Q. In the expression 5.00 × 10^3 + 2.1 × 10^2, how many significant figures should the final answer have?
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Solution
The term 2.1 × 10^2 has 2 significant figures, so the final answer should be rounded to 2 significant figures.
Correct Answer:
B
— 3
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Q. In the expression 5x + 3y = 15, if x = 2, what is the value of y?
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Solution
Substituting x = 2 into the equation gives 5(2) + 3y = 15, which simplifies to 10 + 3y = 15. Thus, 3y = 5, and y = 5/3.
Correct Answer:
C
— 3
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Q. In the expression 5x + 3y = 20, if x = 2, what is the value of y? (2021)
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Solution
Substituting x = 2 into the equation gives 5(2) + 3y = 20. This simplifies to 10 + 3y = 20, leading to 3y = 10, thus y = 10/3, which is approximately 3.33. The closest integer option is 4.
Correct Answer:
B
— 4
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Q. In the following data set: 1, 2, 2, 3, 3, 4, 4, 4, what is the mode?
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Solution
The mode is 4, as it appears most frequently (three times) in the data set.
Correct Answer:
D
— 4
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Q. In the following data set: 4, 4, 4, 5, 5, 6, 7, 8, what is the mode?
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Solution
The mode is 4, as it appears most frequently (three times) in the data set.
Correct Answer:
A
— 4
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Q. In the following data set: 9, 10, 10, 11, 12, 12, 12, 13, what is the mode?
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Solution
The mode is 12, which appears three times, more than any other number.
Correct Answer:
D
— 12
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Q. In the following set of scores: 45, 50, 50, 60, 70, 70, 70, 80, what is the mode?
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Solution
The mode is 70, as it appears 3 times, which is more than any other score.
Correct Answer:
D
— 70
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Q. In the reaction 2Fe + 3Cl2 → 2FeCl3, how many moles of FeCl3 are produced from 4 moles of Fe? (2021)
A.
2 moles
B.
4 moles
C.
6 moles
D.
8 moles
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Solution
From 2 moles of Fe, 2 moles of FeCl3 are produced. Therefore, from 4 moles of Fe, 4 moles of FeCl3 are produced.
Correct Answer:
B
— 4 moles
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Q. In the reaction 2Na + Cl2 → 2NaCl, how many grams of NaCl can be produced from 2 moles of Na? (2021)
A.
58.5 g
B.
117 g
C.
29.25 g
D.
146 g
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Solution
2 moles of Na produce 2 moles of NaCl. Molar mass of NaCl = 58.5 g/mol. Therefore, 2 moles of NaCl = 2 × 58.5 g = 117 g.
Correct Answer:
B
— 117 g
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Q. In the reaction 2Na + Cl2 → 2NaCl, how many grams of sodium chloride are produced from 4 moles of sodium? (2023)
A.
236 g
B.
118 g
C.
472 g
D.
59 g
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Solution
4 moles of Na produce 4 moles of NaCl. Molar mass of NaCl = 58.5 g/mol. Therefore, 4 × 58.5 = 236 g.
Correct Answer:
A
— 236 g
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Q. In the reaction 2Na + Cl2 → 2NaCl, how many moles of NaCl are produced from 4 moles of Na? (2023)
A.
2 moles
B.
4 moles
C.
6 moles
D.
8 moles
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Solution
From 2 moles of Na, 2 moles of NaCl are produced. Therefore, from 4 moles of Na, 4 moles of NaCl are produced.
Correct Answer:
B
— 4 moles
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Q. In the set of numbers 10, 20, 20, 30, 30, 30, 40, what is the mode?
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Solution
The mode is 30, as it appears 3 times, more than any other number.
Correct Answer:
C
— 30
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Q. In the set of numbers 5, 5, 6, 7, 8, 8, 8, 9, what is the mode?
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Solution
The mode is 8, as it appears 3 times, which is more than any other number.
Correct Answer:
D
— 8
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Q. In the set {1, 1, 2, 3, 3, 4, 4, 4, 5}, which number is the mode?
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Solution
The mode is 4, as it appears 3 times, more than any other number.
Correct Answer:
D
— 4
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Q. In the set {5, 5, 6, 7, 8, 8, 9}, which number is the mode?
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Solution
The mode is 5, as it appears 2 times, while 8 also appears 2 times. However, 5 is the smallest mode.
Correct Answer:
A
— 5
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Q. In triangle ABC, if AB = AC and angle A = 40 degrees, what is the measure of angle B? (2023)
A.
70 degrees
B.
80 degrees
C.
60 degrees
D.
50 degrees
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Solution
In an isosceles triangle, angles opposite to equal sides are equal. Therefore, angle B = angle C = (180 - 40) / 2 = 70 degrees.
Correct Answer:
B
— 80 degrees
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Q. In triangle ABC, if angle A = 30 degrees and angle B = 60 degrees, what is the measure of angle C? (2021)
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
120 degrees
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Solution
The sum of angles in a triangle is 180 degrees. Therefore, angle C = 180 - (30 + 60) = 90 degrees.
Correct Answer:
C
— 90 degrees
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Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the length of side DE if DF = 10 cm? (2023)
A.
5√2 cm
B.
10 cm
C.
10√2 cm
D.
20 cm
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Solution
In an isosceles right triangle, the sides opposite the 45-degree angles are equal. DE = DF/√2 = 10/√2 = 5√2 cm.
Correct Answer:
A
— 5√2 cm
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Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the type of triangle? (2020)
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
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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 = 45 degrees and angle E = 45 degrees, what type of triangle is DEF? (2021)
A.
Scalene
B.
Isosceles
C.
Equilateral
D.
Right
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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 DE = 12 cm, EF = 16 cm, and DF = 20 cm, what is the semi-perimeter? (2021)
A.
24 cm
B.
28 cm
C.
30 cm
D.
20 cm
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Solution
Semi-perimeter s = (12 + 16 + 20) / 2 = 48 / 2 = 24 cm.
Correct Answer:
B
— 28 cm
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Q. In triangle DEF, if DE = 5 cm, EF = 12 cm, and DF = 13 cm, is triangle DEF a right triangle? (2019)
A.
Yes
B.
No
C.
Cannot be determined
D.
Only if angle D is 90 degrees
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Solution
Using the Pythagorean theorem, 5^2 + 12^2 = 25 + 144 = 169 = 13^2. Thus, triangle DEF is a right triangle.
Correct Answer:
A
— Yes
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Q. In triangle GHI, if angle G = 30 degrees and side GH = 10 cm, what is the length of side HI if angle H = 60 degrees? (2023)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
Using the sine rule, HI/sin(60) = GH/sin(30). Therefore, HI = (10 * sin(60)) / sin(30) = 10 * (√3/2) / (1/2) = 10√3 cm.
Correct Answer:
C
— 15 cm
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Q. In triangle GHI, if angle G = 90 degrees and GH = 9 cm, HI = 12 cm, what is the length of side GI? (2022)
A.
15 cm
B.
10 cm
C.
12 cm
D.
9 cm
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Solution
Using the Pythagorean theorem, GI = √(HI² - GH²) = √(12² - 9²) = √(144 - 81) = √63 = 15 cm.
Correct Answer:
A
— 15 cm
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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the area of the triangle? (2019)
A.
120 cm²
B.
130 cm²
C.
140 cm²
D.
150 cm²
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Solution
Using Heron's formula, semi-perimeter s = (10 + 24 + 26) / 2 = 30. Area = √(s(s-a)(s-b)(s-c)) = √(30*20*6*4) = 120 cm².
Correct Answer:
A
— 120 cm²
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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the length of the longest side? (2022)
A.
10 cm
B.
24 cm
C.
26 cm
D.
Cannot be determined
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Solution
The longest side of triangle GHI is GI, which measures 26 cm.
Correct Answer:
C
— 26 cm
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Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the perimeter? (2019)
A.
50 cm
B.
60 cm
C.
70 cm
D.
80 cm
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Solution
Perimeter = GH + HI + GI = 10 + 24 + 26 = 60 cm.
Correct Answer:
A
— 50 cm
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Q. In triangle GHI, if the lengths of sides GH, HI, and GI are in the ratio 3:4:5, what type of triangle is it? (2019)
A.
Equilateral
B.
Isosceles
C.
Scalene
D.
Right-angled
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Solution
Since the sides are in the ratio 3:4:5, it follows the Pythagorean theorem, indicating it is a right-angled triangle.
Correct Answer:
D
— Right-angled
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Q. In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of JL? (2022)
A.
10 cm
B.
12 cm
C.
15 cm
D.
25 cm
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Solution
Using the Pythagorean theorem, JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12.25 cm.
Correct Answer:
B
— 12 cm
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Q. In triangle JKL, if angle J = 90 degrees and JK = 15 cm, KL = 20 cm, what is the length of side JL? (2023)
A.
10 cm
B.
12 cm
C.
15 cm
D.
25 cm
Show solution
Solution
Using Pythagoras theorem: JL = √(KL² - JK²) = √(20² - 15²) = √(400 - 225) = √175 = 12 cm.
Correct Answer:
B
— 12 cm
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