Interactive multiple-choice quiz: Math Final Mock Exam - G8 ADV
اختبار تجريبي نهائي في مادة الرياضيات - الصف الثامن المتقدم (G8 ADV). تم إعداد هذا الاختبار بواسطة المعلمة نجلاء أبو صالح في أكاديمية تمكين الرقمية. يغطي الاختبار موضوعات التحويلات الهندسية، والتشابه، وحساب الحجوم، وتحليل البيانات الإحصائية والارتباط.
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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.
Triangle QRS has vertices Q(-2, 2), R(-3, -4), and S(1, -2). Write the coordinate notation for each translation given. Then write the coordinates of $\Delta Q'R'S'$ after this translation: 2 units \left and 3 units up
Explanation
Translation 2 units \left means subtracting 2 from the x-coordinate (x-2), and 3 units up means adding 3 to the y-coordinate (y+3). Applying this to each vertex: $Q(-2-2, 2+3) = Q'(-4, 5)$, $R(-3-2, -4+3) = R'(-5, -1)$, and $S(1-2, -2+3) = S'(-1, 1)$.
Question 2
Points: 4
Write the coordinates of the image of triangle ABC after a reflection across the x-axis. $A(1, 2) \to A'(1, \dots)$ $B(2, 4) \to B'(2, \dots)$ $C(4, 1) \to C'(4, \dots)$
Explanation
Reflection across the x-axis follows the rule $(x, y) \to (x, -y)$. Thus, the y-coordinates change sign while the x-coordinates remain the same.
Question 3
Points: 4
The coordinates of $\Delta LMN$ and its image are shown. Describe the transformation. $L(0, 0) \to L'(0, 0)$ $M(-4, 1) \to M'(-4, -1)$ $N(-1, 3) \to N'(-1, -3)$
Explanation
Observing the coordinates, the x-values remain the same while the y-values change signs ($y \to -y$). This is the rule for reflection across the x-axis.
Question 4
Points: 4
Triangle XYZ has vertices X(-2, -1), Y(0, 2), and Z(2, -1). Graph the figure and its image after a clockwise rotation of $180^\circ$ about vertex Z.
Explanation
A $180^\circ$ rotation about a point (h, k) maps (x, y) to (2h - x, 2k - y). Centered at Z(2, -1), X(-2, -1) maps to (2(2)-(-2), 2(-1)-(-1)) = (6, -1) and Y(0, 2) maps to (2(2)-0, 2(-1)-2) = (4, -4). Graph D correctly represents this image.
Question 5
Points: 4
Point Z is located at Z(1, -2). Write the coordinates of the point after a clockwise rotation of $90^\circ$ about the origin.
Explanation
A clockwise rotation of $90^\circ$ about the origin follows the rule $(x, y) \to (y, -x)$. Applying this to Z(1, -2) results in (-2, -1).
Question 6
Points: 4
Use coordinate notation to describe the dilation.
Explanation
The original point P is at (-4, 4) and its image $P'$ is at (-1, 1). The scale factor k is found by $x' / x = -1 / -4 = 1/4$. Thus, the notation is $(x,y) \to (\frac{1}{4}x, \frac{1}{4}y)$.
Question 7
Points: 4
Trapezoid QRST and its image are shown. What transformation maps trapezoid QRST onto trapezoid LMNO?
Explanation
The image LMNO is a flipped version of QRST across the x-axis (y=0), which is a horizontal line.
Question 8
Points: 4
Write congruence statements comparing the corresponding angles in this set of congruent figures.
Explanation
By matching the arc markings on the angles: $\angle K$ and $\angle Q$ have one arc, $\angle M$ and $\angle L$ have two arcs, and $\angle R$ and $\angle P$ have three arcs.
Question 9
Points: 4
In the baseball diamond shown, $\Delta BEA \cong \Delta ARB$. The length of BE is 90 feet. What is the length of AR?
Explanation
In congruent triangles, corresponding sides are equal. Since $\Delta BEA \cong \Delta ARB$, the side BE corresponds to AR. Therefore, AR = BE = 90 ft.
Question 10
Points: 4
Square ABCD is similar to square EFGH. Determine which sequence of transformations maps square ABCD onto square EFGH.
Explanation
Square ABCD has a side length of 4 units, while square EFGH has a side length of 1 unit, implying a dilation of 1/4. Vertex A(-8, 8) dilates to (-2, 2), and a $180^\circ$ rotation maps (-2, 2) to G(2, -2).
Question 11
Points: 4
Triangle ABC is similar to $\Delta XYZ$. Determine which sequence of transformations maps $\Delta ABC$ onto $\Delta XYZ$.
Explanation
The side lengths of $\Delta XYZ$ are twice those of $\Delta ABC$, indicating a dilation by 2. Point B(2, 1) dilates to (4, 2), and a $90^\circ$ counterclockwise rotation $(x, y) \to (-y, x)$ maps (4, 2) to X(-2, 4).
Question 12
Points: 4
Determine whether this pair of polygons is similar. If so, write a similarity statement.
Explanation
The correct correspondence is \(A \leftrightarrow E\), \(B \leftrightarrow F\), \(C \leftrightarrow G\), and \(D \leftrightarrow H\). Comparing corresponding sides: AB/EF = 15/5 = 3, BC/FG = 22.8/7.6 = 3, CD/GH = 45/15 = 3, and DA/HE = 24/8 = 3. Since all corresponding side ratios are equal and the corresponding angles match, the polygons are similar. Therefore, \(ABCD \sim EFGH\).
Question 13
Points: 4
In the figure, the triangles are similar. What is the distance d from the water ride to the roller coaster?
Explanation
Using similar triangles: the ratio of height to base is d / 45 = 10 / 21. Solving for d: $d = (45 \times 10) / 21 \approx 21.4$ m.
Question 14
Points: 4
Find the volume of the cylinder. Express your answer in terms of $\pi$.
Explanation
The radius r is 10/2 = 5 ft and the height h is 6 ft. Volume $V = \pi r^2 h = \pi (5^2)(6) = 150 \pi$.
Question 15
Points: 4
Find the volume of this cone. Express your answer in terms of $\pi$.
Explanation
Volume of a cone $V = \frac{1}{3} \pi r^2 h$. With r = 2 ft and h = 7 ft, $V = \frac{1}{3} \pi (2^2)(7) = \frac{28}{3} \pi = 9 \frac{1}{3} \pi \text{ ft}^3$.
Question 16
Points: 4
Find the volume of this hemisphere. Round to the nearest tenth.
Explanation
Volume of a hemisphere $V = \frac{2}{3} \pi r^3$. With r = 6.7 ft, $V = \frac{2}{3} \pi (6.7^3) \approx 629.9 \text{ ft}^3$.
Question 17
Points: 4
Find the volume of this sphere. Express your answer in terms of $\pi$.
Explanation
The diameter is 9 in, so the radius r = 4.5 in. Volume $V = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi (4.5^3) = 121.5 \pi \text{ in}^3$.
Question 18
Points: 4
Find the volume of the flower vase. Round to the nearest tenth.
Select the scatter plot that correctly represents the data.
Explanation
Graph A correctly represents the data points. The other graphs do not match the given data.
Question 20
Points: 4
The scatter plot shows the relationship between the birth month of every student in Mari’s class and their height. Which is the best interpretation of the data?
Explanation
The points are scattered randomly across the plot without forming a line or a curve, indicating that birth month is not related to height.
Question 21
Points: 4
Use the line of fit to make a conjecture about the shoe size of a boy on the team that is 59 inches tall.
Explanation
By observing the line of best fit at the height of 59 inches on the x-axis, the corresponding shoe size on the y-axis is approximately 7.5.
Question 22
Points: 4
Write an equation in slope−intercept form for the line of fit that is drawn.
Explanation
The y-intercept is 90. Another point on the line is (72, 0). Slope m = (0 - 90) / (72 - 0) = -90 / 72 = -1.25. The equation is y = -1.25x + 90.
Question 23
Points: 4
How many more T-shirts were sold for 9 than16?
Explanation
From the line of fit, at 9, about 27.5 shirts were sold. At16, about 10 shirts were sold. The difference is 27.5 - 10 = 17.5.
Question 24
Points: 4
The table shows the results of a survey about the number of bus riders at McGuffey Junior High. Find the column relative frequencies. Round to the nearest hundredth. Are male students or female students more likely to not ride the bus?
Explanation
Column relative frequencies: Males (No Bus) = 85/195 ≈ 0.44. Females (No Bus) = 42/126 ≈ 0.33. Since 0.44 > 0.33, male students are more likely not to ride.
Question 25
Points: 4
The two-way table shows the enrollment in language classes at Carson Middle School. Which of the following are valid conclusions about the data?
Explanation
Total students = 120. Total enrolled in French = 95. Since 95 out of 120 is approximately 79%, it is more than half.
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