Interactive multiple-choice quiz: اختبار الوحدة الثانية - منهج ريفيل
اختبار تقييمي شامل لمادة الرياضيات لطلاب الصف الثامن. يغطي الاختبار مواضيع الأعداد النسبية، الجذور التربيعية والتكعيبيية، ومهارات التقدير الحسابي. تم تصميم الأسئلة لقياس فهم الطالب لكيفية التعامل مع الكسور العشرية الدورية والعمليات على الجذور.
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اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
Write the decimal as a fraction or mixed number in simplest form: $4.\overline{45}$
Explanation
$4.\overline{45}$ is equivalent to $4 + \frac{45}{99}$. Simplifying the fraction $\frac{45}{99}$ by dividing both by 9 gives $\frac{5}{11}$, so the mixed number is $4 \frac{5}{11}$.
Question 2
2
Points: 1
Write the rational number in decimal form. Then determine whether the decimal is a terminating decimal: $\frac{5}{33}$
Explanation
Dividing 5 by 33 results in 0.151515..., which is a repeating decimal written as $0.\overline{15}$.
Question 3
3
Points: 1
In one soccer season, Milica saved 155 out of 180 shots on goal. At this rate, about how many saves would she make out of 600 shots on goal?
Explanation
Using a proportion: $\frac{155}{180} = \frac{x}{600}$. Multiplying gives 180x = 93000, so $x = 93000 / 180 \approx 516.67$, which rounds to 517.
Question 4
4
Points: 1
Simplify using rational numbers. If the expression cannot be simplified, explain why: $\sqrt{-441}$
Explanation
In the set of real/rational numbers, the square root of a negative number is undefined or not a rational number.
Question 5
5
Points: 1
Simplify using rational number: $\sqrt[3]{343}$
Explanation
The cube root of 343 is 7 because 7 × 7 × 7 = 343.
Question 6
6
Points: 1
A photo collage consists of seven equal-sized square photos arranged in a row to form a rectangle. If the total area of the collage is 567 square inches, what is the length of the collage?
Explanation
Area of one square = 567 / 7 = 81 sq inches. The side of each square is $\sqrt{81} = 9$ inches. Since there are 7 squares in a row, the total length is 7 × 9 = 63 inches.
Question 7
7
Points: 1
Identify whether the number is rational or irrational: $\frac{\sqrt{2}}{\sqrt{2}}$
Explanation
$\frac{\sqrt{2}}{\sqrt{2}}$ simplifies to 1. Since 1 can be expressed as a fraction (1/1), it is a rational number.
Question 8
8
Points: 1
Estimate each square root or cube root to the nearest integer: $\sqrt{125} \approx$
Explanation
Since 112 = 121 and 122 = 144, 125 is much closer to 121, so the square root is approximately 11.
Question 9
9
Points: 1
Estimate each square root to the nearest tenth: $\sqrt{62} \approx$
Explanation
Since 7.82 = 60.84 and 7.92 = 62.41, 62 is closer to 62.41, so the square root is approximately 7.9.
Question 10
10
Points: 1
If the area of a square is 32 square feet, estimate the length of each side of the square to the nearest whole number.
Explanation
The side length is $\sqrt{32}$. Since 52 = 25 and 62 = 36, 32 is closer to 36, so the side length rounds to 6 feet.
Question 11
11
Points: 1
The radius of a circle with area A can be approximated using the formula $r = \sqrt{\frac{A}{3}}$. Estimate the radius of a wrestling mat circle with an area of 452 square feet. Round to the nearest integer.
Explanation
$r = \sqrt{452 / 3} = \sqrt{150.66...}$. Since 122 = 144 and 132 = 169, 150.66 is closer to 144, so the radius rounds to 12.
Question 12
12
Points: 1
Complete the statement using <, >, or =: $-\pi^2$ ________ $-\sqrt{93}$
Explanation
$\pi^2 \approx 9.87$, so $-\pi^2 \approx -9.87$. $\sqrt{93} \approx 9.64$, so $-\sqrt{93} \approx -9.64$. Since -9.87 < -9.64, the correct sign is <.
Question 13
13
Points: 1
The table shows the foul-shot statistics for three players in a recent basketball game. Which player had the greatest foul-shot statistic?
Explanation
Converting all to decimals: Player 1 = $7/9 \approx 0.777$, Player 2 = $72\% = 0.72$, Player 3 = 8/10 = 0.80. Player 3 has the highest value.
Question 14
14
Points: 1
The time in seconds that it takes an object to fall d feet can found using the expression $\frac{\sqrt{d}}{4}$. In an egg drop contest, Clara successfully dropped her egg container from a height of 35 feet, while Vladimir successfully dropped his egg container from a height of 23 feet. How much longer did it take Clara's egg to reach the floor than Vladimir's egg? Round to the nearest tenth.
A shipping box, in the shape of a cube, has a volume of 2,300 cubic inches. Estimate the length of the side of the shipping box to the nearest integer.
Explanation
The side length is $\sqrt[3]{2300}$. Since 133 = 2197 and 143 = 2744, 2300 is closer to 2197, so the length is approximately 13 inches.
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