P6 - Area, Perimeter, Construction, Angles, Net, Data Analysis, Num Patterns, Algebra

for Primary 6 students | taught by Math Arena

Course description

Overview

This course is targeted at Singapore primary school level 6, but is also suitable for primary school level 5 students.

Based on feedback, many parents have used the videos to learn the methods to help their children to learn faster.

Math Arena students gain an edge using techniques that we teach here in our videos, these methods provide accuracy and speed. We believe it also provides better understanding of their solution to the question that they are solving.

It can also be used as independent learning or for revision.

The PDF files will contain questions for you to practice on. They are arranged by similarity for easy question pattern recognition.

The Number of stars indicates level of difficulty. One star is fundamental, 2 stars are moderate. 3 and 4 stars are difficult and challenging. Note due to the student’s ability he may experience difficult questions as easy and easy questions as difficult. So do not be over anxious, if an “easy question” stumped you, just keep practicing.

Course Content

You will :

  • print from the PDF files
  • be able to watch and learn from 160 videos
  • learn fast, accurate methods in solving questions

Course Pre-requisites

You will need to know:

  • Fundamental Heuristic Concepts
  • How to watch videos on your computer

Notes:

  • PDF files contain the questions, the videos are the solutions to the questions.
  • Question header may not contain the full question as it it limited to 255 characters.
  • Our Videos complements the student’s math lessons in Math Arena.
  • It is common that parents do learn from our videos and work with their children too.
  • The bar model is good for understanding but may be less useful for more complicated questions. It can also lead to harder transition to algebra in their secondary schools.

Take a moment to ...

Math Arena
Math Arena

The instructor is from Math Arena.The instructor is absolutely passionate about teaching and you'll find the lessons engaging and ultimately rewarding.

Course Curriculum

Introduction
Hide Content
Area Perimeter Set A
94:22
P6APV1-A - learnbrill FREE PREVIEW
1) The figure shows two identical semicircles. O and P are the centers of the semicircles. 1/5 of each semicircle is shaded. Find the total area of the shaded parts.
2) In the figure, O is the center of the circle. The shaded sector has an angle of 45. Find the perimeter of the unshaded part.
3. The figure below shows 2 identical circles within a rectangle. The two circles overlap each other. The area, X, where they overlap is 73 cm2. What is the area of the shaded-part? (Take π = 3.14)
4) The figure below shows 2 identical circles within a rectangle. The two circles overlap each other. The area, X, where they overlap is 73 cm2. What is the area of the shaded-part? (Take π = 3.14) FREE PREVIEW
5) The figure below is made up of a circle and 2 semi-circles. XY is the diameter of the circle. XY is 15 cm, XZ is 12 cm and YZ is 9 cm. FREE PREVIEW
6) The figure shown is made up of a square and sectors of circles. Find the area of the shaded region below.
7) A circle of radius 4 cm is drawn in a square as shown. Find the area of the shaded parts.
8) Given that the radius of the semicircle is 7 cm, find the area of the shaded regions.
9. The diagram below is not drawn to scale. ABE is an isosceles, right-angled triangle. AB = BE and O is the center of the semi-circle BCE of radius 8 cm. OCDE is a square. Find the shaded area. (Take π = 3.14)
10) The figure below is made up of a right-angled triangle WXY and two semicircles with XY and WX as their diameters respectively. The two semicircles and the line WY meet Z as shown. WX = 12cm, XY = 16 cm and WY = 20 cm. (Take π = 3.14)
11) The figure below is made up of a quadrant and a rectangle. a. What is the total perimeter of the unshaded parts and B? b. What is the difference in area between the unshaded parts A and B? (Correct your answer to 2 decimal places.)
12) The figure below is made up of a big quadrant OBD, a small quadrant OAE and a square ACEO. The radius of the big quadrant OBD is 12 cm. The area of the big quadrant OBD is twice the area of the small quadrant OAE.
13) The figure shows 2 identical circles enclosed in a rectangle EFGH. Find the area of the shaded parts.
14) The figure below (not drawn to scale) shows 2 semicircles in a rectangle. The figure is split into two by a diagonal.
15) The diagram below (not drawn to scale) is made up of 1 large square of side 14 cm, 1 large quadrant, and 2 identical small semi-circles. Find the area of the shaded part. FREE PREVIEW
16) The figure below, not drawn to scale, is made up of triangles and a quadrant drawn within two similar squares, STOP and TMNO. The area of each square is 100 cm2. XY is 2/5 of the side of a square. Z is the mid-point of ON.
17) In the diagram below, the ratio of the shaded region to the non-shaded region is 1 : 13. The area of the shaded region is 24 cm2.
18) The figure below (not drawn to scale) is made up of 2 quadrants and a rectangle with length 56 cm and width 28 cm. Find the area of the shaded region.
19) The figure below shows a circle and two quadrants enclosed within a square. O is the center of the circle. The length of each side of the square is 30 cm. Find the total area of the shaded parts. (Take π = 3.14)
20) The figure below shows a semi-circle and a rectangle. Point O is the center of the circle and the diameter ST is 8 cm long. When π = 3.14,
21) The figure below is not drawn to scale. O is the center of the circle. OQ = QR = RS = 4 cm. Find the shaded area. Leave your answers in terms of π.
22) The figure below is made up of semicircles, a square ABDF and a rectangle BCEF. The length of the square ABDF is 20 cm. Find the area of the shaded figure. Leave your answer in terms of π.
23) In the figure below, not drawn to scale, ABCD is a square of side 10 cm. If O is the center of the square, find the area of the shaded part. (Take π = 3.14)
24) The figure is made up of 4 identical squares of sides 7 cm and 4 semi-circles. Find the total area of the shaded parts.
25) The figure below (not drawn to scale) is made up of 4 identical squares and 8 identical quadrants.(Take π = 3.14)
26) The figure below is not drawn to scale. It consists of a big circle and 4 identical smaller circles. The length of AD is 48 cm.
27) The figure below is made up of identical quadrants. (Take π = 3.14) a. Find the area of the shaded part. b. Find the perimeter of the shaded part.
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Area Perimeter Set B
110:12
P6APV1-B - learnbrill
1) Find the area of a rectangle if its breadth is 2/7 m and its length is 4 times its breadth.
2) The perimeter of a rectangle is 15/8 times the perimeter of a square. The area of the square is 225 cm2. The length of the rectangle is 1.2 times the breadth of the rectangle. Find the area of the rectangle
3) There were 12 rows of chairs with 13 chairs in each row in the hall. At a party, all the chairs were rearranged to form a square around the hall. The number of chairs along each side of the square is the same.
4) The rectangle below is divided into 6 different parts. Each part has a different ratio. Find the total area of A and B.
5) In the figure below, not drawn to scale, Rectangle ABCD is made up of 4 isosceles right-angled triangle and a square. The ratio of the area of Triangle ABF to the area of Triangle BCE is 9 : 8.
6) The figure below shows a rectangular cardboard with 3 rectangular stickers pasted on it. The stickers have a width of 13 cm each. Find the area of the region that is not covered by the stickers.
7) The figure below shows a rectangle ABCD which has been divided in to 3 parts, P, Q and R. The ratio of the length of AB to that of EB is 7 : 2. The area of P is 72cm2 larger than that of the area of R. Find the area of rectangle ABCD.
8) Figure 1 shows a rectangle ABCD. It is folded along AC to form Figure 2. The area of Figure 2 is 5/8 of the area of Figure 1. The area of the shaded part in Figure 2 is 36 cm2. Find the area of rectangle ABCD.
9) Rectangle ABCD is made up of an unshaded square, an unshaded rectangle and two shaded rectangles. The area of the square is 36 cm2 and the perimeter of the unshaded rectangle is 76 cm. What is the total area of the 2 shaded rectangles?
10) Figure A is made up of a rectangle and a triangle. Figure B is a rectangle. Figures A and B have the same area. Find the perimeter of Figure B.
11) Figure 1 is made up of a rectangle and 2 identical triangles. The height of the triangle is equal to the breadth of the rectangle as shown in Figure 1.
12) A 0.75-m long ribbon is used to tie a cubic box as shown in the picture. The tying of the bow used up 0.11m of the ribbon. Find the length of each side of the box in meters.
13) The figure below is folded using a rectangular strip of paper. Find the length of the strip of paper.
14) The figure below is not drawn to scale. Rectangle PQRS is made up of 5 identical rectangles and a small shaded rectangle. The shaded area is 12 cm2. Find the length of QR.
15) The figure below shows rectangle WXYZ which is made up of 7 identical small rectangles. The area of a circle with radius 56 cm is 2.2 times the area of rectangle WXYZ. Find the perimeter of rectangle WXYZ.
16) In the figure below, rectangle EFGH is made up of 7 identical rectangles. a. Find the perimeter of rectangle EFGH. b. Find the area of the shaded triangle.
17) The figure below shows 3 identical big rectangles measuring 24 cm by 16 cm overlapping one another. Each shaded identical rectangle has a perimeter of 42 cm. What is the total area of the unshaded parts of the figure?
18) A, B, C, D and E are identical squares. The perimeter of GHLM is 192 cm. If FGPO and JKLQ are squares, find the shaded area.
19) The figure below, not drawn to scale, comprises of 1 right-angled triangle and 6 identical squares. The total area of the squares is 150cm2. Find the area of the triangle.
20) The figure below shows 4 identical right-angled triangles. Two squares of total area 160 cm2 are joined to the triangles as shown. What is the ratio of the area of the shaded parts to the area of the unshaded parts?
21) The figure below is not drawn to scale. It is made up of 4 identical right-angled isosceles triangles. There is a square in the center. The shaded area of the figure is 72 m2. Find the side of the square.
22) In the figure below, the area of triangle A is 3/5 that of triangle B. What is the area of triangle A?
23) A square piece of paper, ABCD, is shaded on one side as shown on Figure 1. It is then folded at its corner B to form an isosceles triangle as shown in Figure 2.
24) In the figure, ABCD is a rectangle and BCE is a triangle. BC = 9 cm and CE = 7 cm. Shaded area X is 13.5 cm2 smaller than shaded area Y. What is the length of AB?
25) The figure below is formed using 4 isosceles triangles, ABG, BCH, ADF and DCE. ABCD is a square where E, F, G and H are midpoints of its sides. Given that FJ = CJ, HK = DK and AB = 14 cm, find the total area of the shaded parts.
26. A rectangle hall, WXYZ, not drawn to scale, is portioned into 4 areas, A, B, C and D. What is the area of A? The area of B is doubled when Point R is moved to Point S. What is the ratio of the area of A to the new area of D?
27) During an Art lesson, James cut out a figure as shown below. Find the perimeter of the figure. Give your answers correct to 2 decimal places. (Take π = 3.14)
28.) The figure below, not drawn to scale, is made up of a circle within 3 different squares of different sizes touching each other at the mid-point of each side. ABCD has a perimeter of 24 cm. What is the circumference of the circle? ( Take π = 3.14
29) Danny built a skateboard using two identical wheels of radius 2.9 cm each and a wooden board as shown below. The distance between the centers of the two wheels is 59.2 cm.
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Construction, Angles, Nets Set A
65:07
P6CANV1-A - learnbrill
1. Construct a square PQST and an equilateral triangle QSR. Square PQST shares side QS with the equilateral triangle QSR. When side QS = 4 cm.
2) a. On the figure below, draw and label two lines BC and CD such that ABCD is a parallelogram.
3) Study the figure shown below. a. How many triangular faces does it have? b. In the following figure, cross out (X) the extra shape to make it the net of a solid.
4) In the figure below, AD and CD form two sides of a trapezium ABCD. Given that ∠ BCD = 45°, complete the drawing of trapezium ABCD. Label your drawing.
5) In the square grid below, AB and CD are straight lines. a. Using CD as a line of symmetry, draw a straight line that is symmetrical to AB. Label the line XB. b. From Point D, draw a line DE such that ∠ BDE = 135° and BD // AE.
6) In the figure below, TU and VW are straight lines. a. Find ∠ WOU. b. Find ∠ XOW.
7) The figure below is made up of straight lines. ∠ FHG = 106° and ∠ JKH = 44°. Find the sum of ∠ w, ∠ x, ∠ y and ∠ z
8) In the figure below, DB = BC, DQ = CQ. Find the sum of the angles x, y and z.
9) In the figure below not drawn to scale, O is the centre of the semi-circle. MRQ and MNP are straight lines. MR = OP and ∠ RMN = 21°. Find a. ∠ ORQ b. ∠ OPQ
10) The figure below, not drawn to scale, consist of three parallel lines. XW = XY = XZ. ∠ a and ∠ b are in the ratio of 2 : 3 respectively. Find ∠ a, ∠ b and ∠ c.
11) The figure, not drawn to scale, is made up of 4 triangles and a parallelogram AHGF. ABF, BCF and CDF are identical triangles. Find ∠ FAB.
12) In the figure below, not drawn to scale, DFH is a right-angled triangle. Find ∠ EFG.
13) In the figure, ABC and ADE are right-angled triangles and EA is parallel to BC. Find a. ∠ ACB b. ∠ AEB
14) In the figure below, not drawn to scale, there are two overlapping triangles, ABC and STU. Given that LAUS = 35°, find ∠ a + ∠ b + ∠ c + ∠ d + ∠ e + ∠ f.
15) SVW is an isosceles triangle. SU // WV and TX // UV. Find ∠ UVW.
16) In the figure below, ABCD is a trapezium and DEF is an isosceles triangle. ADE is a straight line. BC is parallel to DF and DC is parallel to EF. ∠ EDF = 40° and ∠ DFC = 90°. a. Find ∠ x b. Find ∠ y
17) The figure below is not drawn to scale. PQRS is a trapezium. PTRS is a parallelogram and QRU is an isosceles triangle. RQW and QUV are straight lines. ∠ SPT = 75o, ∠ RUV = 142o and TQW = 110o. Find ∠ TRU.
18) In the figure below ABCD is a square. AEF and CEF are isosceles triangles and ∠ BAE = 25°. Find ∠ AFE.
19) The figure below (not drawn to scale), shows a trapezium ADEF, an isosceles triangle CDF and a straight line EFG. a. Find ∠ BCD. b. Find ∠ FDE.
20) In the figure below, ACDE is a parallelogram and ABF is an isosceles triangle. EFCB is a straight line. ∠ CDE = 100°, ∠ ACF = 56°, and LCAB =14°. Find ∠ EAF.
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Construction, Angles, Nets Set B
65:55
P6CANV1-B - learnbrill
1) In the figure below, not drawn to scale, ABC and XYC are isosceles triangles. ∠ YXZ is 3 times that ∠ CXZ. ∠ ABC = 50°. Find ∠ XZC.
2) In the figure below, not drawn to scale, ABCD is a rhombus and DEF is an isosceles triangle. Find ∠ DEF.
3) In the figure below, ABCD is a trapezium where AB is parallel to DC. CDE and BEF are 2 identical isosceles triangles. DE = DC = BE = BF. Given that ∠ DCE is twice of ∠ EDC, find ∠ ABF.
4) In the figure, PQRS is a rhombus. TSU is a straight line, ∠ RPQ = 39° and ∠ RSU = 36°. a. Find ∠ QRS b. Find ∠ PST
5) In the figure shown below, ADGJ is a rectangle, GHJK is a rhombus and DEFG is a parallelogram. ∠ GHJ = 76° and ∠ FGH = 92°. a. Find ∠ CGD b. Find ∠ GFE
6) The figure below is not drawn to scale. ABCD is a rhombus and ∠ BCF is 98°. BDF, CGF, EGD are straight lines. Find ∠ DFG.
7) In the figure below, STUV is a rhombus. ∠ UWT = 65° and ∠ WUS = 11°. Find ∠ SVU.
8) In the figure below, PQRS, is a parallelogram, UVQ and UTR are straight lines. ∠ PVQ = 27°, ∠ VUT = 38° and ∠ TSR = 43°. Find a. ∠ STU b. ∠ QRU
9) In the diagram below, ABCD is a parallelogram. AC = CE = CF. LAEC = 55° and LAFC = 30°. AF and CE are straight lines. Find LABC.
10) In the figure, CDGH is a parallelogram. BCF and DFG are straight lines. ∠ BCD = 145°, ∠ CDG = 50° and ∠ GCF = 30° Find a. ∠ CHA b. ∠ BCH c. ∠ CGH
11) In the figure below, not drawn to scale, parallelogram ABCD, rhombus EFGC and rectangle FSTC overlap to form ∠ x and ∠ y . ∠ ECD = 8° and ∠ EAB = 78° a. Find ∠ x b. Find ∠ y
12) In the figure, not drawn to scale, ABCD is a rhombus. Given that ∠ BAD = 64o and ∠ DXY = 37o Find a. ∠ DCX b. ∠ BDC
13) In the figure, ABCD is a parallelogram. EBF is a straight line, ∠ DAB = 104°, ∠ ABF = 160° and ∠ DBE = 9°. Find ∠ CBF. Find ∠ CDB.
14) In the figure below, ABCD is a parallelogram with length AB twice the length of AD. ABE is an equilateral triangle. F is a point on AE such that AF = FE. ∠ BCD is 104°. Find ∠ FDC.
15) In the diagram below, not drawn to scale, ABCD is a rhombus. BEF and BHG are straight lines. DA is parallel to FG. a. Find ∠ GBF. b. Find ∠ FBC.
16) In the figure below, ABCD is a trapezium and PQCR is a square. AB//CQ. The size of ∠ DCR is 5/4 of ∠ DCQ. Find ∠ SDC.
17) In the figure below, not drawn to scale, BH and AK are straight lines. BD//EA//FG and AG//CJ. Find a. ∠ a b. ∠ b c. ∠ c
18) The figure shown below, a trapezium ABCD was folded as shown. AB is parallel to CD. AE is parallel to BF. ∠ AEF = 65°. Find ∠ FAE.
19) The figures below are not drawn to scale. Figure 1 shows a rectangular piece of paper ACDF that measures 18 cm by 14 cm. AB = ED = 5 cm. The paper is folded along the dotted line BE such that C touches point F, as shown in Figure 2.
20) A piece of paper in the shape of a rectangle is folded along the dotted line as shown below. Find a. ∠ x b. ∠ y
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Data Analysis Number Patterns Set A
54:40
P6DANPV-A - learnbrill
1) The average mass of 5men is 78 kg. If the average mass of 3 of the men is 75 kg, what is the average mass of the other 2 men?
2) 100 people went for a health check at a polyclinic. Their average mass was 65kg. Given that the average mass of the women was 50kg and the average mass of men was 70kg, how many men were there?
3) Mr and Mrs Cheng went on an excursion with their 6 children. An average amount of $84 was spent by each adult while an average amount of $62 was spent on each child. What was the average amount of money spent on each person?
4) The average mass of a cupboard, a sofa and a few television sets was 36 kg. When the cupboard and the sofa which weighed 41 kg and 39 kg respectively were exclude, the average mass of the television sets became 34 kg.
5) Find the average of all the even numbers between 10 and 27.
6) The average height of 4 girls was 120 cm. When Jane joined them, the average height increased by 9 cm. What was Jane’s height?
7) Mr. Goh arranged 12 containers of toys in a straight line. The average mass of the 3rd to the 12th container is 230 g. This is 20 g less than the average mass of all the 12 containers. What is the total mass of the first 2 containers?
8) The mass of 5 children were recorded. Andy, Bryan, Charles and David weighed a total of 190 kg. Andy, Bryan, Charles and Eugene weighed a total of 195 kg. Andy, Bryan, David and Eugene weighed a total of 200 kg.
9) Three 2-digit numbers were written on a piece of paper. The average of the three numbers was 42. A digit of two of the numbers was covered by a stain. What were the two 2-digit numbers?
10) The tables below shows part of Devi’s results of her class tests. The maximum mark for each test is 100. Devi obtained an average of 93.25 marks for her tests.
11) The total amount of water in Jar A and Jar B is 1050 ml. The total amount of water in Jar B and Jar C is 1320 ml. The amount of water in Jar A is 1/2 the amount of water in Jar C. What is the average amount of water in the three jars?
12) Some girls sew a pillowcase for their home economics lessons. Amelia used 800cm of cloth. She used 4/5 as much cloth as the amount Bianca used. Clarris used 3/10 of the amount of cloth that Bianca used.
13) Helen had twice as many stickers as Lisa at first. After Helen bought another 20 stickers and Lisa bought another 105 stickers, Lisa had three times as many stickers as Helen. a. How many stickers did Lisa have at first?
14) The average number of books that were owned by Alice, Billy and Cathy each was 10. After Cathy’s sister gave her another 8 books and Alice gave away 5 books, Alice and Cathy had the same number of books.
15) A farmer in a farm picked pears every day. He picked 18 on every cloudy day and 10 pears on every sunny day. He had picked a total of 144 pears before going on holiday. On the average he had picked 12 pears per day. How many sunny days were there?
16) Alicia has four times as much money as Jenny while Carol has $9 less than Jenny. The 3 girls have an average of $87.
17) 4 children share some stamps. The average number of stamps Abel and Betty has is 168. The average number of stamps Don and John has is 140. What is the average number of stamps each child has?
18) A group of boys had an average number of 42 marbles. One of the boys had wrongly counted his marbles as 35. The correct number of marbles he had should be 53. After re-counting the marbles, the average number of marbles they had increased to 45.
19) The table below shows the number of hours which some pupils spent on their homework In a week. a. The total number of hours which the pupils spent on their homework in a week was 108. How many pupils spent 12 hours on their homework?
20) The line graph below shows the number of books sold by a shop from July to December in 2013. a. What was the average number of books sold per month from July to December in 2013?
21) The bar graph below shows the number of stamps collected by 5 members of a local stamp club in the month of October.
22) The bar graph below shows the number of messages and phone calls Mr Loh made through his mobile phone from Sunday to Friday.
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Data Analysis Number Patterns Set B
85:35
P6DANPV-B - learnbrill
1) The pie chart represents the Co-curricular activity chosen by 90 pupils. Each pupil chose only one activity. An equal number of pupils chose Softball and Tennis. a. How many pupils are there in Tennis?
2) The pie chart below shows how Joy spent her time on a certain day. She spent an equal number of hours watching television and on other leisure activities after spending 6 hours in school.
3) Use the information below to answer questions (a) and (b). The graph below shows the number of cream puffs sold from January to May. The number of cream puffs sold was recorded at the end of every month.
4) The line graph below shows the average waiting time from 2008 to 2012 for the patients at the emergency department of a hospital.
5) The graph shows the number of books read by the pupils in a class. a. What was the total number of books read by all the pupils? b. What percentage of the pupils in the class read at least 3 books?
6) The graph shows the number of brownies sold by Mrs Smith from Monday to Friday. Each brownie was sold for the same price. The total amount of money collected for the first 5 days of the week was $520. She collected $200 on Saturday.
7) What is the digit in the ones place in the following? 9 × 99 × 999 × 9 999 × 99 999 × 999 999
8) From 100 to 199, how many times does the digit “1” appear?
9) 3 locks and 8 keys are mixed up. If each lock can be opened by only one key and no two locks can be opened by the same key, what is the least number of tries required to ensure the correct key for every lock is found?
10) In 9 days, Nelly used a total of 84.6 kg of flour for baking. Each day, she used 1.04 kg less flour than the previous day. How many kilograms of flour did Nelly use on the first day?
11) Danny wants to start saving. He puts in a dollar on Day 1. On Day 2, he puts in two dollars. On Day 3, he puts in three dollars. He increases his savings by a dollar each day. a. What is his total savings after 10 days?
12) Observe the following number pattern and fill in the blank:
13) Black and white squares are used to form the pattern as shown below.
14) Pins are used to form the pattern shown below. a. How many pins were used to form Figure 8? b. Find the number of rectangles that can be formed with 98 pins.
15) Look at the pattern below. a. How many *squares* are there in figure 16?
16) The number pattern below shows the top 7 layers of a pyramid. a. What is the missing number in Layer 7? b. How many numbers are there in Layer 25
17) The figures below are made up of circles and rectangles Study the figures carefully and answer the following questions.
18) 1 cm square tiles and triangular tiles were used to make some figures. The area of each triangular tile was half that of a square tile. The first four figures are shown below
19) The pattern below is made up of triangles. a. How many triangles are there in the 6th pattern? b. How many triangles are there in the 51st pattern? c. Which pattern is made up of 569 triangles?
20) Haoming made patterns using triangles, circles and sticks and recorded the pattern in the table shown below. a. How many circles are needed for Figure 20? b. How many sticks are needed for Figure 20? c. Which Figure needs a total of 115 sticks?
21) The pattern below is made up of circles and triangles. Study the pattern carefully and answer the questions below.
22) On a table top was a deck of coloured cards such that for every two blue cards, there were three red cards. The cards were arranged in the order as shown Figure 1.
23) Look at the pattern below carefully. a. Draw the in the correct position(s) in the 35th column. b. What is the total number of in the first 43 columns?
24) Study the following pattern. In which column will 100 appear?
25) The following shows a series of patterns. a. What is the total number of triangles in Pattern 6? b. What fraction of the figure in Pattern 12 is shaded? c. What is the total number of triangles in Pattern 36?
26) Study the pattern below. a. Fill the table above for the number of shaded hexagons in Pattern 5. b. How many hexagons are there for Pattern 7? c. Which pattern has 613 hexagons?
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Algebra Set A
34:13
P6ALGB-A - learnbrill
1) A windmill turns 6 degrees per second. How long will it take to turn 2k rounds? Express your answer in terms of k.
2) Amir bought 3 pencils and 4 exercise books for $14d. If each exercise book cost $2d, how much did each pencil cost in terms of d?
3) A pen cost x cents and a pencil cost 20 cents less than the pen. Daniel bought 5 similar pens and a pencil. How much did Daniel pay in terms of x?
4) A purse cost $x. A bag cost thrice as much as the purse. A watch cost $12 less than the purse. Find the total cost of the 3 items.
5) Gillian had 3 types of coins, 10cents, 20cents and 50ents. The ratio of the number of 10cents coins to the number of 20cents coins to the number of 50cents coins is 2 : 5 : n.
6) a. Find the value of (8y-44)/10 if y = 8 b. Jie Min had n boxes of beads. There were 24 beads in each box. Her mother gave her another 50 beads. She then sold 4n + 7 beads. How many beads does she have now?
7) Alan is 14 m years old and Danial is 3 times as old as he is now. a. How old will Daniel be 22 years later? Express your answer in terms of m. b. If m = 2, how much older will Daniel be than Alan now?
8) The total mass of Cathy, Jack and Mark is 15p kg. Cathy has a mass of 5p kg. Jack is 2 kg heavier than Cathy. a. What is Mark’s mass in terms of p? b. If p = 10, what is Mark’s mass?
9) Michelle bought 18 donuts at $y each and 16 loaves of bread at $1.50 each. She gave the cashier $100. a. Express her change in terms of y.
10) Alice decided to save part of her pocket money every day for a year. She saved $3 on the first day of the year. She continued to save $y more each day than the day before.
11) Four men carried 2r sacks of rice each. The 5th man carried 6 more sacks of rice than each of the four men.
12) k boys each rented a bicycle and went on an excursion for 5 hours. For each bicycle, the bicycle shop charged $8 for the first hour and an hourly rate of $5 for the subsequent hours.
13) A gardener planted some rubber trees in a row at fixed intervals apart. The distance between the first and the fourth tree is 24m m. Express your answers in terms ofm.
14) The figure below is made up a rectangle and an isosceles triangle. The length of the rectangle is (4a) cm and its breadth is (a + 2) cm.
15) The table shows the number of pens sold at a bookshop last week. a. What was the total number of pens sold last week? Express your answer in terms of p in the simplest form. b. If p = 30, how many pens were sold on Sunday?
16) Mrs Wong is 9k years old now. He has 2 sons, Bryan and Nigel. He is 3 times as old as Nigel now. Bryan is 2k years younger than Nigel.
17) Mrs Jones paid a total of $38 for 3m pens and 4 markers. Each pen cost $2. a. Express the cost of 1 marker in terms of m. b. If m = 4, how much did each marker cost
18) Andy had 1.4m of wire. He used some of it to make the figure show below. a. How much wire did Andy use to make the figure? Leave your answers in the simplest form in terms of p. b. If p = 12, how much wire was not used to make the figure?
19) Mr Gopal is 12p years old. He is now four times as old as his son. How old will Mr Gopal be when his son is 25 years old?
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