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Practice Test Unit 3 Geometry
Tuesday, September 18, 2018Tuesday, September 18, 2018
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A B C D E A. (1,10) B. (2,7) C. (3,5) D. (4,3) E. (5,1)
Which of the following points is the greatest distance from the y-axis? 1 A A. (1,10) B. (2,7) C. (3,5) D. (4,3) E. (5,1) B C D E
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Points P, Q, R, and S lie on a line in that order
Points P, Q, R, and S lie on a line in that order. If QR = RS, PQ = 10, and PS = 38, what does QR equal? 2 38 – 10 = 28 10 P Q R S 38 QR = 28 ÷ 2 = 14
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Find the midpoint between the points (3,–6) and (7,13).
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x + x + 44 = 180 Straight Line 180 2x + 44 = 180 –44 –44 2x = 136
In the figure below, is a straight line. What is the value of x? x + x + 44 = 180 Straight Line 180 2x + 44 = 180 –44 –44 2x = 136 x = 68
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h b 7 – (–1) = 7 + 1 = 8 Find the area of ABC. 5 8 Side
Note: The y-coordinates are the same. 7 – (–1) = = 8 Subtract x-coordinates.
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Find the area of ABC. 5 5 h 8 b = 20
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Find the length of the line segment AB. 6 Find the length by
finding the distance between the points. A(–3,4) B(2,1)
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d ≈ 5.83 Find the length of the line segment AB. 6
Find the length by finding the distance between the points. A(–3,4) B(2,1) d ≈ 5.83
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7 Solve for x. Congruent Angles 4 = 8 (x+80) x + 80 = 5x –x –x
m || n m (x+80) x + 80 = 5x n –x –x (5x) 80 = 4x 20 = x m || n 1 2 m 4 3 1 = 3 = 5 = 7 5 6 n 2 = 4 = 6 = 8 8 7
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Find the value of x. 5y 9x + 8 80 9x + 8 = 80 Vertical Angles – 8 – 8
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9 If PRQ is an isosceles triangle with PQ = PR, find the measure of QPX. ∆PRQ: Isosceles Triangle The base angles are equal. QPX: Exterior Angle 60 ?
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2z = 70 + z – z – z z = 70 70 2z In the figure, if x = 2z and y = 70,
what is the value of z? 10 70 2z 2z = 70 + z Exterior Angles Rule – z – z z = 70
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11 If the ratio of the angles of a triangle is 2:3:4, what is the degree measure of the largest angle? Largest Angle 4x 4(20) = 80
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12 In the isosceles right triangle ABC, leg equals 6. What is the length of ? 3x = 6 x = 2 6 = 5x = 5(2) = 10
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A C = 180° – 80° – 50° = 50° 80° AB = AC 2x – 12 = x – 3 –x –x
In ABC, the measure of A is 80° and the measure of B is 50°. If the length of AB is 2x – 12 and the length of AC is x – 3, what is the length of AB? 14 A C = 180° – 80° – 50° = 50° 80° AB = AC 2x – 12 = x – 3 –x –x x – 12 = –3 50° 50° x = 9 B C AB = 2(9)–12 = 18 –12 = 6
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In the right ABC, the length of leg is
15 In the right ABC, the length of leg is and D is the midpoint of Find the length of x= = 3 30° C = 180° – A – B = 180° – 60° – 90° = 30°
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16 Find the length of JK. L 34.6 mm 18 K J 1 x = 34.6 x x = cos 18 = .9511
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x x 140 140 x x Step 1: Find the sum of interior
17 Two angles of a hexagon measure 140° each. The other four angles are equal in measure. What is the measure of each of the other four equal angles, in degrees? Step 1: Find the sum of interior angles in a hexagon. x x Number of sides = 6 140 140 Number of sides – 2 = 6 – 2 = 4 x x Multiply 4 by 180 = 4(180) = 720
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Measure of each the four equal angles is 110
17 Two angles of a hexagon measure 140° each. The other four angles are equal in measure. What is the measure of each of the other four equal angles, in degrees? Step 1: Find the sum of interior angles in a hexagon. x x 720 Step 2: Set up equation by letting sum of angles equal 720. 140 140 x + x + x + x = 720 4x = 720 x x – 280 – 280 Measure of each the four equal angles is 110 4x = 440 x = 110
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A regular octagon is shown. What is the measure, in degrees, of X?
18 A regular octagon is shown. What is the measure, in degrees, of X? Step 1: Find sum of the interior angles in the regular octagon. Number of sides = 8 X Number of sides – 2 = 8 – 2 = 6 Multiply 6 by 180 = 6(180) = 1080 Step 2: Find value of each interior angle, X. Divide sum by number of sides, 8. 1080 8 = 135
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∆ABC is Isosceles ∆AED Big Triangle A = 45 D = 90 E = 45
19 In the figure, right triangle ABC is contained within right triangle AED. What is the ratio of the area of AED to the area of ABC? ∆ABC is Isosceles 45 ∆AED Big Triangle 45 A = 45 D = 90 E = 45 ∆AED is Isosceles 45 8
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19 In the figure, right triangle ABC is contained within right triangle AED. What is the ratio of the area of AED to the area of ABC? Area of ∆ABC Small Triangle 45 = 18 45 Area of ∆AED Big Triangle = 32 45 8
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x 5 5 5 x x x 5 Area of square QROS = 5 5 = 25 20
The figure above shows a square region divided into four rectangular regions, three of which have areas 5x, 5x, and x2, respectively. If the area of MNOP is 64, what is the area of square QROS? x 5 Area of square QROS Length Width 5 5 = 5 5 = 25 x x x 5
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V = Volume V = lwh 2l + 2w 126 = l w 6 = 2(7) + 2(3) = 14 + 6
21 All the dimensions of a certain rectangular solid are integers greater than 1. If the volume is 126 cubic inches and the height is 6 inches, what is the perimeter of the base? V = Volume Perimeter of Base V = lwh 2l + 2w l w h 126 = l w 6 = 2(7) + 2(3) = 6 21 = l w = 20 (Base) Base l = 3 or 7 w = 3 or 7
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A and B supplementary 75° + x = 180°
22 In trapezoid ABCD, AB = CD. What is the value of x? Method #1 Isosceles Trapezoid A and B supplementary 75° + x = 180° –75 –75 x = 105°
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22 In trapezoid ABCD, AB = CD. What is the value of x? Method #2 Sum of all angles = 360° x + x = 360 2x = 360 –150 –150 2x = 210 x = 105
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23 Cube A has an edge of 2. Each edge of cube A is increased by 50%, creating a second cube B. The surface area of cube B is how much greater than the surface area of cube A? 2 Cube A Cube B 3 50% of 2 = .50 2 = 1 50% increase = 2 + 1 = 3
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= = 622 = 632 = 64 = 69 = 24 = 54 – 54 – 24 30 SA = 6s2 SA = 6s2
23 Cube A has an edge of 2. Each edge of cube A is increased by 50%, creating a second cube B. The surface area of cube B is how much greater than the surface area of cube A? SA = Surface Area 2 Cube A Cube B 3 SA = 6s2 SA = 6s2 = 622 = 632 = 64 = 69 = 24 = 54 SA Cube B SA Cube A – – = 30
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VZ = 12 VX = 6 VW = 6 WX = 6 Perimeter VWX = 6 + 6 + 6 = 18
24 In the figure, VW = WX = VX = XY = YZ = XZ. If VZ = 12, what is the perimeter of the triangle VWX? VZ = 12 VX = 6 VW = 6 WX = 6 Perimeter VWX = = 18
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d: diameter r: radius d = 2r d = 8 r = 4 C = 2πr A = πr2 = 2π4 = 8π
25 If the diameter of circle is 8, what is the ratio between the circle’s area and its circumference? d: diameter r: radius d = 2r Step 1: Find the radius, given diameter is 8. d = 8 r = 4 Step 2 Find circumference of circle. Step 3 Find area of circle. C = 2πr A = πr2 = 2π4 = 8π = π42 = π16 = 16π
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C = 2πr A = πr2 = 2π4 = 8π = π42 = π16 = 16π = 2 = 2:1 25
If the diameter of circle is 8, what is the ratio between the circle’s area and its circumference? Step 2 Find circumference of circle. Step 3 Find area of circle. C = 2πr A = πr2 = 2π4 = 8π = π42 = π16 = 16π Step 4: Find ratio. = 2 = 2:1
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C: Circumference C = 2πr A: Area Find the radius A = πr2 A = π
26 Find the circumference of a circle with area π. C: Circumference C = 2πr A: Area Find the radius A = πr2 A = π C: Circumference π = πr2 C = 2πr C = 2π 1 C = 2π 1 = r2 1 = r
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27 If a circle with an area of 4 is inscribed in a square , what is the perimeter of the square? 4 A: Area P: Perimeter A = 4π P = 4s A = πr2 d = 4 P = 4(4) r = 2 4π = πr2 P = 16 (Find radius) 4 = r2 2 = r
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= Square Area – Circle Area
In the figure, the circle inscribed inside the square has a radius of 3. What is the area of the shaded region? 28 6 Circle Area Square Area A = πr2 A = s2 d = 6 A = π·32 A = 62 3 A = π·9 A = 36 A = 9π Area of shaded region = Square Area – Circle Area = 36 – 9π
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29 The circle has a diameter of 12. What is the length of ? Length of major arc 6 C = 2πr = 9π C = 2π 6 = 12π
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30 If the circumference of the circle is 8, what is the area of the shaded region? Circumference Area of circle C = 2πr A = πr2 C = 8π A = π 42 8π = 2πr A = π 16 4 = r Central Angle = 90° A = 16π Area of sector = 4π
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ABC = 48°. Find the measure of the major arc .
31 Major Arc in red 48 48 Major Arc = 360 – 48 = 312
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If , find the measure of CDE.
32 = 60
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In the figure, if the slope of line m is ,
what is the value of y ? 33 Use the slope formula. 4(y – 8) = –8 3 4y – 32 = –24 +32 +32 4y = 8 y = 2
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34 If a straight line intersects the x-axis at 5 and the y-axis at 3, what is the slope of the line? –5 3
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2y = 3x + 4 Which line is parallel to the line 2y = 3x + 4 ?
35 Which line is parallel to the line 2y = 3x + 4 ? Note: Parallel lines have the same slope. Step 1: Find the slope of 2y = 3x + 4 by rewriting in slope-intercept form, y = mx + b 6y = 3x – 4 2y = x + 2 C. 4y = 6x – 1 y = 3x + 4 E. 2y = –2x – 1 2y = 3x + 4
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35 Which line is parallel to the line 2y = 3x + 4 ? Note: Parallel lines have the same slope. Step 2: Find the slope of each answer by rewriting in slope-intercept form, y = mx + b 2y = 3x + 4 NO 6y = 3x – 4 Slopes not equal
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35 Which line is parallel to the line 2y = 3x + 4 ? Note: Parallel lines have the same slope. Step 2: Find the slope of each answer by rewriting in slope-intercept form, y = mx + b 2y = 3x + 4 B. NO 2y = x + 2 Slopes not equal
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35 Which line is parallel to the line 2y = 3x + 4 ? Note: Parallel lines have the same slope. Step 2: Find the slope of each answer by rewriting in slope-intercept form, y = mx + b 2y = 3x + 4 C. 4y = 6x – 1 Slopes are equal
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form a rectangle. The slope of line AB is .
36 A, B, C, and D are points in the coordinate system. Segments AB, BC, CD, and DA form a rectangle. The slope of line AB is What is the slope of line BC. A B C D A B C D
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form a rectangle. The slope of line AB is .
36 A, B, C, and D are points in the coordinate system. Segments AB, BC, CD, and DA form a rectangle. The slope of line AB is What is the slope of line BC. A B C D Perpendicular Lines have slopes that are negative reciprocals
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37 Which line segment in the figure has a slope of ? Use
to find the slope for each line segment. Segments and have positive slopes. They rise as you trace them from left to right. Thus, they can not be the answer.
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–5 4 37 Which line segment in the figure has a slope of ? Use
to find the slope for each line segment. –5 4
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–3 3 37 Which line segment in the figure has a slope of ? Use
to find the slope for each line segment. –3 3
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–3 2 37 Which line segment in the figure has a slope of ? Use
to find the slope for each line segment. –3 2
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Find the equation of the given graph. 38 Start at origin.
Shift left 2 units. Shift down 1 unit.
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Find the equation of the given graph. 39 Start at origin.
Shift right 3 units. Reflect on x-axis.
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40 A parabola with in equation of the form y = ax2 + bx + c has the point (3,1) as its vertex. If (1,3) also lies on the parabola, which of the following is another point on this parabola? Mirror Image Points x = 1 x = 3 x = 5 (1,3) (?,3) (5,3) x-coordinates are same distance from axis of symmetry (3,1)
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Which parabola intersects the x-axis in two distinct points? 41
A. y = (x + 5)2 B. y = (x – 5)2 Touches x-axis at 1 point Touches x-axis at 1 point
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Which parabola intersects the x-axis in two distinct points? 41
C. y = x2 – 25 D. y = x2 + 25 E. y = (x – 4)2 Touches x-axis at 1 point Touches x-axis at 2 points Touches x-axis at 0 points
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Which of the following are solutions to the equation x2 + 2x = 8 ?
42 Which of the following are solutions to the equation x2 + 2x = 8 ? Substitute each answer for x into equation x2 + 2x = 8. Then, determine if both sides are equal. –8 and 1 –1 and 8 –4 and –2 4 and –2 E. –4 and 2 NO Test x = 1 Test x = –8 x2 + 2x = 8 x2 + 2x = 8 (1)2 + 2(1) = 8 (–8)2 + 2(–8) = 8 1 + 2 = 8 64 + (–16) = 8 3 8 48 8
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If one answer does not work, then the whole answer is wrong.
42 Which of the following are solutions to the equation x2 + 2x = 8 ? Substitute each answer for x into equation x2 + 2x = 8. Then, determine if both sides are equal. –8 and 1 –1 and 8 –4 and –2 4 and –2 E. –4 and 2 NO Test x = 8 If one answer does not work, then the whole answer is wrong. x2 + 2x = 8 NO (8)2 + 2(8) = 8 = 8 80 8
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If one answer does not work, then the whole answer is wrong.
42 Which of the following are solutions to the equation x2 + 2x = 8 ? Substitute each answer for x into equation x2 + 2x = 8. Then, determine if both sides are equal. –8 and 1 –1 and 8 –4 and –2 4 and –2 E. –4 and 2 NO Test x = –2 If one answer does not work, then the whole answer is wrong. NO x2 + 2x = 8 (–2)2 + 2(–2) = 8 NO 4 + (–4) = 8 NO 0 8
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Which of the following are solutions to the equation x2 + 2x = 8 ?
42 Which of the following are solutions to the equation x2 + 2x = 8 ? Substitute each answer for x into equation x2 + 2x = 8. Then, determine if both sides are equal. –8 and 1 –1 and 8 –4 and –2 4 and –2 E. –4 and 2 NO Test x = 2 Test x = –4 x2 + 2x = 8 x2 + 2x = 8 NO (2)2 + 2(2) = 8 (–4)2 + 2(–4) = 8 NO 4 + 4 = 8 16 + (–8) = 8 NO 8 = 8 8 = 8
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