加拿大安大略省十年级数学试卷英文

合集下载

国际学校数学十年级试卷

tion and write capital letters A, B, C or D in the brackets.
1. The prime factorisation form of 156
A) 2 ´ 3´ 13
B) 22 ´ 32 ´ 13
2. The logarithemic form of 8x = 2
Chapter Real numbers
2.
Sets
3.
Polynomials
Weightage % 48% 20% 32% 100%
Marks 12 5 8 25
Table : 3 Weightage to difficulty level
S. No.
Difficulty level
Weightage % Marks
A) logx 8 = 2
B) log 2 = x 8
p 3. The q form of the decimal 0.875
7
A) 23
7
B) 16
C) 22 ´ 3 ´ 13 C) log 2 = 8
x
3
C) 8
() D) 2 ´ 32 ´ 13
() D) log x = 8
2
7
D) 22
()
3
1.
Easy
24%
06
2.
Average
3.
Difficulty
52%
13
24%
06
100%
25
Table : 4 Weightage to type of questions
S. No. Type of Questions
Weightage % No. of Questions Marks

国际学校十年级数学期末测试卷(英语)

a) 1.42814 b) 0.57358 c) 0.81915 d) 0.022126
2. If cos q = 0.6691306, then q = a) 48° b) 42° c) 33.8° d) 22.9°
3. If DABC ~ DPQR, then a) AB = PQ b) A = P c) a = b d) c = r
Final Practice Exam
4. The cost of 4 L of milk is $7.35. The unit cost per litre is a) $3.68 b) $1.84 c) $2.45 d) $0.735
5. A 10% discount off an item priced at $30.00 would save you a) $3.00 b) $27.00 c) $10.00 d) $1.00
8. A rotation of a shape is a) a slide b) a translation c) a turn d) a mirror image
9. Which statement is true about angles with parallel lines with a transversal? a) All angles are 60° b) Interior alternate angles are complementary c) Corresponding angles are supplementary d) Exterior alternate angles are congruent
Final Practice Exam
3
4
Grade 10 Essential Mathematics

加拿大数学十年级(高一)省考模拟试题A

© Province of British Columbia
PART A: MULTIPLE-CHOICE QUESTIONS (calculator not permitted)
Value: 12 marks
Suggested Time: 30 minutes Allowable Time: 40 minutes
Page 1
Use the following graph to answer question 2.
y
10
5
–10
–5
–5
x
5
10
–10
2. Which of the following equations describes the linear relation graphed above?
Do not access your calculator until directed by the supervisor. At the end of the 40 minutes, the supervisor will give you permission to access your calculator.
where n is the number of students attending the prom. Calculate the cost of renting the hall if 70 students attend. A. $108 B. $500 C. $780 D. $970
6. Which of the following statements are true?
Contents: 31 pages 54 multiple-choice questions (maximum of 54 marks) 6 numeric-response questions (maximum of 6 marks)

加拿大安大略地区十学年数学试卷英文

GRADE 10 PRINCIPLES OF MATHEMATICS (ACADEMIC)MPM 2DTotal Marks:INSTRUCTIONS:1. Calculators may be used.2. Read all instructions carefully in order to maximize your mark.A/C[K] Part A – Multiple Choice 25 Marks (25 questions * 1 mark each)For each of the following questions in this section, circle the letterrepresenting the correct answer.1. A linear system of two equations that has one solution represents twolines that are:a) parallel b) coincident c) intersecting d) none of these2. The midpoint of RS is M(8, -1). If point S has coordinates (11, 4) what are the coordinates of point R ? a) (3, -6)b) (15, -6)c) (5, -6)d) (3, 9)3. The midpoint of the line segment with end points A(-8, 8) and B(6, 4) is: a) (0, 10)b) (1, 2)c) (7, 2)d) (-1, 6)4. The equation of a horizontal line passing through the point (4, 2) is: a) 2=xb) 4=yc) 2=yd) 4=x5. The equation of a line with a slope of 5=m and a y intercept of 8 is: a) 85+=x yb) 85+-=x yc) 85--=x yd) 58+=x y6. The slopes of 2 lines are -7 and 71. These lines are said to be:a) parallelb) perpendicularc) coincidentd) none of these7. The slope of a line segment passing through 2 points (10,- 4) and (-2, -16) is: a) 1b) 2c) -1d) -28. The length of a line segment with end points (-6, 7) and (-1, -5) is: a) 12b) 5c) 13d) 1699. The diameter of a circle whose equation is 28922=+y x is:a) 15b) 16c)17d) none of these10. T he equation of a circle with a centre of (0, 0) that also passes through the point (-8, -6) is: a) 1022=+y xb) 10022=+y xc) 1422=+y xd) 4822=-y x11. T he y-intercept of the line 01052=+-y x is: a) 2b) -2c) 10d) 512. T he slope of the line 0124=-+y x is: a) 2b) -2c) 1d) 013. I f (-3, y) is a solution to the equation 132=+y x , what is the value of y ? a) 3b) 6c) 5d) 814. T he product ()()z y x z y x 323243-- is equal to:a) 2612z xyb) 26412z y xc) 2612z xy -d) 00412z y x15. A simplified expression for ()()n m n m ----52 is: a) m 7b) n m 27+c) m 3-d) n m 27-16. A simplified expression for 242927abcbc a -- is:a) ac 3 b) abc 3 c) 23acd) 223c a17. T he slope of the line, which is perpendicula r to the line, 084=+-y x is: a) -4 b) 4 c) 1 d) -118. T he shortest distance from the point (2, -3) to the line 4-=x is: a) 5 b) 3 c) 2 d) 619. T he value of the polynomial 8542+-a a when 3-=a is: a) 59 b) 44 c) 13 d) 2920. W hich of the following is not a function : a)()()(){}7,6,5,4,3,2b) 22x y =c) 22y x =d) ()()(){}3,8,3,7,2,621. T he range of the relation whose equation is 52--=x y is: a) 5-≤y b) 5≤y c) 5-≥y d) 5≥y22. T he vertex of the parabola ()642--=x y is:a) ()6,4- b) ()6,4- c) ()4,6- d) ()4,6-23. T he equation of the axis of symmetry of the parabola ()5242+--=x y is:a) 5=x b) 5-=x c) 2=xd) 2-=x 24. A parabola with a vertex of ()3,2 and a stretch factor of 41- (relative to2x y =) would have an equation of: a) ()32412+--=x y b) ()32412++-=x y c)()23412-+-=x y d) ()23412++-=x y25 The parabola k x y +-=24 passes through the point ()3,2-. T he value of k is: a) -19b) 11c) 13d) 19A/CPart B – Short AnswersFor each of the questions in this section, write your answers in the spaces provided . Use the foolscap provided for any rough work. Show details of calculations wherever requested.1. In the accompanying diagram, state each of the following: (4 Marks) [K] a) domain: __________ (1 Mark)[K]b)range: __________ (1 Mark)[C]c)Is the relation a function? Justify your answer. (2 marks)[A] 2. The x-intercepts of the parabola 2892-y are: __________ and=x__________.(Show your work) (2 Marks)[A] 3. The roots of the quadratic equation 032=1710x are: __________ and+-x__________.(Show your work) (3 Marks)[A] 4. Write the equation of the parabola with a vertex of (4, 23) if it passesthrough the point (-1, -2): (Show your work) (3 Marks)____________________[T] 5. A line passes through 2 points (1, 4) and (2,-4). Calculate the slope of the line. Also show the equation of the line in the form 0ByAx. (Show+=+Cyour work) (4 Marks)____________________ ____________________Slope Equation[K] 6. The Tangent of 45 is: __________ (1 Mark)[A] 7. a) In the accompanying diagram, the two triangles are similar. What is thevalue of x?(Show your work) (2 Marks) Array=x__________[T] b) If the area of the smaller triangle is 8 cm 2, what is the area of the larger triangle?(Show your work) ( 2 Marks)Area = __________[K]8 Given that sin A = 21, find A ∠ (to the nearest degree) __________ (1Mark)[A] 9. In the accompanying right triangle , find the value of x to one decimal place.(Show your work) (2 Marks)=x ________[A] 10. U se the SINE LAW to find the value of side x to one decimal place.(Show your work) (2 Marks)3028︒x56︒42︒x30x = ________[A] 11. U se the COSINE LAW to find the value of side x to one decimal place.(Show your work) (2 Marks)x = ________[T] 12. F actor each of the following to the fullest extent possible: (4 Questions * 2 marks each)a) y x my mx 22--+________________________b) 31142--x x________________________c) 2416916y x -________________________56︒2030xd) 2225rs-________________________ r+9s30A/C Part C – Full Solutions RequiredFor each of the questions in this section, full solutions are required.Record your answers in the spaces provided. Use the foolscap providedfor any rough work.[A] 1. Solve the linear system using the elimination method. Remember tofind values for both x and y. (5 Marks)22+yx5=-yx=32-21[C] Explain what the solution above represents geometrically. How do youknow that the solution you arrived at is the correct answer? (2 Marks)[A]2. Expand and simplify the polynomial ()()()21432+-+-x x x . (4 Marks)[T]3. Find the equation of the line perpendicular to the line 088=-+y x and passing through the point (-4, 1). (4 Marks)[T] 4. From the window of one building, a man finds that the angle ofelevation to the top of a second building is 47︒ and the angle ofdepression to the bottom of the same building is 58︒. The buildings are 60 m apart. Find the height of the 2nd building to the nearest metre.A diagram is required. (6 Marks)[T] 5. ABC has vertices A(1, 7), B(-5, 3) and C(3, -1). Determine the equation for AE, the altitude from vertex A to the opposite side BC.(5 Marks)6. The hypotenuse of a right triangle is 26 cm. The sum of the other twosides is 34 cm. (9 Marks)[T] a) Find the length of the other two sides of the triangle. (3 Marks)[T] b) Find the measure of the other two angles. Round to the nearest degree. (3 Marks)[C] c) Describe a situation where you would be able to use knowledge ofthe Pythagorean theorem in a practical, real life situation. (3 Marks)[T] 7. A rectangular skating rink measures 20m by 20m. It has been decided to increase the area of the rink by a factor of 4. Determine how mucheach side should be extended. Assume that each side is extendedby the same amount. (6 Marks)[C]What is the significance of keeping the skating rink in the shape of a square? Justify your answer. (3 Marks)[A]8. a) Solve 35122+=d d using the quadratic formula. (2 Marks)[A] b) Solve 03122=-x by factoring. Check your solutions. (2 Marks)。

加拿大数学十年级(高一)省考模拟试题B汇编

You have Examination Booklet Form B. In the box above #1 on your Answer Sheet, fill in the bubble as follows.
Exam Booklet Form/ A B C D E F G H Cahier d’examen
A. decreased by 15 km h B. decreased by 5 km h C. increased by 15 km h D. increased by 11 km h
3. Solve the following system of equations:
4x + 2y = 8 3x + y = 1
13. Marbles are placed in a jar one at a time. Which graph below best represents the total mass of the jar and marbles as the marbles are added?
A.
B.
Total Mass
INSTRUCTIONS: No calculator may be used for this part of the examination. For each question, select the best answer and record your choice on the blue Answer Sheet provided.
Foundations of Mathematics and Pre-Calculus 10 – 2010–2011 Sample B
Page 5
PART B: MULTIPLE-CHOICE QUESTIONS (calculator permitted)

加拿大数学10年级练习第四部分几何

加拿⼤数学10年级练习第四部分⼏何1. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.2. Find the area of the triangle with ∠A = 41, b = 5 ft, and c = 4 ft. Round your answer to two decimal places.6.56 ft210.00 ft27.55 ft213.12 ft23. Find the area of kite ABCD if BD = 48 cm, AB = 25 cm, and BC = 26. The kite is not drawn to scale.289 cm270 cm2816 cm2408 cm24. The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. Abouthow much room is there between the ball and the rim in a shot in which the ball goes in exactly in the center of the rim?none of these5. Find the area.718 square units545 square units534.5 square units701 square units6. Name the major arc and find its measure.m = 275m = 170m = 85m = 2757. Find the area of the regular polygon. Round your answer to the nearest tenth.110.2 in.28. Name the minor arc and find its measure.m = 275m = 85m = 170m = 2759. Find the area of ΔABC. The figure is not drawn to scale.26.06 cm228.00 cm222.73 cm224.95 cm210. Find the circumference of the circle. Use as an approximation of π.11 cm5 cm6 cm11. If a dart hits the target at random, what it the probability that it will land in the unshaded region?12. Find the area of the circle. Use π = 3.14 and round to the nearest hundredth.91.56 m216.96 m25.72 m222.89 m213. Find the area of a regular pentagon with side 6 cm.45.2 cm2123.9 cm214. Find the probability that an object falling randomly on the figure will land in the shaded area.0.320.360.50.2615. Find the area.102.9 yd2205.8 yd235.35 yd2105.5 yd216. Two concentric circles have radii of 14 cm and 24 cm. Find the probability to the nearest thousandth that a point chosen at random from the circles is located outside the smaller circle and inside the larger one.0.0660.58317. A slide that is inches by inches is projected onto a screen that is 3 feet by 7 feet, filling the screen.What will be the ratio of the area of the slide to its image on the screen?1 : 1121 : 23042 : 42051 : 12,54418. Find the area of a regular octagon with perimeter 48 cm.188.1 cm2190.5 cm2347.6 cm2173.8 cm219. Dorothy ran 6 times around a circular track that has a diameter of 47 m. Approximately how far did she run? Use π = 3.14 and round your answer to the nearest meter.885 m1328 m443 m1734 m20. Find the area.10.26 cm2。

加拿大数学10年级练习第四部分几何

1. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.••••2. Find the area of the triangle with ∠A = 41, b = 5 ft, and c = 4 ft. Round your answer to two decimal places.• 6.56 ft2•10.00 ft2•7.55 ft2•13.12 ft23. Find the area of kite ABCD if BD = 48 cm, AB = 25 cm, and BC = 26. The kite is not drawn to scale.•289 cm2•70 cm2•816 cm2•408 cm24. The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. Abouthow much room is there between the ball and the rim in a shot in which the ball goes in exactly in the center of the rim?•none of these5. Find the area.•718 square units•545 square units•534.5 square units•701 square units6. Name the major arc and find its measure.•m = 275•m = 170•m = 85•m = 2757. Find the area of the regular polygon. Round your answer to the nearest tenth.•110.2 in.28. Name the minor arc and find its measure.•m = 275•m = 85•m = 170•m = 2759. Find the area of ΔABC. The figure is not drawn to scale.•26.06 cm2•28.00 cm2•22.73 cm2•24.95 cm210. Find the circumference of the circle. Use as an approximation of π.•11 cm•5 cm•6 cm11. If a dart hits the target at random, what it the probability that it will land in the unshaded region?••••12. Find the area of the circle. Use π = 3.14 and round to the nearest hundredth.•91.56 m2•16.96 m2• 5.72 m2•22.89 m213. Find the area of a regular pentagon with side 6 cm.•45.2 cm2•123.9 cm214. Find the probability that an object falling randomly on the figure will land in the shaded area.•0.32•0.36•0.5•0.2615. Find the area.•102.9 yd2•205.8 yd2•35.35 yd2•105.5 yd216. Two concentric circles have radii of 14 cm and 24 cm. Find the probability to the nearest thousandth that apoint chosen at random from the circles is located outside the smaller circle and inside the larger one.•0.066•0.58317. A slide that is inches by inches is projected onto a screen that is 3 feet by 7 feet, filling the screen.What will be the ratio of the area of the slide to its image on the screen?• 1 : 112• 1 : 2304• 2 : 4205• 1 : 12,54418. Find the area of a regular octagon with perimeter 48 cm.•188.1 cm2•190.5 cm2•347.6 cm2•173.8 cm219. Dorothy ran 6 times around a circular track that has a diameter of 47 m. Approximately how far did she run?Use π = 3.14 and round your answer to the nearest meter.•885 m•1328 m•443 m•1734 m20. Find the area.•10.26 cm21. Find the volume of the cylinder in terms of π.•24π in.3•48π in.3•56π in.3•288π in.32. Find the volume of the cylinder in terms of π.•287π in.3•275π in.2•275π in.3•287π in.23. A sphere has a volume of 288π ft3. Find the surface area of the sphere.•864π ft2•48π ft2•144π ft2•96π ft24. The volumes of two similar solids are 2197 m3 and 64 m3. The surface area of the larger one is 845 m2. What is•64 m2•320 m2•80 m2•none of these5. Use a net to find the surface area of the prism.•114 m2•240 m2•290 m2•145 m26. Find the surface area of a sphere that has a diameter of 4 cm.•64π cm2•π cm3•4π cm2•16π cm27. Find the lateral area and the surface area of the cone. Use 3.14 for πand round the answer to the nearest hundredth.The diagram is not to scale.•lateral area: 733.33 ft2; surface area: 690.80 ft2•lateral area: 690.80 ft2; surface area: 1004.80 ft2•none of these8. If the ratio of the radii of two spheres is 7 : 2, what is the ratio of the surface areas of the two spheres?•7 : 2•7r2π : 2r2π•49 : 4•343 : 89. Use a net to find the surface area of the prism.•465 m2•720 m2•918 m2•930 m210. Find the height of the cylinder to the nearest tenth of an inch.•94.6 in.•96.6 in.• 4.3 in.• 4.1 in.11. Use formulas to find the lateral area and the surface area of the prism. Show your answer to the nearest hundredth.•63.00 m2; 567.00 m2•36.00 m2; 1134.00 m2•479.22 m2; 533.22 m2•542.22 m2; 596.22 m212. Find the volume of the prism.•942 m3•38 m3•945 m3•1890 m313. The volumes of two similar solids are 1331 m3 and 343 m3. The surface area of the larger one is 484 m2. Whatis the surface area of the smaller one?•343 m2•1372 m2•196 m2•none of these14. Find the surface area of the sphere.•648π m2•72π m2•324π m2•1296π m215. Find the volume of the prism.•40.5 m3•162 m3•9 m3•81 m316. Find the surface area of the solid. Round to the nearest square foot.•36 ft2•68 ft217. Use formulas to find the surface area of the prism. Show your answer to the nearest hundredth.•75.42 cm2•170.16 cm2•86.94 cm2•69.52 cm218. Which figure is a net for a cube?••••19. Cylinder A has radius 1 and height 4 and cylinder B has radius 2 and height 4. Find the ratio of the volumesof the two cylinders.• 1 : 4• 1 : 120. Neil had a job helping a jeweler. He had the assignment of counting the faces, vertices, and edges on the emeralds.On the first emerald, Neil counted 9 faces and 16 edges. He quickly realized he didn't have to count the vertices.How many vertices were there?•10 vertices•7 vertices•8 vertices•9 vertices1. Find the value of x if AB = 20, BC = 12, and CD = 13. (not drawn to scale)•18.8•16.5•13.4•14.92. Find the measure of each variable if m∠A = 22 and m = 97. (not drawn to scale)•53; 210•53; 105•75; 210•75; 1053. In the plane of lines X and Y, what is the locus of points equidistant from lines X and Y?•line A•line D•line B•line C4. A small messenger company can only deliver within a certain distance from the company. On the graph below, thecircular region represents that part of the city where the company delivers, and the center of the circle represents the location of the company. Which equation represents the boundary for the region where the company delivers?•(x + 3)2 + (y– 1)2 = 49•(x + 3)2 + (y– 3)2 = 98•(x + 1)2 + (y– 3)2 = 98•(x + 3)2 + (y– 3)2 = 495. A low-watt radio station can be heard only within a certain distance from the station. On the graph below, thecircular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. Which equation represents the boundary for the region where the station can be heard?•(x– 4)2 + (y– 5)2 = 50•(x + 5)2 + (y– 5)2 = 59•(x + 5)2 + (y + 4)2 = 25•(x + 5)2 + (y– 5)2 = 256. Find the center and radius of (x– 8)2 + (y + 7)2 = 64.•(–8, 7); 8•(–7, 8); 64•(8, –7); 8•(–7, –8); 87. is tangent to circle O at B. How close to the circle is point A? (The diagram is not to scale.)• 3• 4.5• 6•7.58. Compare the quantity in Column A with the quantity in Column B.•The quantity in Column A is greater.•The quantity in Column B is greater.•The two quantities are equal.•The relationship cannot be determined from the information given.9. Solve for x.•22•710. Find the value of x.•14.6•8.1•9.4•13.411. Write the standard equation for the circle with center (14, –48) that passes through (0, 0).•(x– 14)2 + (y + 48)2 = 2500•(x + 14)2 + (y– 48)2 = 2500•(x + 14)2 + (y– 48)2 = 50•(x– 14)2 + (y + 48)2 = 5012. Find the measure of ∠BAC.•30°•150°13. Find the value of x.•79•39•99•15914. In space, which description fits the locus of points 3 cm from ?•an open cylinder of diameter 6 cm•an open cylinder of radius 3 cm and two hemispheres of diameter 6 cm each•an open cylinder of radius 3 cm and height 6 cm•an open cylinder of diameter 6 cm and two spheres of radius 3 cm each15. and are tangent to circle O and bisects ∠BPA. If m∠AOC= 68°, how much greater is m∠BCO thanm∠OAD? (The diagram is not to scale.)•22°•112°16. Write the standard equation for the circle with center (6, –8) that passes through (0, 0).•(x + 6)2 + (y– 8)2 = 0•(x– 6)2 + (y + 8)2 = 0•(x + 6)2 + (y– 8)2 = 100•(x– 6)2 + (y + 8)2 = 10017. Find the center and radius of (x + 3)2 + (y + 8)2 = 169.•(3, 8); 13•(–8, 3); 13•(–3, –8); 13•(–8, –3); 16918. , , and are all tangent to circle O. If JA= 8, AL= 13, and CK= 11, what is the perimeter of ΔJKL?(The diagram is not to scale.)•32•64•45•5319. If m = 38, what is m∠YAC?•109°•52°20. Write the standard equation for the circle with center (–16, 30) that passes through (0, 0).•(x + 16)2 + (y– 30)2 = 34•(x + 16)2 + (y– 30)2 = 1156•(x– 16)2 + (y + 30)2 = 1156•(x– 16)2 + (y + 30)2 = 34。

加拿大数学十年级(高一)省考模拟试题A

© Province of British Columbia
PART A: MULTIPLE-CHOICE QUESTIONS (calculator not permitted)
Value: 12 marks
Suggested Time: 30 minutes Allowable Time: 40 minutes
INSTRUCTIONS: No calculator may be used for this part of the examination. For each question, select the best answer and record your choice on the blue Answer Sheet provided.
This is the end of Part A (calculator not permitted).
If there is some time left, you have two options: i) Make sure you have answered all the questions. You will not be able to go back to this section at the end of 40 minutes. ii) You may proceed to the rest of the examination without the use of a calculator; there are many questions that do not require a calculator. Make sure you flag any questions you skip to remember to go back to them later.

加拿大数学10年级练习第四部分几何电子教案

加拿大数学10年级练习第四部分几何1. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.••••2. Find the area of the triangle with ∠A = 41, b = 5 ft, and c = 4 ft. Round your answer to two decimalplaces.• 6.56 ft2•10.00 ft2•7.55 ft2•13.12 ft23. Find the area of kite ABCD if BD = 48 cm, AB = 25 cm, and BC = 26. The kite is not drawn to scale.•289 cm2•70 cm2•816 cm2•408 cm24. The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches.About how much room is there between the ball and the rim in a shot in which the ball goes in exactly in the center of the rim?• 4.2 in.• 4.78 in.•none of these5. Find the area.•718 square units•545 square units•534.5 square units•701 square units6. Name the major arc and find its measure.•m = 275•m = 170•m = 85•m = 2757. Find the area of the regular polygon. Round your answer to the nearest tenth.•40.0 in.2•67.6 in.2•110.2 in.28. Name the minor arc and find its measure.•m = 275•m = 85•m = 170•m = 2759. Find the area of ΔABC. The figure is not drawn to scale.•26.06 cm2•28.00 cm2•22.73 cm2•24.95 cm210. Find the circumference of the circle. Use as an approximation of π.•11 cm•5 cm•6 cm11. If a dart hits the target at random, what it the probability that it will land in the unshaded region?••••12. Find the area of the circle. Use π = 3.14 and round to the nearest hundredth.•91.56 m2•16.96 m2• 5.72 m2•22.89 m213. Find the area of a regular pentagon with side 6 cm.•76.6 cm2•45.2 cm2•123.9 cm214. Find the probability that an object falling randomly on the figure will land in the shaded area.•0.32•0.36•0.5•0.2615. Find the area.•102.9 yd2•205.8 yd2•35.35 yd2•105.5 yd216. Two concentric circles have radii of 14 cm and 24 cm. Find the probability to the nearest thousandth thata point chosen at random from the circles is located outside the smaller circle and inside the larger one.•0.066•0.583•0.01717. A slide that is inches by inches is projected onto a screen that is 3 feet by 7 feet, filling thescreen. What will be the ratio of the area of the slide to its image on the screen?• 1 : 112• 1 : 2304• 2 : 4205• 1 : 12,54418. Find the area of a regular octagon with perimeter 48 cm.•188.1 cm2•190.5 cm2•347.6 cm2•173.8 cm219. Dorothy ran 6 times around a circular track that has a diameter of 47 m. Approximately how far did she run?Use π = 3.14 and round your answer to the nearest meter.•885 m•1328 m•443 m•1734 m20. Find the area.•10.26 cm2•61.56 cm21. Find the volume of the cylinder in terms of π.•24π in.3•48π in.3•56π in.3•288π in.32. Find the volume of the cylinder in terms of π.•287π in.3•275π in.2•275π in.3•287π in.23. A sphere has a volume of 288π ft3. Find the surface area of the sphere.•864π ft2•48π ft2•144π ft2•96π ft24. The volumes of two similar solids are 2197 m3 and 64 m3. The surface area of the larger one is 845 m2. Whatis the surface area of the smaller one?•64 m2•320 m2•80 m2•none of these5. Use a net to find the surface area of the prism.•114 m2•240 m2•290 m2•145 m26. Find the surface area of a sphere that has a diameter of 4 cm.•64π cm2•π cm3•4π cm2•16π cm27. Find the lateral area and the surface area of the cone. Use 3.14 for π and round the answer to the nearesthundredth. The diagram is not to scale.•lateral area: 733.33 ft2; surface area: 690.80 ft2•lateral area: 6908.00 ft2; surface area: 1004.80 ft2•lateral area: 690.80 ft2; surface area: 1004.80 ft2•none of these8. If the ratio of the radii of two spheres is 7 : 2, what is the ratio of the surface areas of the twospheres?•7 : 2•7r2π : 2r2π•49 : 4•343 : 89. Use a net to find the surface area of the prism.•465 m2•720 m2•918 m2•930 m210. Find the height of the cylinder to the nearest tenth of an inch.•94.6 in.•96.6 in.• 4.3 in.• 4.1 in.11. Use formulas to find the lateral area and the surface area of the prism. Show your answer to the nearesthundredth.•63.00 m2; 567.00 m2•36.00 m2; 1134.00 m2•479.22 m2; 533.22 m2•542.22 m2; 596.22 m212. Find the volume of the prism.•942 m3•38 m3•945 m3•1890 m313. The volumes of two similar solids are 1331 m3 and 343 m3. The surface area of the larger one is 484 m2.What is the surface area of the smaller one?•343 m2•1372 m2•196 m2•none of these14. Find the surface area of the sphere.•648π m2•72π m2•324π m2•1296π m215. Find the volume of the prism.•40.5 m3•162 m3•9 m3•81 m316. Find the surface area of the solid. Round to the nearest square foot.•36 ft2•32 ft217. Use formulas to find the surface area of the prism. Show your answer to the nearest hundredth.•75.42 cm2•170.16 cm2•86.94 cm2•69.52 cm218. Which figure is a net for a cube?••••19. Cylinder A has radius 1 and height 4 and cylinder B has radius 2 and height 4. Find the ratio of thevolumes of the two cylinders.• 1 : 4• 5 : 620. Neil had a job helping a jeweler. He had the assignment of counting the faces, vertices, and edges on theemeralds. On the first emerald, Neil counted 9 faces and 16 edges. He quickly realized he didn't have to count the vertices. How many vertices were there?•10 vertices•7 vertices•8 vertices•9 vertices1. Find the value of x if AB = 20, BC = 12, and CD = 13. (not drawn to scale)•18.8•16.5•13.4•14.92. Find the measure of each variable if m∠A = 22 and m = 97. (not drawn to scale)•53; 210•53; 105•75; 210•75; 1053. In the plane of lines X and Y, what is the locus of points equidistant from lines X and Y?•line A•line D•line B•line C4. A small messenger company can only deliver within a certain distance from the company. On the graph below,the circular region represents that part of the city where the company delivers, and the center of the circle represents the location of the company. Which equation represents the boundary for the region where the company delivers?•(x + 3)2 + (y– 1)2 = 49•(x + 3)2 + (y– 3)2 = 98•(x + 1)2 + (y– 3)2 = 98•(x + 3)2 + (y– 3)2 = 495. A low-watt radio station can be heard only within a certain distance from the station. On the graph below,the circular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. Which equation represents the boundary for the region where the station can be heard?•(x– 4)2 + (y– 5)2 = 50•(x + 5)2 + (y– 5)2 = 59•(x + 5)2 + (y + 4)2 = 25•(x + 5)2 + (y– 5)2 = 256. Find the center and radius of (x– 8)2 + (y + 7)2 = 64.•(–8, 7); 8•(–7, 8); 64•(8, –7); 8•(–7, –8); 87. is tangent to circle O at B. How close to the circle is point A? (The diagram is not to scale.)• 3• 4.5• 6•7.58. Compare the quantity in Column A with the quantity in Column B.•The quantity in Column A is greater.•The quantity in Column B is greater.•The two quantities are equal.•The relationship cannot be determined from the information given.9. Solve for x.•22•710. Find the value of x.•14.6•8.1•9.4•13.411. Write the standard equation for the circle with center (14, –48) that passes through (0, 0).•(x– 14)2 + (y + 48)2 = 2500•(x + 14)2 + (y– 48)2 = 2500•(x + 14)2 + (y– 48)2 = 50•(x– 14)2 + (y + 48)2 = 5012. Find the measure of ∠BAC.•30°•150°13. Find the value of x.•79•39•99•15914. In space, which description fits the locus of points 3 cm from ?•an open cylinder of diameter 6 cm•an open cylinder of radius 3 cm and two hemispheres of diameter 6 cm each•an open cylinder of radius 3 cm and height 6 cm•an open cylinder of diameter 6 cm and two spheres of radius 3 cm each15. and are tangent to circle O and bisects ∠BPA. If m∠AOC= 68°, how much greater is m∠BCOthan m∠OAD? (The diagram is not to scale.)•22°•112°16. Write the standard equation for the circle with center (6, –8) that passes through (0, 0).•(x + 6)2 + (y– 8)2 = 0•(x– 6)2 + (y + 8)2 = 0•(x + 6)2 + (y– 8)2 = 100•(x– 6)2 + (y + 8)2 = 10017. Find the center and radius of (x + 3)2 + (y + 8)2 = 169.•(3, 8); 13•(–8, 3); 13•(–3, –8); 13•(–8, –3); 16918. , , and are all tangent to circle O. If JA = 8, AL = 13, and CK = 11, what is the perimeter ofΔJKL? (The diagram is not to scale.)•32•64•45•5319. If m = 38, what is m∠YAC?•142°•71°•109°•52°20. Write the standard equation for the circle with center (–16, 30) that passes through (0, 0).•(x + 16)2 + (y– 30)2 = 34•(x + 16)2 + (y– 30)2 = 1156•(x– 16)2 + (y + 30)2 = 1156•(x– 16)2 + (y + 30)2 = 34。

2007加拿大bc省考

1tremulous: shaking and trembling 2prayerwheels: a wheel on a spindle upon which prayers are written
English 10 – 0708 Form A
1. What does the first stanza suggest about the speaker? A. He views life as a series of insurmountable obstacles. B. He has come to appreciate the solitude of his quiet existence. C. He is relieved to have made it successfully back to the valley. D. He believes he has faced the biggest challenge he will ever face.
English 10 – 0708 Form A

Page 3
In the following poem, a mountain climber speaks about his life after climbing Mount Everest.
Page 4
Here in Katmandu
by Donald Justice
• Read the short context statement before each passage for useful information. • The numbers in the left margin next to passages tell you where to find information.

加拿大数学10年级练习第四部分几何

1. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.∙∙∙∙2. Find the area of the triangle with ∠A = 41, b = 5 ft, and c = 4 ft. Round your answer to two decimal places. ∙ 6.56 ft2∙10.00 ft2∙7.55 ft2∙13.12 ft23. Find the area of kite ABCD if BD = 48 cm, AB = 25 cm, and BC = 26. The kite is not drawn to scale.∙289 cm2∙70 cm2∙816 cm2∙408 cm24. The diameter of a basketball rim is 18 inches. A standard basketball has a circumference of 30 inches. Abouthow much room is there between the ball and the rim in a shot in which the ball goes in exactly in the center of the rim?∙none of these5. Find the area.∙718 square units∙545 square units∙534.5 square units∙701 square units6. Name the major arc and find its measure.∙m = 275∙m = 170∙m = 85∙m = 2757. Find the area of the regular polygon. Round your answer to the nearest tenth.∙110.2 in.28. Name the minor arc and find its measure.∙m = 275∙m = 85∙m = 170∙m = 2759. Find the area of ΔABC. The figure is not drawn to scale.∙26.06 cm2∙28.00 cm2∙22.73 cm2∙24.95 cm210. Find the circumference of the circle. Use as an approximation of π.∙11 cm∙5 cm∙6 cm11. If a dart hits the target at random, what it the probability that it will land in the unshaded region?∙∙∙∙12. Find the area of the circle. Use π = 3.14 and round to the nearest hundredth.∙91.56 m2∙16.96 m2∙ 5.72 m2∙22.89 m213. Find the area of a regular pentagon with side 6 cm.∙45.2 cm2∙123.9 cm214. Find the probability that an object falling randomly on the figure will land in the shaded area.∙0.32∙0.36∙0.5∙0.2615. Find the area.∙102.9 yd2∙205.8 yd2∙35.35 yd2∙105.5 yd216. Two concentric circles have radii of 14 cm and 24 cm. Find the probability to the nearest thousandth that apoint chosen at random from the circles is located outside the smaller circle and inside the larger one.∙0.066∙0.58317. A slide that is inches by inches is projected onto a screen that is 3 feet by 7 feet, filling the screen.What will be the ratio of the area of the slide to its image on the screen?∙ 1 : 112∙ 1 : 2304∙ 2 : 4205∙ 1 : 12,54418. Find the area of a regular octagon with perimeter 48 cm.∙188.1 cm2∙190.5 cm2∙347.6 cm2∙173.8 cm219. Dorothy ran 6 times around a circular track that has a diameter of 47 m. Approximately how far did she run?Use π = 3.14 and round your answer to the nearest meter.∙885 m∙1328 m∙443 m∙1734 m20. Find the area.∙10.26 cm21. Find the volume of the cylinder in terms of π.∙24π in.3∙48π in.3∙56π in.3∙288π in.32. Find the volume of the cylinder in terms of π.∙287π in.3∙275π in.2∙275π in.3∙287π in.23. A sphere has a volume of 288π ft3. Find the surface area of the sphere.∙864π ft2∙48π ft2∙144π ft2∙96π ft24. The volumes of two similar solids are 2197 m3 and 64 m3. The surface area of the larger one is 845 m2. What is∙64 m2∙320 m2∙80 m2∙none of these5. Use a net to find the surface area of the prism.∙114 m2∙240 m2∙290 m2∙145 m26. Find the surface area of a sphere that has a diameter of 4 cm.∙64π cm2∙π cm3∙4π cm2∙16π cm27. Find the lateral area and the surface area of the cone. Use 3.14 for πand round the answer to the nearest hundredth.The diagram is not to scale.∙lateral area: 733.33 ft2; surface area: 690.80 ft2∙lateral area: 690.80 ft2; surface area: 1004.80 ft2∙none of these8. If the ratio of the radii of two spheres is 7 : 2, what is the ratio of the surface areas of the two spheres? ∙7 : 2∙7r2π : 2r2π∙49 : 4∙343 : 89. Use a net to find the surface area of the prism.∙465 m2∙720 m2∙918 m2∙930 m210. Find the height of the cylinder to the nearest tenth of an inch.∙94.6 in.∙96.6 in.∙ 4.3 in.∙ 4.1 in.11. Use formulas to find the lateral area and the surface area of the prism. Show your answer to the nearest hundredth.∙63.00 m2; 567.00 m2∙36.00 m2; 1134.00 m2∙479.22 m2; 533.22 m2∙542.22 m2; 596.22 m212. Find the volume of the prism.∙942 m3∙38 m3∙945 m3∙1890 m313. The volumes of two similar solids are 1331 m3 and 343 m3. The surface area of the larger one is 484 m2. Whatis the surface area of the smaller one?∙343 m2∙1372 m2∙196 m2∙none of these14. Find the surface area of the sphere.∙648π m2∙72π m2∙324π m2∙1296π m215. Find the volume of the prism.∙40.5 m3∙162 m3∙9 m3∙81 m316. Find the surface area of the solid. Round to the nearest square foot.∙36 ft2∙68 ft217. Use formulas to find the surface area of the prism. Show your answer to the nearest hundredth.∙75.42 cm2∙170.16 cm2∙86.94 cm2∙69.52 cm218. Which figure is a net for a cube?∙∙∙∙19. Cylinder A has radius 1 and height 4 and cylinder B has radius 2 and height 4. Find the ratio of the volumesof the two cylinders.∙ 1 : 4∙ 1 : 120. Neil had a job helping a jeweler. He had the assignment of counting the faces, vertices, and edges on the emeralds.On the first emerald, Neil counted 9 faces and 16 edges. He quickly realized he didn't have to count the vertices.How many vertices were there?∙10 vertices∙7 vertices∙8 vertices∙9 vertices1. Find the value of x if AB = 20, BC = 12, and CD = 13. (not drawn to scale)∙18.8∙16.5∙13.4∙14.92. Find the measure of each variable if m∠A = 22 and m = 97. (not drawn to scale)∙53; 210∙53; 105∙75; 210∙75; 1053. In the plane of lines X and Y, what is the locus of points equidistant from lines X and Y?∙line A∙line D∙line B∙line C4. A small messenger company can only deliver within a certain distance from the company. On the graph below, thecircular region represents that part of the city where the company delivers, and the center of the circle represents the location of the company. Which equation represents the boundary for the region where the company delivers?∙(x + 3)2 + (y– 1)2 = 49∙(x + 3)2 + (y– 3)2 = 98∙(x + 1)2 + (y– 3)2 = 98∙(x + 3)2 + (y– 3)2 = 495. A low-watt radio station can be heard only within a certain distance from the station. On the graph below, thecircular region represents that part of the city where the station can be heard, and the center of the circle represents the location of the station. Which equation represents the boundary for the region where the station can be heard?∙(x– 4)2 + (y– 5)2 = 50∙(x + 5)2 + (y– 5)2 = 59∙(x + 5)2 + (y + 4)2 = 25∙(x + 5)2 + (y– 5)2 = 256. Find the center and radius of (x– 8)2 + (y + 7)2 = 64.∙(–8, 7); 8∙(–7, 8); 64∙(8, –7); 8∙(–7, –8); 87. is tangent to circle O at B. How close to the circle is point A? (The diagram is not to scale.)∙ 3∙ 4.5∙ 6∙7.58. Compare the quantity in Column A with the quantity in Column B.∙The quantity in Column A is greater.∙The quantity in Column B is greater.∙The two quantities are equal.∙The relationship cannot be determined from the information given.9. Solve for x.∙22∙710. Find the value of x.∙14.6∙8.1∙9.4∙13.411. Write the standard equation for the circle with center (14, –48) that passes through (0, 0). ∙(x– 14)2 + (y + 48)2 = 2500∙(x + 14)2 + (y– 48)2 = 2500∙(x + 14)2 + (y– 48)2 = 50∙(x– 14)2 + (y + 48)2 = 5012. Find the measure of ∠BAC.∙30°∙150°13. Find the value of x.∙79∙39∙99∙15914. In space, which description fits the locus of points 3 cm from ?∙an open cylinder of diameter 6 cm∙an open cylinder of radius 3 cm and two hemispheres of diameter 6 cm each∙an open cylinder of radius 3 cm and height 6 cm∙an open cylinder of diameter 6 cm and two spheres of radius 3 cm each15. and are tangent to circle O and bisects ∠BPA. If m∠AOC= 68°, how much greater is m∠BCOthan m∠OAD? (The diagram is not to scale.)∙22°∙112°16. Write the standard equation for the circle with center (6, –8) that passes through (0, 0).∙(x + 6)2 + (y– 8)2 = 0∙(x– 6)2 + (y + 8)2 = 0∙(x + 6)2 + (y– 8)2 = 100∙(x– 6)2 + (y + 8)2 = 10017. Find the center and radius of (x + 3)2 + (y + 8)2 = 169.∙(3, 8); 13∙(–8, 3); 13∙(–3, –8); 13∙(–8, –3); 16918. , , and are all tangent to circle O. If JA= 8, AL= 13, and CK= 11, what is the perimeter of ΔJKL?(The diagram is not to scale.)∙32∙64∙45∙5319. If m = 38, what is m∠YAC?∙109°∙52°20. Write the standard equation for the circle with center (–16, 30) that passes through (0, 0). ∙(x + 16)2 + (y– 30)2 = 34∙(x + 16)2 + (y– 30)2 = 1156∙(x– 16)2 + (y + 30)2 = 1156∙(x– 16)2 + (y + 30)2 = 34。

加拿大数学10年级练习第一部分几何

1. ABCD is an isosceles trapezoid, and ≅. Which statement is NOT true?•ΔABY≅ΔBAX•≅•≅•∠DXB≅∠DYB2. It appears from the name of the HL Theorem that you actually need to know only two parts of a triangle in orderto prove two triangles congruent. Is this the case?•Yes, you only need to know the hypotenuse and a leg of a triangle.•No, you actually need to know two sides and an angle, because the triangle must be a right triangle.•No, you actually need to know three sides of the triangle.•No, you actually need to know two angles and a side.3. Complete the proof.Given: ≅, ∠1 ≅∠2, and ≅.Prove: ΔCEF≅ΔAEF.∠BEC≅∠DEA by vertical angles. ΔBEC≅ΔDEA by (a)_____. Then by CPCTC, ≅. ≅by the Reflexive Property. So ΔCEF≅ΔAEF by (b)_____.• a. SAS; b. SAS• a. AAS; b. SSS• a. ASA; b. SSS• a. AAS; b. HL4. Complete the proof.Given: ≅, ∠1 ≅∠2Prove: ΔBEA≅ΔDEC≅and ∠1 ≅∠2, so ΔBCA≅ΔDAC by SAS. Then, since (a)_____, ≅, ≅. ∠BEA≅∠DEC by (b)_____, so ΔBEA≅ΔDEC by (c)_____.• a. CPCTC; b. vertical angles; c. SAS• a. CPCTC; b. vertical angles; c. AAS• a. CPCTC; b. vertical angles; c. SSS• a. SAS; b. vertical angles; c. SSS5. What additional information can be used to prove the triangles congruent by the HL Theorem?•m∠BCE = 90•AB > AC•≅•≅6. Suppose ΔCED≅ΔDBC. If m∠EDC = 63 and m∠DBC = 82, what is m∠DCE?•63•82•145•357. If ∠A≅∠D and ∠C≅∠F, which statement would NOT prove that ΔABC≅ΔDEF?••∠B≅∠E•≅•none of these8. Determine what information you would need to know in order to use the SSS Congruence Postulate to show that thetriangles are congruent.•∠BAD≅∠CDB•≅•∠ADB≅∠CBD•≅9. Suppose ΔBCA≅ΔECD. Which statement is NOT necessarily true?•≅•∠A≅∠D•≅•∠BCA≅∠DCE10. In which triangles could you efficiently prove Δ1 ≅Δ2 using the HL Theorem?•II only•III only•II and III•I only11. Complete the proof.Given: ≅, ∠1 ≅∠2, and ≅.Prove: ΔCEF≅ΔAEF.∠BEC≅∠DEA with vetical angles. ΔBEC≅ΔDEA by (a)_____. Then by (b)_____, ≅. ≅by the Reflexive Property. So ΔCEF≅ΔAEF by (c)_____.• a. AAS; b. CPCTC; c. SSS• a. SAS; b. CPCTC; c. SSS• a. AAS; b. CPCTC; c. SAS• a. SSS; b. CPCTC; c. ASA12. In the paper airplane, ABCD≅EFGH, m∠B = m∠BCD = 90, and m∠BAD = 140. Find m∠GHE.•130•90•40•14013. Find the value of x.•x = –2•x = 9•x = 21•none of these14. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove that ∠D≅∠B.•≅and ∠ACB≅∠ACD. By the Symmetric Property, ≅. By SAS, ΔABC≅ΔADC, so by CPCTC ∠D≅∠B.•≅and ∠ACB≅∠ACD. By the Reflexive Property, ≅. By ASA, ΔABC≅ΔADC, so by CPCTC ∠D≅∠B.•≅and ∠ACB≅∠ACD. By the Reflexive Property, ≅. By SAS, ΔABC≅ΔADC, so by CPCTC ∠D≅∠B.•≅and ∠ACB≅∠ACD. By the Reflexive Property, ≅. By SSS, ΔABC≅ΔADC, so by CPCTC ∠D≅∠B.15. Complete the proof.Given: bisects ∠URS and bisects ∠UTS.Prove: ΔURT≅ΔSRT.•Reflexive property•definition of angle bisector•HL Theorem•CPCTC16. Complete the proof.Given: ∠RSQ≅∠TSQ, ∠RQS≅∠TQS.Prove: ≅.∠RSQ≅∠TSQ is given, as is ∠RQS≅∠TQS. By the Reflexive Property, ≅.ΔSRQ≅ΔSTQ by (a)_____, so ≅by (b)_____.• a. ASA; b. CPCTC• a. HL; b. CPCTC• a. SSS; b. CPCTC• a. SAS; b. CPCTC17. Determine which triangles are congruent by AAS using the information in the diagram below.•ΔABF≅ΔEDF•ΔADC≅ΔEBC•ΔABE≅ΔEDA•ΔABE≅ΔCBE18. Complete the proof.Given: bisects ∠EBC and bisects ∠ECC.Prove:ΔEBD≅ΔCBD.•Same-Side Interior Angles Theorem•given•SSS postulate•Triangle Inequality Theorem19. ΔABD≅ΔCBD. Name the theorem or postulate that justifies the congruence.•SAS•AAS•ASA•none of these1. Determine whether each quadrilateral can be a parallelogram. If not, write impossible.a. Two adjacent angles are right angles, but the quadrilateral is not a rectangle.b. All of the angles are congruent.• a. impossible; b. parallelogram• a. parallelogram; b. parallelogram• a. parallelogram; b. impossible• a. impossible; b. impossible2. Which statement is true?•All rectangles are squares.•All quadrilaterals are squares.•All quadrilaterals are parallelograms.•All parallelograms are quadrilaterals.3. Which statement can be used to determine whether quadrilateral XYZW must be a parallelogram?•≅and ≅•≅and ≅•≅and ≅•XW = WZ and XY = YZ4. Choose the best name for the parallelogram and find the measures of the numbered angles.•Square; all numbered angles are equal to 45°.•Rhombus; all numbered angles are equal to 115°.•Rhombus; all numbered angles are equal to 25°.•Square; all numbered angles are equal to 50°.5. Given: quadrilateral ABCD with A(–2, 3), B(2, –4), C(9, 0), D(5, 7). Then ABCD is a rectangle because•the slopes of the sides in pairs are negative reciprocals.•the product of the slopes of the diagonals is –1.•the figure has four vertices.•opposite sides have the same slope.6. Given the parallelogram below, find coordinates for P, without using any new variables.•(a–c, b)•(a + c, b)•(c, b)•(c, a)7. Find the values of the variables for the rectangle. Then find the lengths of the sides.•x = 7, y = 5; side lengths: 70, 45•x = 5, y = 7; side lengths: 33, 94•x = 5, y = 7; side lengths: 50, 63•x = 7, y = 5; side lengths: 45, 458. Determine whether the quadrilateral is a parallelogram. Explain.≅and ≅•Yes; if two opposite sides are congruent, then the quadrilateral is a parallelogram.•No; if the diagonals of a quadrilateral bisect each other, this is not enough to prove that the quadrilateral is a parallelogram.•No; if two opposite sides are congruent, this is not enough to prove that the quadrilateral is a parallelogram.•Yes; if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.9. Can coordinate geometry be used to prove that opposite sides and in quadrilateral EFGH are congruent?•Yes; use the Distance Formula to show that the diagonals are congruent.•No; you can only show that EF is parallel to GH by using coordinate geometry.•Yes; use the Distance Formula between vertices E and F, and between vertices G and H.•No; you can only find the slopes of EF and GH by using coordinate geometry.10. A square WXYZ has the vertices W(b, b), X(b, –b), Y(–b, –b), and Z(–b, b). Which vertex is in QuadrantII?•W•Z•X•Y11. ∠J and ∠M are base angles of isosceles trapezoid JKLM. If m∠J = 21x + 4, m∠K = 12x– 8, and ∠M = 14x+ 10, find the value of x.•• 2•–•–912. Suppose you are using coordinate geometry to prove that quadrilateral WXYZ is a square. Explain why no twosides should be parallel to the y-axis.•The x-axis would intersect two sides of the square, so the coordinates of the corners would not be clear.•Sides which are parallel to the y-axis would have an undefined slope, so you cannot prove numerically that these sides are parallel.•Points on the sides which are parallel to the y-axis could have any y-value.•The sides of the square which are parallel to the y-axis could be easily confused with the y-axis.13. Find AM if PN = 8 and AO = 5.•8• 3•13• 514. Given square ABCD, where A = (0, a), B = (a, a), C = (0, 0), and D = (a, 0). To prove that the diagonal ADis times the length of side CD, first use _____ to find that = a and = a. Therefore, the ratio= , or .•the definition of isosceles triangle ACD•the definition of right angle C•the Distance Formula•the definition of the origin C = (0, 0)15. A farmer is building a fence for his yard. He is considering two designs, which are shown below. Explain whythe quadrilaterals formed by the horizontal rails and the slanting boards are parallelograms in both designs.•The horizontal rails are parallel to each other. A parallelogram has exactly one pair of parallel sides, so both quadrilaterals are parallelograms.•The horizontal rails are congruent to each other. The slanting boards are all congruent to each other. A parallelogram has two pairs of adjacent sides, but opposite sides are not congruent, so both quadrilaterals are parallelograms.•The horizontal rails are congruent to each other. The slanting boards are all congruent to each other. A parallelogram has four congruent sides, so both quadrilaterals are parallelograms.•The horizontal rails are parallel to each other. The identical slanting boards all slant at the same angle, so the sides are parallel. A parallelogram has both pairs of sides parallel, so both quadrilaterals are parallelograms.16. A rhombus is centered on the origin. One side of the rhombus goes through the points (a, 0) and (0, b). Whatare possible coordinates for one of the other sides?•(–a, 0), (a, 0)•(b, 0), (0, –a)•(0, –b), (0, b)•(–a, 0), (0, –b)17. If a quadrilateral is a parallelogram, then its opposite sides are _____.•perpendicular•adjacent•congruent•none of these18. Find the value of each variable in the parallelogram. m∠1 = 10x, m∠2 = x + y, and m∠3 = 18z.•x = 9, y = 81, z = 5•x = 18, y = 167, z = 5•x = 18, y = 162, z = 10•x = 9, y = 86, z = 019. Complete ≅ _____ for parallelogram EFGH. Then state a definition or theorem as the reason.•; because the angles of a parallelogram bisect each other•; because the diagonals of a parallelogram bisect each other•; because the diagonals of a parallelogram bisect each other•; because the angles of a parallelogram bisect each other20. Which of the following sets of points represents a line segment in Quadrant III and its reflection in the x-axis?(Use the positive numbers a, b, c, d for the coordinates of the endpoints).•(a, b), (c, d); reflection (–a, b), (–c, d)•(–a, –b), (–c, –d); reflection (–a, b), (–c, d)•(a, b), (c, d); reflection (a, –b), (c, –d)•(–a, –b), (–c, –d); reflection (a, –b), (c, –d)1. Solve for a and b.•a = , b =•a = , b =•a = , b =•a = , b =2. State whether ΔADB∼ΔCDB, and if so, identify the theorem that proves the triangles similar.•yes, SSS∼•yes, AA∼•yes, SAS∼•no3. ABCDE∼GHJDF. Complete the congruence and proportion statements.a.∠H≅b.=• a.B; b.AE• a.E; b.DC• a.E; b.AE• a.B; b.DC4. Write a similarity statement for the two triangles.•ΔVUT∼ΔWXY•ΔTVU∼ΔWXY•ΔTUV∼ΔWXY•ΔTUV∼ΔWYX5. Find the geometric mean of 48 and 3.•9•25.5•12•166. The extendable ramp shown below is used to move crates of fruit to loading docks of different heights. When thehorizontal distance AB is 4 feet, the height of the loading dock, BC, is 3 feet. What is the height of the loading dock, DE?•7 ft•9 ft•11 ft7. Find the geometric mean of 20 and 5.•10• 4•12.5•258. In movies and television, the ratio of the width of the screen to the height is called the aspect ratio. Televisionscreens usually have an aspect ratio of 4 : 3, while movie screens usually have an aspect ratio of 1.85 : 1. However, if a movie is made for television in "Letterbox" format, it retains the 1.85 : 1 aspect ratio and fills in the top and bottom parts of the screen with black bars. What would be the height of a movie in "Letterbox" format on a television screen that measures 25 inches along its diagonal? (Hint: First find the width and height of the television screen.)•13.51 in.•10.81 in.•15 in.•8.12 in.9. Use the diagram to determine the height of the tree.•264 ft•72 ft•60 ft•80 ft10. The two rectangles are similar.Which is a correct proportion between corresponding sides?•=•=•=11. Use the Side-Splitter Theorem to find x given that || .•18•12•24• 612. Find OM if bisects ∠NLM, LM = 14, NO = 3, and LN = 4. Round your answer to the nearest hundredth, ifnecessary.•12.27•18.67•0.86•10.513. There is a law that the ratio of the width to length for the American flag should be 10 : 19. Which dimensionsare NOT in the correct ratio?•20 by 38 in.•50 by 95 ft•20 by 44 ft•100 by 190 ft14. If one measurement of a golden rectangle is 6.8 inches, which could be the other measurement?•8.418 in.•11.002 in.• 1.618 in.• 5.182 in.15. If one measurement of a golden rectangle is 8.2 inches, which could be the other measurement?•9.818 in.• 6.582 in.• 1.618 in.• 5.068 in.16. Solve = .•20•19•15•2417. Find OM if bisects ∠NLM, LM =15, NO = 5, and LN = 11. Round your answer to the nearest hundredth, ifnecessary.•33• 6.82• 3.67•8.5918. The width of a golden rectangle is 3 m, which is shorter than the length. What is the length?• 1.85 m• 2.32 m• 3.64 m• 4.85 m19. Find and simplify the ratio of the length to the width of the rectangle.••••20. ΔBGH∼ΔSWQ. What are the pairs of corresponding sides?•BG and SQ, BH and SW, GH and WQ•BG and GB, SQ and QS, GH and HG•BG and SW, BH and SQ, GH and WQ•BG and WQ, BH and SW, GH and SQ1. A building near Atlanta, Georgia, is 181 feet tall. On a particular day at noon it casts a 204-foot shadow. Whatis the sun's angle of elevation at that time?•41.6°•27.5°•62.5°•48.4°2. In right triangle ΔABC, sin A = . What is cos A?••••none of these3. Find the ratio for cos x.••••14. Find the value of x to the nearest meter.•46 m•40 m•35 m•36 m5. Compare the quantity in Column A with the quantity in Column B. The diagram may not be drawn to scale.•The quantity in Column A is greater.•The quantity in Column B is greater.•The two quantities are equal.•The relationship cannot be determined on the basis of the information given.6. How many of these triples could be sides of a right triangle: (27, 36, 45), (12, 17, 20), (24, 32, 40), (14,48, 50)?• 4 triples• 3 triples• 2 triples• 1 triple7. Find the ratio for cos x.•••2•8. Find a third number of the Pythagorean triple that includes 72 and 75.•9•21•37•1049. Find the measure of the marked acute angle to the nearest degree.•62°•28°•61°•118°10. In ΔABC, ∠A is a right angle and m∠B = 60. If AB = 20 ft, find BC. If necessary, round your answer tothe nearest tenth.•10 ft.•40 ft•20 ft•ft11. Find the value of the variable to the nearest hundredth.• 5.28 cm•0.32 cm• 3.13 cm• 5.12 cm12. Find the length of the leg of the right triangle. Leave your answer in simplest radical form.•48••288•13. In ΔABC, ∠A is a right angle and m∠B = 45. If AB = 20 ft, find BC.•10 ft•20 ft•40 ft•20 ft14. Which direction bearing is shown?•19° north of east•19° north of west•19° south of east•19° south of west15. Leslie used the diagram to compute the distance from Ferris to Dunlap to Butte. How much shorter is the distancedirectly from Ferris to Butte than the distance Leslie found?•123 mi•87 mi•36 mi•84 mi16. Which vector has a direction of 31° east of north?••••17. Find the value of x to the nearest tenth.•14.4• 6.3•7.8• 3.118. Find the value of x.•3•6•12• 619. Find the value of x to the nearest tenth.•7.8•18.3•33.0•8.920. Find the value of x to the nearest integer when tan x = 1.483.•58•56•55•571. Which type of isometry is the equivalent of two reflections across two vertical lines?•translation•rotation•glide reflection•none of these2. A section of a tessellated plane is shown below. Which types of symmetry does the tessellated plane have?•glide-reflectional symmetry•translational, rotational, and glide-reflectional symmetry•rotational symmetry•translational and reflectional symmetry3. A blueprint for a house has a scale of 1 : 30. A wall in the blueprint is 7 in. What is the length of the actualwall?•210 ft•21 ft•17.5 ft•none of these4. What is the image of the point (4, –2) after a rotation 270° clockwise about the origin?•(–4, 2)•(4, 2)•(–2, 4)•(2, 4)5. Which graph shows a triangle and its reflection image in the x-axis?••••6. Write a rule to describe a reflection over the y-axis.•(x, y) → (–x, y)•(x, y) → (–x, –y)•(x, y) → (x, –y)•(x, y) → (y, x)•reflectional•rotational•rotational and reflectional•none of these8. Find the image of O(0, 0) after two reflections, first in y = 4, and then in x = –7.•(7, –4)•(–14, 8)•(8, –14)•(–4, 7)9. A section of a tessellated plane is shown below. Which types of symmetry does the tessellated plane have?•rotational symmetry•translational and rotational symmetry•reflectional symmetry•glide-reflectional symmetry•rotational•reflectional•rotational and reflectional•none of these11. Describe the translation 7 units to the left, 12 units up using a vector.•)–12, 7*•)12, –7*•)–7, 12*•)7, –12*12. If the figure has rotational symmetry, find the angle of rotation about the center that results in an imagethat matches the original figure.•120°•90°•72°•It has no rotational symmetry.13. Find the glide reflection image of the solid triangle for the translation )–6, –3* and reflection in y = –1.••••14. If a point P(1, –2) is reflected across the line x = 3, what are the coordinates of its reflection image?•(1, –4)•(1, 8)•(–7, –2)•(5, –2)15. Which translation from thin-lined figure to thick-lined figure is given by the vector )6, 6*?••••16. The dotted triangle is a dilation image of the solid triangle. What is the scale factor?•• 2• 3•17. Find the image of C under the translation described by each vector.a.)4, 5*b.)11, –8*• a.A; b.B• a.B; b.A• a.E; b.D• a.D; b.E18. What is the image of the point (–3, 4) after a rotation of 90° counterclockwise about the point (–3, 0)?•(–7, 0)•(1, 0)•(0, –3)•(–3, –4)19. Which letter has rotational symmetry?• E•X•J•T20. Use scalar multiplication to find the image of the quadrilateral for a dilation with center (0, 0) and scalefactor 2. Graph the quadrilateral and its image.••••。

初中数学英文版试卷

Section 1: Multiple Choice (40 points)1. What is the value of $ 5^3 $?A) 5B) 10C) 25D) 1252. Simplify the expression: $ 8 - 3 \times 2 + 4 $.A) 6B) 10C) 2D) 123. Solve for $ x $: $ 2x + 5 = 19 $.A) 7B) 8C) 9D) 104. What is the area of a rectangle with a length of 12 units and a width of 5 units?A) 60 square unitsB) 70 square unitsC) 40 square unitsD) 50 square units5. If $ \frac{1}{3} $ of a class of 24 students are boys, how many boys are in the class?A) 6B) 8C) 10D) 126. Simplify the expression: $ \frac{7}{12} \times \frac{3}{4} $.A) $ \frac{1}{2} $B) $ \frac{1}{3} $C) $ \frac{1}{4} $D) $ \frac{1}{6} $7. Solve for $ y $: $ 3y - 2 = 11 $.A) 3B) 4C) 5D) 68. What is the perimeter of a square with a side length of 8 units?A) 32 unitsB) 24 unitsC) 16 unitsD) 12 units9. Simplify the expression: $ (2x - 3) + (4x + 5) $.A) 6x + 2B) 6x - 2C) 6x + 8D) 6x - 810. If a number is increased by 20 and then multiplied by 3, the result is 180. Find the original number.A) 5B) 10C) 15D) 20Section 2: Short Answer (60 points)11. Solve the following equations:a) $ 4x - 7 = 15 $b) $ 2(x + 3) = 10 $12. Find the value of $ x $ in the following equation:$ \frac{3x - 5}{2} = 4 $13. Simplify the following expressions:a) $ 3(2x - 5) + 4x $b) $ \frac{5}{6} - \frac{1}{3} $14. Calculate the area of a triangle with a base of 10 units and a height of 6 units.15. Simplify the following expression:$ \frac{4x^2 - 9}{x + 3} $Section 3: Problem Solving (100 points)16. A farmer has a rectangular field that is 30 meters long and 20 meters wide. He wants to fence the field. How much fencing will he need if he wants to build a fence on all four sides of the field?17. A train travels at a speed of 60 kilometers per hour. How far willit travel in 3 hours?18. A box has a volume of 216 cubic centimeters. If the length of the box is 6 centimeters, what is the width and height of the box?19. A school has 500 students. If 30% of the students are boys, how many boys are in the school?20. A garden is in the shape of a rectangle with a length of 8 meters and a width of 4 meters. If the garden is surrounded by a path of uniform width, and the total area of the garden and the path is 100 square meters, what is the width of the path?---This test is designed to assess the mathematical knowledge and skills of grade 8 students. Good luck!。