Q. A quadrilateral has angles measuring 70 degrees, 80 degrees, and 90 degrees. What is the measure of the fourth angle?
A.
100 degrees
B.
110 degrees
C.
120 degrees
D.
130 degrees
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Solution
The sum of angles in a quadrilateral is 360 degrees. Therefore, the fourth angle is 360 - (70 + 80 + 90) = 120 degrees.
Correct Answer:
B
— 110 degrees
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Q. A quadrilateral has sides of lengths 5 cm, 12 cm, 13 cm, and 14 cm. What is the perimeter of the quadrilateral?
A.
34 cm
B.
36 cm
C.
38 cm
D.
40 cm
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Solution
The perimeter is the sum of all sides: 5 + 12 + 13 + 14 = 44 cm.
Correct Answer:
B
— 36 cm
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Q. A quadrilateral has vertices at (1, 2), (4, 5), (7, 2), and (4, -1). What type of quadrilateral is it?
A.
Rectangle
B.
Rhombus
C.
Trapezium
D.
Parallelogram
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Solution
The opposite sides are equal and parallel, making it a parallelogram.
Correct Answer:
D
— Parallelogram
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Q. A recipe requires 4 cups of flour for 8 servings. How many cups of flour are needed for 20 servings?
A.
10 cups
B.
12 cups
C.
8 cups
D.
6 cups
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Solution
Flour per serving = 4 cups / 8 servings = 0.5 cups. For 20 servings, 20 * 0.5 = 10 cups.
Correct Answer:
A
— 10 cups
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Q. A rectangle has a length of 10 cm and a width of 5 cm. What is its area?
A.
30 cm²
B.
40 cm²
C.
50 cm²
D.
60 cm²
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Solution
Area = length × width = 10 cm × 5 cm = 50 cm².
Correct Answer:
C
— 50 cm²
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Q. A rectangular box has a length of 10 cm, a width of 5 cm, and a height of 2 cm. What is its volume?
A.
100 cm³
B.
50 cm³
C.
20 cm³
D.
70 cm³
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Solution
Volume = length × width × height = 10 × 5 × 2 = 100 cm³.
Correct Answer:
A
— 100 cm³
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Q. A rectangular prism has dimensions 2 cm, 3 cm, and 4 cm. What is its surface area?
A.
24 cm²
B.
28 cm²
C.
20 cm²
D.
18 cm²
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Solution
Surface area = 2(lw + lh + wh) = 2(2*3 + 2*4 + 3*4) = 2(6 + 8 + 12) = 2(26) = 52 cm².
Correct Answer:
A
— 24 cm²
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Q. A shopkeeper sells an article for $120 after allowing a discount of 20%. What was the marked price of the article?
A.
$100
B.
$120
C.
$150
D.
$160
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Solution
Let the marked price be x. After a 20% discount, selling price = x - 0.2x = 0.8x. Given selling price = $120, so 0.8x = 120. Therefore, x = 120 / 0.8 = $150.
Correct Answer:
D
— $160
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Q. A store increases the price of a shirt by 25% and then offers a 20% discount on the new price. If the original price was $40, what is the final price after the discount?
A.
$32
B.
$30
C.
$28
D.
$25
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Solution
New price after 25% increase = 40 + 0.25 * 40 = 40 + 10 = $50. Discount = 20% of 50 = 0.2 * 50 = $10. Final price = 50 - 10 = $40.
Correct Answer:
B
— $30
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Q. A student scored 75% in Mathematics and 85% in Science. If both subjects have equal weightage, what is the average percentage score?
A.
80%
B.
82%
C.
83%
D.
84%
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Solution
Average percentage = (75% + 85%) / 2 = 160% / 2 = 80%.
Correct Answer:
A
— 80%
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Q. A synthetic fiber is made from 60% polyester and 40% nylon. If you have 200 grams of this fiber, how many grams of polyester are there?
A.
80 g
B.
100 g
C.
120 g
D.
140 g
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Solution
200 g * 60% = 120 g of polyester
Correct Answer:
C
— 120 g
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Q. A tank can be filled by a pipe in 6 hours and emptied by another pipe in 8 hours. How long will it take to fill the tank if both pipes are open?
A.
24 hours
B.
12 hours
C.
48 hours
D.
18 hours
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Solution
Filling rate = 1/6 tank/hour, emptying rate = 1/8 tank/hour. Net rate = (1/6 - 1/8) = 1/24 tank/hour. Time = 1 / (1/24) = 24 hours.
Correct Answer:
B
— 12 hours
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Q. A train leaves a station at 3 PM and travels at a speed of 80 km/h. How far will it travel by 5 PM?
A.
160 km
B.
180 km
C.
200 km
D.
220 km
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Solution
Time = 2 hours; Distance = speed × time = 80 km/h × 2 h = 160 km.
Correct Answer:
A
— 160 km
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Q. A tree planting initiative aims to plant 2000 trees in 5 years. If they have already planted 800 trees, how many trees do they need to plant each year for the next 4 years?
A.
300
B.
350
C.
400
D.
450
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Solution
Trees left to plant = 2000 - 800 = 1200. Trees per year = 1200 / 4 = 300.
Correct Answer:
C
— 400
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Q. A triangular prism has a base area of 10 cm² and a height of 5 cm. What is its volume?
A.
25 cm³
B.
50 cm³
C.
15 cm³
D.
30 cm³
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Solution
Volume = Base area × height = 10 cm² × 5 cm = 50 cm³.
Correct Answer:
A
— 25 cm³
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Q. A virus can infect a cell every 5 minutes. If a cell can be infected by 3 viruses at a time, how many cells can be infected in 1 hour?
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Solution
In 1 hour (60 minutes), there are 60/5 = 12 infection cycles. Since each cycle can infect 3 cells, the total is 12 * 3 = 36 cells.
Correct Answer:
C
— 18
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Q. A wildlife reserve has 150 deer. If the population increases by 15% each year, how many deer will there be after 2 years?
A.
173
B.
180
C.
200
D.
225
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Solution
After 1 year: 150 * 1.15 = 172.5 (approx 173). After 2 years: 173 * 1.15 = 198.95 (approx 199).
Correct Answer:
A
— 173
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Q. According to the line graph, what was the sales trend for Product B over the year?
A.
Increasing
B.
Decreasing
C.
Stable
D.
Fluctuating
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Solution
The line graph shows that sales for Product B were consistently increasing over the year.
Correct Answer:
A
— Increasing
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Q. At what age does a person typically enter adolescence?
A.
8 years
B.
10 years
C.
12 years
D.
14 years
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Solution
Adolescence typically begins around the age of 12.
Correct Answer:
C
— 12 years
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A.
5/4
B.
5/16
C.
5/8
D.
1/4
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Solution
To divide 5/8 by 1/2, multiply by the reciprocal: 5/8 * 2/1 = 10/8 = 5/4.
Correct Answer:
A
— 5/4
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Q. Factor the expression: 2x^2 + 8x
A.
2x(x + 4)
B.
2(x^2 + 4x)
C.
x(2x + 8)
D.
2x(x + 2)
Show solution
Solution
The expression 2x^2 + 8x can be factored by taking out the common factor 2x, resulting in 2x(x + 4).
Correct Answer:
A
— 2x(x + 4)
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Q. Factor the expression: 3x^2 - 12
A.
3(x - 2)(x + 2)
B.
3(x - 4)(x + 1)
C.
3(x + 4)(x - 1)
D.
3(x - 3)(x + 3)
Show solution
Solution
The expression 3x^2 - 12 can be factored by taking out the common factor 3, resulting in 3(x^2 - 4), which further factors to 3(x - 2)(x + 2).
Correct Answer:
A
— 3(x - 2)(x + 2)
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Q. Factor the expression: 4x^2 - 25
A.
(2x - 5)(2x + 5)
B.
(4x - 5)(4x + 5)
C.
(2x + 5)(2x + 5)
D.
(4x + 5)(4x - 5)
Show solution
Solution
The expression 4x^2 - 25 is a difference of squares, which factors to (2x - 5)(2x + 5).
Correct Answer:
A
— (2x - 5)(2x + 5)
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Q. Factor the expression: x^2 + 3x - 10
A.
(x + 5)(x - 2)
B.
(x - 5)(x + 2)
C.
(x + 10)(x - 1)
D.
(x - 3)(x + 4)
Show solution
Solution
The expression x^2 + 3x - 10 factors to (x + 5)(x - 2) since 5 and -2 add to 3 and multiply to -10.
Correct Answer:
A
— (x + 5)(x - 2)
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Q. Factor the expression: x^2 + 5x + 6
A.
(x + 2)(x + 3)
B.
(x + 1)(x + 6)
C.
(x - 2)(x - 3)
D.
(x + 3)(x + 2)
Show solution
Solution
The expression x^2 + 5x + 6 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. Factor the expression: x^2 + 7x + 10
A.
(x + 5)(x + 2)
B.
(x + 1)(x + 10)
C.
(x - 5)(x - 2)
D.
(x + 10)(x - 1)
Show solution
Solution
The expression x^2 + 7x + 10 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. Factor the expression: x^2 - 4x + 4
A.
(x - 2)(x - 2)
B.
(x + 2)(x + 2)
C.
(x - 4)(x + 1)
D.
(x + 4)(x - 1)
Show solution
Solution
The expression x^2 - 4x + 4 is a perfect square trinomial and factors to (x - 2)(x - 2) or (x - 2)^2.
Correct Answer:
A
— (x - 2)(x - 2)
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Q. Factor the expression: x^2 - 6x + 9
A.
(x - 3)(x - 3)
B.
(x + 3)(x + 3)
C.
(x - 9)(x + 1)
D.
(x + 6)(x - 3)
Show solution
Solution
The expression x^2 - 6x + 9 is a perfect square trinomial and factors to (x - 3)(x - 3) or (x - 3)^2.
Correct Answer:
A
— (x - 3)(x - 3)
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Q. Factor the expression: x^2 - 9
A.
(x - 3)(x + 3)
B.
(x - 9)(x + 1)
C.
(x - 1)(x + 9)
D.
(x + 3)(x + 3)
Show solution
Solution
The expression x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
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Q. Find x if 5(x - 2) = 3x + 4.
A.
x = 6
B.
x = 2
C.
x = 4
D.
x = 8
Show solution
Solution
Distribute: 5x - 10 = 3x + 4. Subtract 3x from both sides: 2x - 10 = 4. Add 10: 2x = 14. Divide by 2: x = 7.
Correct Answer:
C
— x = 4
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