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New Syllabus Mathematics Book 1 7th Edition Teh Keng Seng, Loh Cheng Yee, Joseph Yeo, Ivy Chow - Solutions

An open rectangular tank of length 0.2 m and breadth 0.15 m contains water to a height of 0.16 m. Find(i) the volume of water in the tank, giving your answer in litres,(ii) the surface area of the tank that is in contact with the water.
Find the volume of the hollow glass structure, 10 cm 2cm 3 cm 15 cm 45 cm
The internal dimensions of an open, wooden rectangular box are 3.2 m by 2.2 m by 1.5 m. If the wood has a thickness of 0.2 m, find the volume of wood used. 0.2 m 2.2 m 0.2 m 3.2 m 0.2 0.2 m 1.5 m 40.2 m
An open rectangular tank that is 4 m long, 2 m wide and 4.8 m high, is initially three-quarters filled with water. Find the depth of water in the tank after 4000 litres of water are added to it.
A rectangular block of metal is 0.24 m long, 0.19 m wide and 0.15 m high. If the metal block is melted to form a cube, find the length of each side of the cube.
A cuboid, with dimensions 28 cm by bcm by 15 cm, has a volume of 6720 cm'. 28 cm bcm 15 cm (i) Find the breadth, b, of the cuboid. (ii) The cuboid is melted to form smaller cubes of length 4 cm. How many cubes can be obtained?
Complete the table for each cuboid. Total Length Breadth Height Volume surface (a) 24 mm 18 mm 5 mm (b) 5 cm 3 cm 120 cm (c) 6 cm 3.5 cm 52.5 cm (d) 12 m 6 m 576 m' area
For each of the following cuboids, find (i) its volume, (a) (ii) its total surface area. (b) 5 cm 12 cm 6 cm 8 cm 10 cm 7 cm (c) (d) 120 mm 96 mm 10 mm (e) cm cm (1) cm 10 cm cm 1.5 cm 10.7 cm 3.9 cm
Express(a) 0.84 m²(i) in cm³,(ii) in millilitres,(b) 2560 cm(i) in m³,(ii) in litres.
(a) Express each of the following in cm³.(i) 4 m³(ii) 0.5 m(b) Express each of the following in m³.(i) 250 000 cm³(ii) 67 800 cm³
A metal cube has a volume of 27 cm³. It is to be painted on all its faces. Find the total area of the faces that will be coated with paint.
2. An open rectangular tank of length 16 cm and breadth 9 cm contains water to a height of 8 cm. Find(i) the volume of water in the tank, giving your answer in litres,(ii) the surface area of the tank that is in contact with the water.
1. A cuboid is 8 cm long, 5 cm wide and 10 cm high. Find(i) its volume,(ii) its total surface area.
A cuboid is 6 cm long, 4 cm wide and 3 cm high.Calculate(i) its volume,(ii) its total surface area. 6 3 cm 4 cm
An open rectangular tank, with dimensions 55 cm by 35 cm by 36 cm, is initially half-filled with water. Find the depth of water in the tank after 7700 cm³ of water is added to it.
A cuboid, with dimensions / cm by 18 cm by 38 em, has a volume of 35 568 cm³.(i) Find the length, I, of the cuboid.(ii) The cuboid is melted to form cubes of length 2 cm. How many cubes can be obtained? 1cm 38 cm 18 cm
A cuboid, with dimensions 9 cm by 7 cm by hcm, has a volume of 378 cm' (i) Calculate the height, h, of the cuboid. (ii) The cuboid is melted to form smaller cuboids with dimensions 2 cm by 3 cm by 3 cm. How many smaller cuboids can be obtained? 9 cm hcm 7 cm
Express (a) 10 m' (i) in cm, (ii) in millilitres, (b) 165 000 cm (i) in m', (ii) in litres.
Express (a) 1 m in cm, (b) 1 cm in m, (c) 5 m (i) in cm, (ii) in millilitres, (d) 80 000 cm (i) in m, (ii) in litres.
A trapezium ABCD is such that AD // BC. The diagonals AC and BD of the trapezium intersect at E. If the lengths of BD and BE are in the ratio 5:4 and the area of AABE is 20 cm, find the area of the trapezium.
(i) The figure shows five semicircles of different diameters. If AB = 70 cm, find the perimeter of the figure.(ii) The figure shows a semicircle with a diameter of 70 cm. Find the perimeter of the figure.(iii) From your answers in (i) and (ii), what can you conclude? A- 70 cm B - 70 cm
In the figure, ABC is an isosceles triangle where the lengths of AB, BC and AC are in the ratio 1:2:2. If DE = 9cm and DF = DG = 7cm find the possible heights of triangle ABC C 7 cm F 9 cm B A E
A rope which is wound round a drum of diameter 21 cm is attached to a bucket that is resting at the bottom of a well of depth 9.89 m. Find the number of complete turns of the handle required to bring up the bucket such that the bottom of the bucket is suspended just above the mouth of the well. 21
Find the difference between the perimeter of a square of area 1 m² and the circumference of a circle that has the same area as the square.
8. The area of a trapezium is 36 cm² and the perpendicular distance between its parallel sides is 6 cm.(i) If the lengths of these parallel sides are x cm and y cm respectively, find the value of x + y.(ii) If the value of x is twice that of y, find the value of x and of y.
In the figure, AB = 20m BC = AF = 15m DE = 3.5m and FG = 7m Find the area of the figure, giving your answer in hectares.(1 hectare 10 000 m²) GJE 7m' F 3.5m D C -15 m A B 20 m
The figure shows four circles of equal radius of 12 cm touching one another. Find the area of the shaded region.
The figure shows a parallelogram ABCD where AB=9m and AD = 30.8 m. If CE=25 m, find (i) the area, (ii) the perimeter, of the parallelogram. 30.8 m A D C -9m 25 m B E
The figure shows a rectangle ACDF that has an area of 24 cm. If AB=BC=CD=DE=EF= AF, find the area of the parallelogram BCEF. E B C
The figure shows a rectangle ABCD of length 8 cm and of breadth 6 cm. AQC is a diagonal of the rectangle. If BP = PC, find the area of the trapezium ABPQ. 6 cm D 8 cm C A B
The figure shows three semicircles. Find (i) the perimeter, (ii) the area, of the shaded region. -28 cm-
For each of the following figures, find the (total) area of the shaded region(s). In (b), O is the centre of the circle. (a) 9 cm 13 cm 14 cm 11 cm 7 cm 12cm 9.m 20 cm (b) 13.6 cm h 0 LA 1 cm 35 cm
In the figure, ABCD is a parallelogram, and AFE and BCE are straight lines. If the area of the parallelogram is 80 cm³, BC = CE and DF = FC, find the area of (i) AABE, (ii) AADF. E A D
In the figure, ABCD is a parallelogram and AED is a right-angled triangle. If the area of AAED is 25 cm², and the lengths of AE and EB are in the ratio 1: 3, find the area of the trapezium BCDE. A B E C
In the figure, a parallelogram GHDE and a semicircle are removed from a trapezium ABCE. BOC is the diameter of the semicircle with centre O. If AB = 24 cm, BC= 15 cm, EG = 13 cm, AG = 12 cm and DF = 16 cm, find the area of the figure. E 13 cm F 16 cm D C 12 cm G [L A H' 0:15 cm 24 cm B
For each of the following figures, find the (total) area of the shaded region(s), where O is the centre of the circle. (a) 5 cm 5cm 2 cm (b) 10 cm .5 cm em -12 cm 14 cm- 35 cm 18 cm 0cm 18 cm
In the figure, ABFG and CDEF are two parallelograms such that the sum of their areas is 702m ^ 2 If AB = CD = EF = FG = 1/2 * BC find the area of the 27 m G F E A B C D
The figure shows a trapezium PQRS where PQ = 12m and PS = 13m If PT = 10m and the area and the perimeter of the trapezium are 150m ^ 2 and 54.7 m respectively, find the length of(i) RS,(ii) QR. R S 10 m 12 m 13 m.
The figure shows a trapezium ABCD where AB = 35.5cm BC = 18cm CD = 20 cm and AD = 16cm If CE = 15cm find(i) the area,(ii) the perimeter, of the trapezium. D 20 cm 16 cm 18 cm 15 cm A -35.5 cm- B E
The figure shows a trapezium ABCD where AB is perpendicular to AD, AB = 12 cm, BC = 14 cm and AD 10 cm. Find the area of the shaded regions. 10 cm 12 cm B E 14 cm D
The figure shows a parallelogram PQRS where QR 10 m. If ST = 8 m and SU = 11.2 m, find the length of PQ. T R. 11.2 m 10 m 8 m
The figure shows a parallelogram ABCD where AB = 10 cm and BC = 6 cm. If DE = 9cm find(i) the area,(ii) the perimeter, of the parallelogram. 10 cm 9 cm 6
Complete the table for each trapezium. Parallel Parallel Height Area side 1 side 2 339 (a) 7 cm 11 cm 6 cm (b) 8m 10 m 126 m (c) 5 mm 8 mm 72 mm
Complete the table for each parallelogram. Base Height Area (a) 12 cm 7 cm (b) 6 m 42 m (c) 7.8 mm 42.9 mm
A goat, tethered by a rope 1.5 m long, is able to eat a square metre of grass in 14 minutes. Find the time it needs to eat all the grass within its reach.
In the figure, two identical circles, with centres at A and B respectively, have an area of 0.785 cm² each. If A is directly above D, find the area of the shaded region. D B C
In the figure, ABCD is a square of sides 10 m and BCD is a semicircle of diameter sqrt(200) * m Find(i) the perimeter,(ii) the area, of the shaded region. B 10 m A 200 m C D
BOD is the diameter of the semicircle with centre O. OD is the diameter of the smaller semicircle. AB and CE are arcs of two quadrants with different radii. If OD = 10cm and AE = BC = A 13 om B 10cm D
A figure is made up of a triangle ABD and a semicircle. BOD is the diameter of the semicircle with centre O. If AB = AD = 5.7cm BD = 7 cm and AOC8 cm, find(i) the perimeter,(ii) the area, of the figure. B C 7 cm O 5.7 cm D -8 cm-
(i) Find the area of the surface of a circular pond that has a diameter of 12 m.(ii) The pond is surrounded by a path of width 2 m. If it costs $55 per m ^ 2 to pave the path with tiles, find the cost incurred.
In the figure, AC = 20cm CD = 22cm and AE = 16cm Find the length of BD. D 16 cm E B -20 cm- 22 cm C
10. In the figure, AB = 20m BC = 21m AD = 10m and DE = 10.5m Find the area of the shaded region. C 10 m 10.5 m A 20 m- E 21 m B
In the figure, AD = 23 m, DP = 7 m and BR = 13.5 m. If P is directly above R, find the area of the shaded region. D 7m P S 23 m 13.5 m B
The perimeter of a rectangular field is 70 m and its length is 15 m longer than its breadth. The field is surrounded by a concrete path as shown in the figure. Find the area of the path. 25 m 5 m
In the figure, 4 quadrants, each of radius 2 m, are removed from a rectangle. Find (i) the perimeter, (ii) the area, of the figure. 2 m 2 m 2 m 2 m 3 m 3 m 2 m 2 m 2 m 2 m -9m-
The circular portions of the following figures are semicircles. For each of the following figures, find(i) its perimeter,(ii) its area. (a) 21 cm -36 cm
A piece of wire 144 cm long is bent to form a semicircle as shown in the figure. Find the diameter of the semicircle, giving your answer in metres. (Take to be 22/7 )
Complete the table of each circle. Diameter Radius Circumference Area 10 cm (a) (b) 3.6 m (c) (d) 176 mm 616 cm
3. In the figure, a triangle is removed from a square of sides 9 m. Find the area of the figure. 2.5 m 3 m 9 m
The area of a rectangle is 259c * m ^ 2 and its length is 18.5 cm. Find(i) its breadth,(ii) its perimeter.
1. Express(a) 40m ^ 2 in c * m ^ 2(c) 0.03m ^ 2 in c * m ^ 2(b) 16c * m ^ 2 in m ^ 2(d) 28 * 0c * m ^ 2 in m ^ 2
The figure shows a circle of radius 14 cm with one quadrant removed, touching the sides of a square. Find (i) the perimeter of the unshaded region, (ii) the area of the unshaded region, (iii) the area of the shaded region. 14 cm
The figure shows a circle of radius 7 cm, touching two sides of a rectangle. The length of the rectangle is 9 cm longer than its width. Calculate (i) the circumference of the circle, (ii) the area of the circle, (iii) the area of the shaded region. 7 cm
The length of a rectangular field is 4 m longer than its breadth. (a) If the perimeter of the field is 44 m, calculate (i) the breadth, (ii) the area, of the field. (b) The field is surrounded by a cement path of width 2.5 m. Calculate the area of the path.
Construct a quadrilateral ABCD such that AB = 7.6cm AD = 5.3cm A hat BC = 105 deg B hat AD = 110 deg and A hat DC = 82 deg Measure and write down the length of BC and of CD.
One of the interior angles of an in-sided polygon is 95° and the remaining interior angles are 169° each. Find the value of n.
In the figure, PAQ and ASB are straight lines. If PQ // RS, AB // CD, A hat DC = 62 deg and D hat AQ = 26 deg find the value of x and of y. T- B 1.0 R 269 620 C
At 0845 hours, a lorry leaves Town A for Town B at an average speed of 52 km/h. It arrives at Town B at 1230 hours. On the return journey, the lorry leaves Town B at 1455 hours and arrives at Town A at 1815 hours. Find the average speed of the lorry on the return journey.
If light can travel 31 times around the world in 4 seconds, find the number of times it can circle the world in 10 seconds.
An alloy consists of three metals, X, Y and Z. If X / Y = 8/15 and Y / Z = 21/32 find X: Z.
In a class of 40 students, 25% of them were made to stay back for detention. Find the number of students who did not have to stay back for detention.
After a pay raise, Kate's monthly salary increased from $3500 to $3780. Find the percentage increase in her pay raise.
(i) Construct AABC such that AB = 6 cm, BC = 7 cm and AC = 6.5cm(ii) Construct the angle bisector of ABC such that it culs AC. Measure and write down the length of BX, such that X is the point where the angle bisector of ABC cuts AC.
The interior angles of a hexagon are (2x + 17) deg (3x-25)°, (2r + 49) deg (x + 40) deg (4.x-17)° and(3x-4)°. Find(i) the value of x,(ii) the smallest interior angle,(iii) the smallest exterior angle.
In a parallelogram ABCD, B hat AC = 56 deg and B hat CD = 70 deg . Find(1) ABC,(ii) ACB.
A train leaves Town A at 0845 hours and arrives at Town B at 1510 hours.(i) How long does the train take to travel from Town A to Town B?(ii) If the average speed of the train is 108 km/h, find the distance between Town A and Town B.
Priya can type 575 words in 25 minutes. She starts typing a report at 1035 hours and finishes at 1128 hours. Assuming she types non-stop at her usual rate and does not make any mistakes, find the number of words in the report.
The length and breadth of a hall are 28 m and 21 m respectively. If the ratio of its length to its height is 7: 6, find the ratio of its breadth to its height.
The number 5600 is first decreased by 15%. The value obtained is next increased by 10%. Find the final number.
35% of students who take part in a dance competition are girls. If 140 girls take part in the competition, find the total number of students who take part in the competition.
Construct APQR such that PQ = 7 , PR = 6 and QR = 8 cm. Construct a circle which will touch the sides of PQ, PR and QR. What is the special name given to this circle?
Construct APQR such that PQ = 8 cm, PR = 5 and QR = 6 cm. Construct a circle which will pass through P, Q and R. What is the special name given to this circle?
6. Construct a circle with diameter AC = 10cm(i) Find and label a point B on the circumference of the circle such that AB = BC.(ii) Find and label the point D on the circumference of the circle such that it lies on the side of AC opposite to B and C hat AD = 45 deg .(iii) Join the points to form a
Construct a quadrilateral PQRS such that PQ = 8cm PS = 6cm P hat QR = 90 deg and Q hat PS = 60 deg . QR = 2cm( Measure and write down the size of QRS.(ii) Construct a line parallel to PR that passes through S to meet QR produced at U. Measure and write down the length of QU.
4. Construct a parallelogram ABCD such that AB = 8cm BC = 5.5 cm and A hat BC = 120 deg .(i) Measure and write down the length of the diagonal BD.(ii) Construct the perpendicular bisector of BD such that it cuts AB and CD. Measure and write down the length of ST, such that S and T are the points
3. Construct AXYZ such that YZ = 8 cm and X hat Y Z=X hat ZY = 60 deg .(i) Construct the perpendicular bisector of YZ, which passes through X, and let U be the point where it cuts YZ.(ii) Find and label V on XU produced such that XU = UV.(iii) Join YV and ZV to obtain a quadrilateral. State the
Construct APQR such that PQ = 12cm PR = 10.2cm and QR = 8.8cm(i) Measure and write down the size of the angle facing the shortest side.(ii) Construct the perpendicular bisector of QR such that it cuts PQ. Measure and write down the length of RT, such that T is the point where the perpendicular
1. Construct AABC such that AB = 4.5cm BC = 6cm and A hat BC = 60 deg .(i) Measure and write down the length of AC.(ii) Construct the angle bisector of BẬC such that it cuts BC. Measure and write down the length of CS, such that S is the point where the angle bisector of BAC cuts BC.
Construct a quadrilateral PQRS such that PQ = 6.5cm QR = 4.6c , PS = 5.8cm P hat QR = 120 deg and Q hat PS = 105 deg The point T is such that it is equidistant from P and Q, and equidistant from PQ and PS. Find and label T.
Construct a trapezium WXYZ such that WX is parallel to ZY, WX = 5 cm, YZ = 9.8 cm, WZ = 6 cm and X hat WZ = 120 deg(i) Measure and write down the length of WY.(ii) Construct the perpendicular bisector of WY such that it cuts WX produced at S and YZ at T. Measure and write down the length of
Construct a quadrilateral PQRS such that PQ = 11cm QR = 3.1cm PS = 7cm P hat QR = 90 deg and QPS = 50".(i) Measure and write down the size of QRS.(ii) Construct a line parallel to PR that passes through S to meet QR produced at U. Measure and write down the length of RU.
Construct a quadrilateral PQRS such that PQ = 10cm QR = 6cm PS = 3.5cm P hat QR = 45 deg and QPS = 60°.(i) Measure and write down the size of QRS.(ii) Construct the perpendicular bisector of QS such that it cuts PQ. Measure and write down the length of PT, such that T is the point where the
A square PQRS is such that the diagonal PR = 10cm(i) Draw PR.(ii) By constructing the perpendicular bisector of PR, locate the points Q and S and join the points to form the square PQRS.Measure and write down the length of PQ.
Construct a quadrilateral PQRS such that PQ = 4cm QR = RS = 4.8cm PS = 3.6 cm and Q hat PS = 90 deg .(i) Measure and write down the length of QS.(ii) Construct the perpendicular from S to QR. Measure and write down the length of SU, such that U is the point where the perpendicular from S cuts QR.
Construct a parallelogram ABCD such that AB = 9cm BC = 6cm and A hat BC = 115 deg .(1) Measure and write down the length of the diagonal BD.(ii) Construct the perpendicular bisector of AB such that it cuts CD. Measure and write down the length of AT, such that T is the point where the perpendicular
Construct a trapezium WXYZ such that WX = 56 mm, XY = 112mm W hat XY = 80 deg and X hat YZ = 70 deg . Measure and write down the length of WY and of XZ.
Construct a trapezium WXYZ such that WZ is parallel to XY, WX = 4.5cm XY = 8cm WZ = 6cm and W hat XY = 60 deg Measure and write down the length of YZ and of WY.
Construct a quadrilateral PQRS such that P hat QR = 75 deg and Q hat RS = 60 deg . QR = 6.3cm PQ = 5.3cm RS = 6.7cm(i) Measure and write down the length of PR.(ii) Measure and write down the size of RPS.
Construct a rhombus PQRS such that PQ = 60mm and the diagonal PR = 9mm Measure and write down the size of QPS.
Construct a quadrilateral PQRS such that PQ = PS = PR = 9cm QR = 12cm and RS = 7.5cm Measure and write down the size of QPS.

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