. If a population of a town increases by 10% every year, what will be the population after 2 years if the current population is 1,000? (2023)
A.
1,100
B.
1,210
C.
1,300
D.
1,400
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Solution
Population after 2 years = 1000 * (1 + 0.10)^2 = 1000 * 1.21 = 1210.
Correct Answer:
B
— 1,210
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Q. If a population of a town increases by 15% every year, what will be the population after 2 years if the current population is 1000? (2023)
A.
1150
B.
1300
C.
1325
D.
1440
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Solution
After 1 year, the population will be 1000 * 1.15 = 1150. After 2 years, it will be 1150 * 1.15 = 1322.5, rounded to 1325.
Correct Answer:
C
— 1325
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Q. If a population of a town increases by 15% in one year and then decreases by 10% the next year, what is the net percentage change in the population over the two years?
A.
5%
B.
3.5%
C.
4.5%
D.
6%
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Solution
Let the initial population be 100. After a 15% increase, it becomes 115. After a 10% decrease, it becomes 115 - 11.5 = 103.5. The net change is (103.5 - 100) / 100 * 100% = 3.5%.
Correct Answer:
C
— 4.5%
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Q. If a population of a town increases by 5% every year, what will be the population after 2 years if the current population is 1,000?
A.
1,050
B.
1,102.5
C.
1,100
D.
1,120
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Solution
Population after 1 year = 1,000 * 1.05 = 1,050. After 2 years = 1,050 * 1.05 = 1,102.5.
Correct Answer:
B
— 1,102.5
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Q. If a product is bought for $150 and sold for $120, what is the percentage loss incurred?
A.
20%
B.
25%
C.
30%
D.
15%
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Solution
Loss = Cost Price - Selling Price = $150 - $120 = $30. Percentage loss = (Loss/Cost Price) * 100 = ($30/$150) * 100 = 20%.
Correct Answer:
B
— 25%
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Q. If a product is marked at $500 and sold at a 30% discount, what is the profit or loss if the cost price is $350?
A.
Profit of $50
B.
Loss of $50
C.
Profit of $100
D.
Loss of $100
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Solution
Selling Price = $500 - (30% of $500) = $500 - $150 = $350. Since Selling Price = Cost Price, there is no profit or loss.
Correct Answer:
A
— Profit of $50
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Q. If a product is marked at $500 and sold for $450, what is the discount percentage offered? (2023)
A.
5%
B.
10%
C.
15%
D.
20%
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Solution
Discount = Marked Price - Selling Price = 500 - 450 = 50. Discount Percentage = (50/500) * 100 = 10%.
Correct Answer:
C
— 15%
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Q. If a product is sold at a loss of 20% for $80, what was the cost price of the product? (2023)
A.
$100
B.
$90
C.
$80
D.
$70
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Solution
Let the cost price be x. Then, 80 = x - (20% of x) => 80 = x - 0.2x => 80 = 0.8x => x = 100.
Correct Answer:
A
— $100
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Q. If a product is sold for $150 after a discount of 25%, what was its marked price?
A.
$175
B.
$200
C.
$180
D.
$160
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Solution
Let the marked price be x. After a 25% discount, the selling price is x - (0.25 * x) = 0.75x. Setting this equal to $150 gives 0.75x = $150, so x = $200.
Correct Answer:
B
— $200
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Q. If a product is sold for $150 after a discount of 25%, what was the original price?
A.
$175
B.
$200
C.
$180
D.
$160
Show solution
Solution
Let the original price be x. After a 25% discount, the selling price is x - (0.25 * x) = 0.75x. Thus, 0.75x = $150, so x = $150 / 0.75 = $200.
Correct Answer:
B
— $200
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Q. If a product is sold for $150 at a profit of 50%, what was the cost price?
A.
$100
B.
$110
C.
$120
D.
$130
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Solution
Let the cost price be x. Selling Price = x + 50% of x = 150. Thus, 1.5x = 150, so x = 100.
Correct Answer:
A
— $100
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Q. If a product's price is increased by 15% and then decreased by 15%, what is the net change in price?
A.
0%
B.
2.25%
C.
3.5%
D.
1.5%
Show solution
Solution
Let the original price be $100. After a 15% increase, the price is $115. After a 15% decrease, the price is $97.75. Net change = (97.75 - 100)/100 * 100 = -2.25%.
Correct Answer:
B
— 2.25%
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Q. If a product's price is increased by 20% and then decreased by 20%, what is the net change in price? (2023)
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Solution
Let the original price be 100. After a 20% increase, the price becomes 120. After a 20% decrease, the price becomes 120 - 24 = 96. The net change is (96 - 100) / 100 * 100% = -4%.
Correct Answer:
B
— 4%
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Q. If a quadrilateral has one angle measuring 120 degrees and the other three angles are equal, what is the measure of each of the equal angles?
A.
30 degrees
B.
40 degrees
C.
60 degrees
D.
80 degrees
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Solution
The sum of the angles in a quadrilateral is 360 degrees. If one angle is 120 degrees, the remaining angles must sum to 240 degrees. If the other three angles are equal, each must be 240/3 = 80 degrees.
Correct Answer:
B
— 40 degrees
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Q. If a quadrilateral has one angle measuring 90 degrees and the opposite angle measuring 90 degrees, what can be inferred about the quadrilateral?
A.
It is a trapezium.
B.
It is a rectangle.
C.
It is a rhombus.
D.
It is a kite.
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Solution
A quadrilateral with two opposite angles measuring 90 degrees is a rectangle.
Correct Answer:
B
— It is a rectangle.
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Q. If a quadrilateral has one pair of opposite sides that are both equal and parallel, what can be inferred?
A.
It is a trapezium.
B.
It is a parallelogram.
C.
It is a rectangle.
D.
It is a kite.
Show solution
Solution
A quadrilateral with one pair of opposite sides that are equal and parallel is classified as a trapezium.
Correct Answer:
A
— It is a trapezium.
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Q. If a quadrilateral has one pair of opposite sides that are both equal and parallel, what type of quadrilateral is it?
A.
Trapezium
B.
Parallelogram
C.
Rectangle
D.
Square
Show solution
Solution
A quadrilateral with one pair of opposite sides that are equal and parallel is a parallelogram.
Correct Answer:
B
— Parallelogram
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Q. If a quadrilateral has one pair of opposite sides that are both parallel and equal in length, what can be inferred about the quadrilateral?
A.
It is a trapezium
B.
It is a parallelogram
C.
It is a rectangle
D.
It is a rhombus
Show solution
Solution
A quadrilateral with one pair of opposite sides that are both parallel and equal is a parallelogram.
Correct Answer:
B
— It is a parallelogram
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Q. If a quadrilateral has one pair of opposite sides that are both parallel and equal, what can be inferred about the quadrilateral?
A.
It is a trapezium
B.
It is a parallelogram
C.
It is a rectangle
D.
It is a rhombus
Show solution
Solution
A quadrilateral with one pair of opposite sides that are both parallel and equal is a parallelogram.
Correct Answer:
B
— It is a parallelogram
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Q. If a quadrilateral has one pair of parallel sides, it is classified as which of the following?
A.
Trapezium
B.
Parallelogram
C.
Rectangle
D.
Rhombus
Show solution
Solution
A quadrilateral with one pair of parallel sides is classified as a trapezium.
Correct Answer:
A
— Trapezium
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Q. If a quadrilateral has one pair of parallel sides, it is classified as which type? (2023)
A.
Parallelogram
B.
Trapezium
C.
Rectangle
D.
Rhombus
Show solution
Solution
A quadrilateral with one pair of parallel sides is classified as a trapezium.
Correct Answer:
B
— Trapezium
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Q. If a quadrilateral has one pair of parallel sides, what type of quadrilateral is it?
A.
Parallelogram
B.
Trapezium
C.
Rectangle
D.
Rhombus
Show solution
Solution
A quadrilateral with one pair of parallel sides is classified as a trapezium.
Correct Answer:
B
— Trapezium
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Q. If a quadrilateral has two pairs of parallel sides, what type of polygon is it?
A.
A trapezoid
B.
A rectangle
C.
A rhombus
D.
A parallelogram
Show solution
Solution
A quadrilateral with two pairs of parallel sides is classified as a parallelogram.
Correct Answer:
D
— A parallelogram
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Q. If a quadrilateral is both a rectangle and a rhombus, what is it called?
A.
Square
B.
Trapezium
C.
Parallelogram
D.
Kite
Show solution
Solution
A quadrilateral that is both a rectangle and a rhombus is called a square.
Correct Answer:
A
— Square
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Q. If a recipe requires 2 cups of flour for every 3 cups of sugar, how many cups of flour are needed for 9 cups of sugar?
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Solution
Using the ratio, if 3 cups of sugar require 2 cups of flour, then 9 cups of sugar require (2/3) * 9 = 6 cups of flour.
Correct Answer:
C
— 6
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Q. If a recipe requires 3 cups of flour for every 2 cups of sugar, how many cups of flour are needed for 8 cups of sugar?
A.
10 cups
B.
12 cups
C.
9 cups
D.
6 cups
Show solution
Solution
The ratio of flour to sugar is 3:2. For 8 cups of sugar, the amount of flour needed is (3/2) × 8 = 12 cups.
Correct Answer:
B
— 12 cups
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