Interactive multiple-choice quiz: اختبار الوحدة الأولى (Proportional Relationships) - ريفيل
اختبار شامل لمادة الرياضيات للصف السابع، يتناول مفاهيم النسب والتناسب، معدل الوحدة، الثابت النسبي، والتمثيل البياني للعلاقات التناسبية. يهدف الاختبار إلى قياس قدرة الطالب على حل المسائل الحياتية باستخدام التفكير الرياضي المنطقي وتطبيق التناسب في مواقف واقعية.
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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.
DeAndre downloaded 8 apps onto his tablet in 12 seconds. At this rate, how many apps could he download in one minute?
Explanation
One minute is 60 seconds. Using a proportion: $\frac{8}{12} = \frac{x}{60}$. Solving for x: $x = \frac{8 \times 60}{12} = 40$.
Question 2
2
Points: 1
During the first seconds after takeoff, a rocket traveled 208 kilometers in 50 minutes at a constant rate. Suppose a penny is dropped from a skyscraper and could travel 153 kilometers in $\frac{1}{2}$ hour at a constant rate. Which of these objects has a faster unit rate per hour? How much faster?
Explanation
Rocket rate: $\frac{208}{50} \times 60 = 249.6$ km/h. Penny rate: $\frac{153}{0.5} = 306$ km/h. Difference: 306 - 249.6 = 56.4 km/h. The penny is faster.
Question 3
3
Points: 1
A salad dressing calls for 3 parts oil and 1 part vinegar. Manuela uses 2 tablespoons of oil to make her salad dressing. Does she maintain the proportional relationship?
Explanation
The original recipe ratio of oil to vinegar is 3:1. To maintain the relationship, any amount used must simplify to that same ratio.
Question 4
4
Points: 1
The pizza dough recipe shown makes one batch of dough. Charlie wants to make a half batch. She has one cup of flour. How much more flour does she need?
Explanation
A full batch needs 3 cups. A half batch needs 3 × 0.5 = 1.5 cups. Since she has 1 cup, she needs 1.5 - 1 = 0.5 (or $\frac{1}{2}$) cup more.
Question 5
5
Points: 1
A baker, in 70 minutes, iced 40 cupcakes and, in 49 minutes, iced 28 cupcakes. What is the constant of proportionality?
Explanation
The constant of proportionality $k = \frac{y}{x}$. If we take time as y and cupcakes as x, $k = \frac{70}{40} = 1.75$ minutes per cupcake.
Question 6
6
Points: 1
The table shows the amount a restaurant is donating to a local school based on various dinner bills. Is the amount of the donation proportional to the dinner bill? If so, what would be the donation for a dinner bill of $50? If not, explain.
Explanation
The constant rate is $\frac{4.50}{25} = 0.18$. For a bill of 50, the donation is 50 × 0.18 = 9.00.
Question 7
7
Points: 1
The cost of pumpkins is shown in the table. Determine whether the cost of a pumpkin is proportional to the number bought by graphing the relationship on the coordinate plane. Explain.
Explanation
A relationship is proportional if its graph is a straight line that passes through the origin (0,0). The table values (0,0), (1,4), (2,8) match Graph A.
Question 8
8
Points: 1
Suppose a relationship is proportional and the point (4, 10) lies on the graph of the proportional relationship. Name another point, other than (0, 0), that lies on the graph of the line.
Explanation
The constant of proportionality is $k = \frac{10}{4} = 2.5$. For the point (8, 20), $\frac{20}{8} = 2.5$, so it lies on the same line.
Question 9
9
Points: 1
Karl said the point (1, 1) represents the constant of proportionality for the graph shown. Find his error and correct it.
Explanation
The graph shown crosses the y-axis at (0, 1), not at the origin (0, 0). Therefore, it is not a proportional relationship.
Question 10
10
Points: 1
Lincoln bought 3 bottles of an energy drink for $4.50. Write an equation relating the total cost y to the number of energy drinks bought x.
Explanation
The unit price per bottle is $\frac{4.50}{3} = 1.5$. Thus, the cost y for x bottles is y = 1.5x.
Question 11
11
Points: 1
The table shows the cost of 4 movie tickets at two theaters. Select the statement that is true about the situation.
Explanation
For Star Cinema, 4 tickets cost 31, so the unit rate is31 / 4 = 7.75. The equation isy = 7.75x$.
Question 12
12
Points: 1
On average, Asia makes 14 out of 20 free throws. Assuming the relationship is proportional, how many more free throws is she likely to make if she shoots 150 free throws?
For every three girls taking classes at a martial arts school, there are 4 boys who are taking classes. If there are 236 boys taking classes, predict the number of girls taking classes at the school.
Explanation
Ratio of girls to boys is 3:4. $\frac{x}{236} = \frac{3}{4} \implies x = \frac{3 \times 236}{4} = 3 \times 59 = 177$.
Question 14
14
Points: 1
Of the 50 students in the cafeteria, 7 have red hair. If there are 750 students in the school, predict the number of students who have red hair.
Explanation
Ratio is $\frac{7}{50}$. For 750 students: $\frac{7}{50} \times 750 = 7 \times 15 = 105$.
Question 15
15
Points: 1
The ratio of laptops to tablets in the stock room of a store is 13:17. If there are a total of 90 laptops and tablets in the stock room, how many laptops are in the stock room?
Explanation
Total ratio parts = 13 + 17 = 30. Value per part = 90 / 30 = 3. Laptops = 13 × 3 = 39.
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