Interactive multiple-choice quiz: اختبار الوحدة 11 (Polynomials) الرياضيات ريفيل
اختبار مادة الرياضيات - الصف العاشر المتقدم الوحدة الحادية عشرة: كثيرات الحدود (Polynomials) الفصل الدراسي الأول لعام 2026 - 2027 شرح وإعداد: الأستاذ عهيد
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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.
Determine whether the expression 8ab - 2c is a polynomial. If it is a polynomial, find its degree and classify it as a monomial, binomial, or trinomial.
Explanation
The expression 8ab - 2c consists of two terms: 8ab (degree 2) and -2c (degree 1). The highest degree is 2, and it is a binomial since it has two terms.
Question 2
2
Points: 1
Write 5b - 10b2 + 35 - b3 in standard form.
Explanation
Standard form of a polynomial is writing the terms in descending order of their exponents.
Expanding both sides: -8q2 + 18q = -8q2 + 15q + 12q + 18. This simplifies to 18q = 27q + 18, so -9q = 18, giving q = -2.
Question 5
5
Points: 1
Simplify the expression: 3x(5x2 - x + 4)
Explanation
Multiply 3x by each term inside the parentheses: 3x(5x2) - 3x(x) + 3x(4) = 15x3 - 3x2 + 12x.
Question 6
6
Points: 1
The dimensions of the composite figure shown are given in terms of the triangle's height, h. If h = 1.42 units, what is the area of the figure? Round to the nearest hundredth, if necessary.
Explanation
Total Area = Area of Rectangle + Area of Triangle. Rectangle = (4h+2)(5-2h), Triangle = 0.5(4h+2)h. Area = -6h2 + 17h + 10. For h = 1.42, Area ≈ 22.04.
Question 7
7
Points: 1
Find the product: (2r - 3t)3
Explanation
Using the cube of a binomial formula (a-b)3 = a3 - 3a2b + 3ab2 - b3 where a=2r and b=3t.
Question 8
8
Points: 1
Find and simplify an expression for the volume of the rectangular prism shown.
Using the difference of squares formula: (a - b)(a + b) = a2 - b2, where a = 6y and b = 13.
Question 10
10
Points: 1
The square of a sum is called a perfect square trinomial. Find c that makes 25x2 - 90x + c a perfect square trinomial.
Explanation
For ax2 + bx + c to be a perfect square, c must equal $(b / (2 √ a))^2$. Here, a=25 and b=-90, so c = (-90 / (2 imes 5))2 = (-9)2 = 81.
Question 11
11
Points: 1
A cylindrical tank is placed along a wall. A cylindrical PVC pipe will be hidden in the corner behind the tank. See the side-view diagram shown. The radius of the tank is r inches, and the radius of the PVC pipe is s inches. Use the Pythagorean Theorem to write an equation for the relationship between the two radii. Simplify your equation so that there is a zero on one side of the equal sign.
Explanation
Based on the geometry, the distance between the centers is r + s. Setting up the Pythagorean relationship 2(r - s)2 = (r + s)2 and simplifying leads to r2 - 6rs + s2 = 0.
Question 12
12
Points: 1
Use the Distributive Property to factor the polynomial: 4a2b2 + 2a2b - 10ab2
Explanation
The greatest common factor (GCF) of the terms is 2ab. Dividing each term by 2ab gives 2ab(2ab + a - 5b).
Question 13
13
Points: 1
The area of a rectangular swimming pool is given by the expression 12w - w2, where w is the width of one side. Factor the expression.
Explanation
Factor out the common term w from the expression 12w - w2, resulting in w(12 - w).
A suspension bridge is a bridge in which the deck is supported by cables with towers spaced throughout the span of the bridge. The height of a cable n inches above the deck measured at distance d in yards from the first tower is given by d2 - 36d + 324. Factor the expression.
Explanation
The expression d2 - 36d + 324 is a perfect square trinomial because (18)2 = 324 and 2 imes 18 = 36, so it factors as (d - 18)2.
Question 16
16
Points: 1
Factor each polynomial, if possible. If the polynomial cannot be factored using integers, write prime. x2 - 14xy - 51y2
Explanation
Find two numbers that multiply to -51 and add to -14. These numbers are -17 and +3, so the factors are (x - 17y)(x + 3y).
Question 17
17
Points: 1
Find all values of k so that 2x2 + kx + 12 can be factored as two binomials using integers.
Explanation
The possible values for k are the sums of the pairs of factors of 2 imes 12 = 24. These pairs are (1,24), (2,12), (3,8), (4,6) and their negatives, summing to $\pm 25, \pm 14, \pm 11, \pm 10$.
Question 18
18
Points: 1
If the trinomial is a perfect square trinomial, factor it. If not, write not a perfect square trinomial. 36x2 - 36x + 9
Explanation
Since (6x)2 = 36x2, (3)2 = 9, and 2(6x)(3) = 36x, the expression is a perfect square trinomial: (6x - 3)2.
Question 19
19
Points: 1
Marvin saw a rug in a store that he would like to purchase. It has an area represented by the expression shown on the rug. He cannot remember the length and width, but he remembers that the length and the width were the same. Factor the expression that represents the area of the rug.
Explanation
The expression on the rug is x2 - 16x + 64. Since the length and width are the same, it must be a perfect square: (x - 8)2.
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