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OXFORD New Syllabus Mathematics Book 2 7th Edition Teh Keng Seng, Loh Cheng Yee, Joseph Yeo, Ivy Chow - Solutions

A translation maps the point (5, 7) onto the point (2, 9) and the point A onto the point (-3, -5). Find the coordinates of A.
1. Given that P is the point (3, 4), find the coordinates of the image of P under(a) an anticlockwise rotation of 90° about the point (2.0),(b) a reflection in the line x + 2 = 0
Under a translation T, the image of the point (5,-1) is (2, 3). Under a translation T, the image of the point (-2, 5) is (4,5). Find the image of the point (7. 6) under the following transformations.(a) T(b) T(c) TT(d) TT(e) T
Tis the translation (p, q) and C is (h, k). 2 A is the point (2, 4), B is(i) Find the coordinates of the image of the point A under T.(ii) Given that T(B)=A, find the value of p and of q(iii) Given that T,(A) = C, find the value of and of k.(iv) Find the coordinates of the point D such that T.(D) =
1A translation T maps the point (6, 2) onto the point (2, 7) and the point (-1,-5) onto the point P. Find the column vector representing the translation T and the coordinates of the point P.
1 The vertices of APQR are P(1, 3), Q(7, 5) and R(2, (0). Find the coordinates of the vertices of the image of APQR under a translation T represented by(2)
1. The vertices of a quadrilateral are A(2, 1), B(3, 3), C(5, 3) and D(5, 2). Find the coordinates of the vertices of the image of the quadrilateral ABCD under a translation T represented d by by 5 Find 2 the image of the new quadrilateral if it undergoes another translation T. represented by Show
Tis the translation and (2/3)T, is a translation that will move the point (1, 2) to (-2, 5), 3(6) Find the image of the point A(7, 4) under T(ii) Find the translation vector represented by T(iii) What is the image of the point B(8, 4) under T? T, is the translation (3)and T, is a translation that
Find out about Escher's tessellations and the transformations he used in his tessellations.
The triangle A'B'C is the image of the triangle ABC under a clockwise rotation of 25° about C. Calculate, giving your answer correct to the nearest 0.5°,(a) CÂA,(b) ACB'. A 60 mm B 1 B C 40 mm
Under a rotation, the line P'Q' is the image of the line PQ. Given that their coordinates are P(1, 1), 2(1, 4), (3, 1) and Q'(k, 1), where k > 0 find(i) the value of k,(ii) the image of the point 1.25(iii) the coordinates of the point whose image is
7. Find the equation of the image of the line y = x + 2 under a clockwise rotation of 90° about the origin.
The coordinates of AABC are A(4, 1), B(6, 1) and C(4, 6) while the coordinates of its image AA'B'C' under a rotation are A'(0, 1), B(-2, -1) and C'(0, -6). On a sheet of graph paper,(1) draw AABC and AA'B'C',(ii) find the centre of rotation by construction and state the angle of rotation.
(a) Triangle A can be mapped onto triangle R by a rotation. Find(i) the coordinates of the centre of rotation,(ii) the angle of rotation.(b) Triangle C can be mapped onto triangle A by a rotation. Find(i) the coordinates of the centre of rotation.(ii) the angle of rotation.(c) Triangle B is rotated
If R represents an anticlockwise rotation of 240° about the origin, describe R³ and R.
Find the coordinates of the image of the point (1, 4) under a clockwise rotation of(a) 90 about the centre (4, 2),(b) 180 about the centre (4, 2).
Given that P is the point (2, 4), Q is the point (4,-1) and R is the point (-1, 0), find(a) the image of P under a clockwise rotation of 90 about R,(b) the image of Q under an anticlockwise rotation of 90 about P.(c) the image of R under a 180° rotation about Q.
The vertices of AABC are A(3, 1), B(4, 1) and C(4, 5). AABC is mapped onto APQR by a 90° clockwise rotation about the point (2, 1).On a sheet of graph paper, draw and label APQR on the same diagram.
(a) State the coordinates of the final image when(i) the point A(1, 2) is reflected in the line x + y = 6 followed by another reflection in the line x = 4(ii) the point A(1, 2) is reflected in the line x = 4 and then in the line x + y = 6(b) Is the reflection commutative in this case?(c) State the
12. (a) State the coordinates of the final image when(i) the point A(1, 4) is reflected in the line y=x followed by another reflection in the line x + y = 6(ii) the point A(1, 4) is reflected in the line x + y = 6 and then in the line y = x.(b) Is the answer in (i) the same as that in (ii)?(c)
Find the equation of the line onto which the line y = 3x + 2 is mapped under a reflection in the(a) x-axis,(b) y-axis,(c) x = 2 by showing your working on a graph paper.
The image of the origin under a reflection in the line y = x + 2 is point A. On a sheet of graph paper,(i) draw the line y = x + 2(ii) find the coordinates of A.
Find the coordinates of the image of the point A(2, 3) under a reflection in the line x = 6 followed by a reflection in the line y=x by showing your working on a graph paper.
8. The point A(3, 4) is reflected in the line x = 2 and then reflected in the line y = 1 .(i) Find the coordinates of the image of A under these two reflections.(ii) State the coordinates of the point which remains invariant under these two reflections.
The point A and its image A' under a reflection are given below. Plot the points A and A' on a sheet of graph paper, construct the line of reflection and find its equation in each case.(a) A(1, 1), A'(3, 1)(b) A(1, 1), A'(1, 9)(c) A(2, 1), A'(0, 3)(d) A(0, 1), A'(1, 2)(e) A(0,-1), A'(2, 1)(f) A(-1,
Under a reflection, the point (3, 5) is mapped onto (5, 3).(1) Find the equation of the line of reflection, The point (5, 3) is then reflected and the coordinates of the final image is (-5, 3).(ii) Find the equation of the line of the second reflection.
The point P(2, 1) is transformed by M₁, a reflection in the y-axis and then M, a reflection in the line x = 4.Give the coordinates of(i) M(P),(ii) M.(P),(iii) MM.(P),(iv) MM, (P).
The reflection of the origin in the line y = x - 2 is the point O'. On a sheet of graph paper,(i) draw the line y = x - 2(ii) find the coordinates of O'.
State the coordinates of the reflection of the point(3, 2) in the line x = 2
(a) State the coordinates of the final image when the point A(-1, 3) is reflected in(i) the x-axis and then in the line y = 4(ii) the line y = 4 and then in the x-axis.(b) Is the answer in (i) the same as that in (ii)?
Write down the coordinates of the reflection of each of the following points in(a) the x-axis,(b) the y-axis, and(c) the line y=x.(i) (3,4)(ii) (-1, 3)(iii) (3, 3)(iv) (-3,-4)(v) (3,-2)(vi) (p. q)
The figure shows an equilateral triangle inscribed inside a circle, which is inscribed inside a bigger equilateral triangle. Find the ratio of the area of the bigger triangle to that of the smaller triangle.
In the figure, APD and BPQ are straight lines. AB, PC and QD are perpendicular to BCD. It is given that AB = 4 cm and QD = 6 cm.(i) Name three pairs of similar triangles.(ii) Find the ratio of the length of BC to the length of CD. 4 cm B P 6 cm D
The floor plan of the basement of a shopping centre is drawn to a scale of 1: 400.(i) if a corridor has a length of 24.5 cm on the plan, find its actual length, giving your answer in metres.(ii) A fast food restaurant occupies a floor area of 400 m². Calculate its area on the plan.(iii) If a
A map of a region of Singapore is drawn to a scale of 1:25000.(i) If two Town Councils are 3,5 km apart, find the corresponding distance on the map.(ii) A reservoir has an area of 16 cm³ on the map. Calculate its actual area in square kilometres.
A map has a scale of 2 cm to 3 km.(i) Express the scale of the map in the form In, where is an integer.(ii) If the distance between two towns is 7 cm on the map, find the actual distance between the two towns, giving your answer in kilometres.(iii) If the actual area of a lake is 81 km², calculate
12. A map of Singapore is drawn to a scale of 1: 180.000.(i) Given that the length of the Circle Mass Rapid Transit Line is 35.7 km, find the corresponding length on the map, leaving your answer correct to 2 decimal places.(ii) Given that the distance between Sentosa and Changi Ferry Terminal is
A map has a scale of 4 cm to 1 km.(i) Express the scale of the map in the form where is an integer.(ii) If a river has a length of 3 cm on the map, find its actual length, giving your answer in kilometres.(iii) If the distance between two towns is 8 km, calculate the corresponding distance on the
A model of a block of flats of The Pinnacle@Duxton housing project is made to a scale of 2 cm to 7.5 m. The height of the model block of flats is 41.6 cm. Find(i) the actual height of the block of flats,(ii) the height of the model block of flats if it is made to a scale of 5 cm to 12 m.
A model of an aircraft is made to a scale of 1:80.(i) If the wingspan of the model aircraft is 25 cm, find the wingspan of the actual aircraft, giving your answer in metres.(ii) If the length of the actual aircraft is 40 m, calculate the length of the model aircraft.
8. It is given that AABC is similar to APQR, ZA 60°, AB = 6 cm, AC = 8 cm and PR = 10 cm.(1) Write down the size of ZP.(ii) Find the length of PQ.
Given that the quadrilateral ABCD is similar to the quadrilateral PQRS, find the values of the unknowns in the quadrilaterals. 12 cm 8 cm A B 6 cm P 85 D C S R
Given that ALMN is similar to AZXY, find the values of the unknowns in the triangles. 10 cm La 6 cm M 9 cm N 2 37 bcm Y
(a) Is AABC similar to APQR? Explain your answer. A 60 P 40 80 40 B Q R (b) Is ADEF similar to ASTU? Explain your answer. 5.4 cm S T 6.84 cm 10.8 cm 3 cm 6 cm E 3.8 cm U
In the figure, Delta ABC equiv Delta*AHK . It is given that angle BAC = 53 deg angle AHK = 90 deg AH = 6cm and the area of triangle ABC is 24c * m ^ 2(i) Write down the size of angle ABC .(ii) Write down the length of AB. Hence, find the length of BC.(iii) Calculate angle BXK . C 6 cm 53 H X K B
In the figure, AABC AAKH. Given that angle BAC = 52 deg angle AHK = 36 deg , AB = 6 cm and AH = 102 cm, find(i) LAKH,(ii) the length of KC. 10.2 cm 36 H A C 52 K 6 cm B
It is given that the quadrilateral ABCD is congruent to the quadrilateral PQRS angle A = 100 deg angle B = 70 deg angle C = 95 deg and PQ = 6cm(1) Write down the length of AB.(ii) Find 2.5.
Are the following pairs of triangles congruent? If so, explain your answer and write down the statement of congruence. If not, explain your answer. B 12 cm. 67 B C R 12 cm a (b) 6cm. D S 6.4 cm 6.4 cm 5cm 70 48 62 70 5 cm F 6cm U E
A triangular field ARC is such that AB = 90 m, BC = 70 m and AC = 85m(i) Using a scale of I em to 10 m, make a scale drawing of the field.(ii) From your scale drawing, find the actual distance from B to the point K, where K is equidistant from A, B and C.Hint: Points on the perpendicular bisector
Use the map of South Malaysia to answer the following questions. You may use a ruler to measure the approximate distances between any two places before finding the actual distances from the given scale. Kuantan Kuala Lumpur Port Dickson Melaka .Segamat Batu Pahat Johor Bahru Singapore km 0 60 120
The Old Trafford soccer field in Manchester, England, is drawn to a scale of 1 em to 5 m. Given that the length and the breadth of the soccer field on the scale drawing are 21 cm and 13.6 cm respectively, find its actual area in square metres. 13.6 cm 21 cm
A map is drawn to a scale of 1: 240 000.(i) If a seawater lake has an area of 3.8 cm² on the map, find its actual area in square kilometres.(ii) lf the actual area of a plot of land is 2 908 800 m², calculate its area on the map.
A map has a scale of 1 cm to 500 m.(i) Express the scale of the map in the form 1: where in is an integer.(ii) If the distance between two districts is 28 km, find the corresponding distance on the map.(iii) If a jungle has an area of 12 cm² on the map, calculate its actual area in square
15. The figure shows a map of the Tampines Mountain Biking Trail. The scale is given in the form of a har at the bottom of the map, showing 0 m to 300 m. TPE 3C Tampines Mountain Biking Trail TAMPINES AVE 100m 200m 300m TAMPINES ST 52 (i) Express the scale of the map in the form 1:n, where n is an
A map of Singapore has a scale of 4 cm to 5 km.The distance between Paragon Shopping Centre and Plaza Singapura on the map is 1.12 cm. Find(i) the actual distance between the two shopping centres,(ii) the distance between the two shopping centres on another map of Singapore that is drawn to a scale
A model of the Marina Bay Sands Tower 1 is made to a scale of 1 cm to 15 m. The height of the model tower is 42.4 cm. Find(i) the actual height of the tower,(ii) the height of the model tower if it is made to a scale of I cm to 12 m.
On the floor plan of an apartment, the length of a bedroom is 12 cm. The actual length of the bedroom is 3 m.(i) What is the scale used?(ii) Find the width of the living room on the floor plan if its actual width is 425 cm.
The figure shows the floor plan of an apartment which has been drawn to a scale of 1 cm to 1.5 m.Find(i) the actual dimensions of Bedroom 1,(ii) the actual area of the kitchen,(iii) the actual total area of the apartment. 2.5 cm 1.5 cm BATH- BEDROOM 1 ROOM LIVING ROOM 3 cm 2 cm BEDROOM 2 KITCHEN
In a television commercial, a toddler of height 75 cm is standing next to a tin of milk of height 24 cm. If the height of the toddler is 25 cm on a television screen, find the height of the tin of milk on the screen.
In the figure, Delta*A * B' * C' is an enlargement of Delta*ABC with a scale factor of 3. Given that B' * C' = 12cm and B * B' = 6cm find the length of BC and of A 6 cm B B' 12 cm C'
A scale of 1 cm to 8 km is used for a map.(i) If a forest has an area of 5c * m ^ 2 on the map, find its actual area.(ii) If the actual area of a park is 128k * m ^ 2 calculate its area on the map.
A map is drawn to a scale of 1: 20 000.(i) Find the actual length that is represented by 5 1/2 * cm on the map, giving your answer in kilometres.(ii) Calculate the length on the map that represents an actual length of 100 m.
A map of Singapore has a scale of 1 cm to 250 m.(i) Given that the Tuas Second Link has a length of 7.68 cm on the map, find its actual length.(ii) Given that the actual width of the Tuas Second Link is 25 m, calculate the corresponding width on the map.(iii) Express the scale of the map in the
The diagram shows a scale drawing of a field ABCD. it is drawn to a scale of 1 cm to 25 m.(a) On the diagram, construct (i) the angle bisector of LC, (ii) the perpendicular bisector of CD.(b) A treasure is hidden in the field.(i) It is equidistant from the points Cand Dand is equidistant from the
Using graph paper, draw a scale diagram for each of the following figures shown with their scales given. (a) 1:2 (b) 1:0.5
The figure shows a map of Singapore. The actual length of Singapore from the North to the South is 28 km.(i) By taking measurements, find the scale of the map.(ii) What is the actual distance between the East and West of Singapore which is represented by x cm on the map? 28 km
In the figure, P'Q'R'S' is an enlargement of PQRS with a scale factor of k.(i) Given that PQ = 8 cm and PQ = 16 cm, find the value of k.(ii) Given that QR = 4 cm and SR = 14 cm, calculate the length of Q'R' and of SR. R' 14 cm R S' S 4 cm P 8 cm Q l' 16 cm P
In the figure, triangle X' * Y' * Z' is an enlargement of triangle XYZ with a scale factor of 2.5. Given that XY = 4 cm and Y' * Z' = 8.75cm find the lengths of X' * Y and YZ. X 2 4 cm Y X" Z' 8.75 cm Y"
A triangular plot of land ABC is drawn to a scale of 1 cm to 3 km. Given that BC = 7 cm and AK = 4 cm, find its actual area. B 4 cm 7 cm K C
1. A scale of 1 cm to 2 km is used for a map.(i) If a plot of land has an area of 3c * m ^ 2 on the map, find its actual area.(ii) If the actual area of a lake is 18 000 000 m², calculate its area on the map.
A scale of 1 cm to 0.5 km is used for a map.(i) If a plot of land has an area of 8c * m ^ 2 on the map, calculate its actual area.(ii) If the actual area of a pond is 5000m ^ 2 find its area on the map.
A map is drawn to a scale of 1:50000.(i) Find the actual length that is represented by 2 cm on the map, giving your answer in kilometres.(ii) Calculate the length on the map that represents an actual length of 14.5 km.
1. A map has a scale of I cm to 5 km.(i) If a road has a length of 6.5 cm on the map, find its actual length.(ii) If the distance between two towns is 25 km, calculate the corresponding distance on the map.(iii) Express the scale of the map in the form, where is an integer.
A map has a scale of 1 cm to 3 km.(i) If a road has a length of 3 cm on the map, calculate its actual length.(ii) If the distance between two stadiums is 7.5 km, find the corresponding distance on the map.(iii) Express the scale of the map in the form, where n is an integer. n
A rectangular school hall is 50 m long and 30 m wide.(i) Using a scale of 1 cm to 5 m, make a scale drawing of the school hall.(ii) From your scale drawing, find the actual distance between the opposite corners of the school hall.
A model of a cruise liner is made to a scale of I cm to 4 m. The length of the model cruise liner is 67 cm. Find(i) the actual length of the cruise liner,(ii) the length of the model cruise liner if it is made to a scale of 1 cm to 10 m.
The scale of the floor plan of a house is I cm to 2.5 m. Find(i) the actual length of the dining room if it is represented by a length of 1.25 cm on the plan,(ii) the length on the plan that represents the width of a bedroom if its actual width is 3.4 m.
The scale of a building plan is I em to 50 cm. Calculate(i) the actual length of a bedroom if it is represented by a length of 9.2 cm on the plan,(ii) the length on the plan that represents an actual length of 28 m.
The scale drawing in the space below shows the positions of the towns A, B and C. A is due North of B and C is due East of B.(i) Given that angle BAD = 80 deg and angle BCD = 65 deg , find and label the position of the town D.(ii) A pole P is to be erected equidistant from towns A, B and C.By
The diagram shows a scale drawing of an apartment.(i) By measuring the scale drawing, find its scale.(ii) Find the actual length L., in metres, of the apartment. BEDROOM 1 BEDROOM 2 L KITCHEN LIVING ROOM DINING ROOM BEDROOM 3 BATHROOM 9600 mm
A photograph shows Mr Goh, who is 180 cm tall, standing in front of his terrace house. In the photograph, the height of Mr Goh is 9 cm and that of his house is 22.5 cm. Find the actual height of the house, giving your answer in metres.
In the figure, triangle XY^ prime prime Z' is an enlargement of triangle XYZ with a scale factor of 1.5. Given that XY = 5 cm and YZ = 12cm find the length of XY and of YZ. 5 cm Y Y' 12 cm X Z
In the figure, Delta * A' * B' * C' is an enlargement of Delta*ABC with a scale factor of 3. Given that AB = 6 cm and AC = 10cm find the length of A ^ * B^ * and of A'C'. 6 cm B A 10 cm B' C A' C
In the figure, AA'B'C' is an enlargement of AABC with a scale factor of 2. Given that AB = 4cm and AC = 5cm find the length of A'B' and of A'C'. 4 cm B A 5 cm C A' C'
9. Two ladders AB and PQ are resting against opposite walls of an alley. The ladders AB and PQ are 2 m and 6 m above the ground respectively and 7 is the point where the 2 ladders meet.(i) Given that ATBP is similar to ATAQ, find an expression, in terms of y, for the length of PA.(ii) Given that
8. Given that APQR is similar to ABAR, find the values of the unknowns in the figure. P 12 cm 60 14 cm R 52 y cm A 9 cm B
Given that AABC is similar to AADE, find the values of the unknowns in the figure. D A 4 cm 56 B 6 cm C 9 cm E
A pole of height 3 m is placed in front of a standing lamp 10 m away. The length of the shadow of the pole that is cast as a result of the light from the lamp is 6 m. Find the height of the lamp.
Two similar toy houses are as shown. Find the values of the unknowns. 180 cm 150 cm y cm z cm 100 180 cm 120 cm
Two similar water bottles are as shown. Find the values of the unknowns. y cm 3 cm 10 cm x cm 5 cm 8 cm
Given that the quadrilateral ABCD is similar to the quadrilateral PQRS, find the values of the unknowns in each of the following pairs of quadrilaterals. (a) 8 cm B 95 495. 105 12 cm 108 D (b) B R 7.2 cm Q S C R 12 cm 9 cm cm 100% A S 14 cm D y cm
(a) Is AABC similar to APQR? Explain your answer. P 40 50 BQ A R (b) Is ADEF similar to ASTU? Explain your answer. D 2.4 cm S 3.3 cm T 5.4 cm E 3.8 cm 3.6 cm 5.7 cm F U
Given that AABC is similar to APQR, find the values of the unknowns in each of the following pairs of triangles. (a) C R 35 (b) P B 281 118 R (c) B 10 cm 12 cm P R 6 cm x cm A 18 cm C (d) C R A 7 cm 8 cm 12 cm B e 10 cm
Given that Delta*ABC is similar to triangle DEC , find the values of the unknowns in the figure. A 10 cm 60 E 7.3 cm 48 8 cm D B
Given that triangle XYZ is similar to triangle XRS , find the values of the unknowns in the figure. 6 cm, R 4 cm Y 5 cm 30Z b cm a S
Given that ΔXYZ is similar to ΔXPQ, calculate the values of the unknowns in the figure. N. 2 cm 4 cm Y X 70 3 cm P a bcm
Given that the quadrilateral ABCD is similar to the quadrilateral PQRS, find the values of the unknowns in the quadrilaterals. A 4 cm B 100' 6 cm y cm D W R 5.4 cm 60 S z cm P 3 cm
Given that AABC is similar to APRQ, find the values of the unknowns in the triangles. B y cm 30 A 6 cm C R 2.8 cm P 4 cm
(a) Are all right-angled triangles similar? Explain your answer.(b) Are all isosceles triangles similar? Explain your answer.(c) Are all equilateral triangles similar? Explain your answer. D A E B C H A A M
Fig. 8.7 shows two triangles. Z X' Fig. 8.9 Z' (i) Measure all the angles. Are all the corresponding angles equal? (ii) Measure the lengths of all the sides. Are all the ratios of the corresponding sides equal? (iii) Are the two triangles similar? (iv) Are we able to find two triangles which have

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