TRIANGLES CONTENT DOMAIN REFERENCES: KS2 SATS 1 2 3 4 5 6 7 8 9 10 G2, G4 PRACTICE QUESTIONS BY TOPIC 12 Here are four triangles drawn on a square grid.
12112 12HereHere areHere are four fourare triangles four triangles triangles drawn drawn drawn on on ona a square squarea square grid.grid. grid. [2002] 1
Write the letter for each triangle in the correct region of Write thethe lettersorting for diagram. each triangle in the correct region of theWrite sorting the diagram.letter for each triangle in the correct region of the sorting diagram. Write theOne letter has been for eachdone fortriangle you. in the correct region of theOne sorting has been diagram. done for you. One has been done for you.
One has been done for you.
A
AA A 12
2 marks
1212 [2 marks] 2 2marks marks
12
12 2 marks
Contains public sector information licensed under the Open Government Licence v3.0 Questions compiled by: www.nationalarchives.gov.uk/doc/open-government-licence @Maths4Everyone 1212
12 13 Jamie, Kate and Hassan run a 50m race.
Kate’s time is 13 seconds.
Jamie finishes 5 seconds before Kate.
Hassan finishes 3 seconds after Jamie.
What is Hassan’s time in seconds?
seconds 13
1 mark
17 On this scale, the arrow ( ) shows the weight of this pineapple. 142 Here are four triangles on a square grid. [2007] 2
Here is a different scale. ACD Mark with an arrow B( ) the weight of the same pineapple.
Write the letters of the two isosceles triangles.
14 and 17 1 mark 1 mark [1 mark]
183 These two shaded triangles are each inside a regular hexagon. 12 [2001] 3
Under each hexagon, put a ring around the correct name of the shaded triangle. KKS2S2 MMathsTestB_275356.inddath1sTes2tB_27 35356 4.indd 5 1212 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 114/2/07 364/2 /0377 33:13:09:13:09 pmpm
equilateral equilateral
isosceles isosceles
18 scalene scalene 1 mark
[1 mark]
12 5 166 Here are fve shaded triangles on a square grid. [2012] [2010]4 This diagram shows a square with dots at the vertices and at the 5 6 middle of each side. [2012] 4 The square is divided into four triangles, A, B, C and D.
166 Here are fve shaded triangles on a square grid. [2010] 6
5
AB C D E
10 WriteWrite the theAB letters letter of of all each the trianglestriangle thatC havehas aa rightright angleD .. E
16a
1 mark WriteWrite the the letters letter of of all each the isoscelestriangle that triangles. has a right angle. T
15 16a M01946 – 26 November 2014 1:55 PM – Version 2 1 mark Write the letter of each triangle that has two equal sides. [2 marks] 12 Anna has four different triangles. 5 Anna has four different triangles. 16b Complete the table to show the size of the angles in each triangle. 1 mark [Extra] Complete the table to show the size of the angles in each triangle. 5 [2 marks][2 marks] Write the letter of each triangle that has two equal sides. Type of triangle Angle 1 Angle 2 Angle 3
Isosceles 90º 16b
1 mark
Right-angled 80º [2 marks]
Isosceles 70º
Isosceles 70º17 Total out of 4 Sourced from SATs-Papers.co.uk https://www.SATs-Papers.co.uk 2 marks [2 marks]
17 Total out of 4
cm
M01946_missing angles S S2a/S2b/SUA1 L5 D00130A01520 Page 15 of 20 Same area
8. (a) The square and the rectangle below have the same area.
Not drawn accurately
Same area Same area 8. (a) The square and the rectangle below have the same area. 8. (a) The square and the rectangle below have the same area. Same area
8. (a) The square and the rectangle below have the same area. Not drawn accuratelyNot drawn Work out the value of y accurately NotT drawn accurately
y =cm 1 mark
Containers, Triangles 18 (b)The The triangle triangle and and the therectangle rectangle below below has the have same the area same. area. Work out the value of y [Extra]12. Here are two containers and the amounts they hold. Work out the value of y NotT drawn 18 166 Here are fve shaded triangles on a square grid. accuratelyT Work out the value of y B [2010] T 166 Here are fve shadedA triangles on a square ygrid.=cm 6 166 Here are fve shaded triangles on a squarey =cm grid. 1 mark 1 mark [2010]6 Here are five shaded triangles on a square grid. Not drawn [2010] 6 166 Here are fve shaded triangles on a square ygrid.=cmaccurately Containers, Triangles 6 [2010]18 (b)The The triangle triangle and and the therectangle rectangle below below has the have same the area same. area. Containers, Triangles 1 mark 6 (b)The TheHere triangle triangle are f veand and shaded the therectangle trianglesrectangle below on below has a square the have same grid. the area same. area. [2010]186166 Here are five shaded triangles on a square grid. [Extra] 750 millilitres 0.5 litre 6 12. Here are two containers and the amounts they hold. Containers, Triangles 18 [Extra][2010][2010]12. (b)The Here The triangle triangleare two and containers and the therectangle rectangleand the below amounts below has the they have same hold. the area same. area. Not drawn 186 18 accuratelyNot drawn 6 166 Here are fve shaded triangles on a squareB grid. accurately [Extra]12. Which Here are container two containers holds the and greater the amounts amount? theyB hold. 18 [2010] A Not drawn 6 A accurately Work out theA value of w. B B 5 Not drawn accuratelyNot drawn Work outAB the valueA of w C D accuratelyE How much more does it hold? Show your working. Not drawn 5 AB750 millilitres C 0.5 litre D E Give yourAB answer750 in millilitres millilitres. C 0.5 litre D accuratelyE T WhichAB container750 holds millilitres the greaterC amount?0.5 litre D E Which container holds the greater amount? AB C D E Work WriteWrite out the the the letter letterA value of of each of each w .triangle triangleB that that has hasa right a right angle. angle. WorkWhich out container the A value holds of w the. greater B amount? millilitres 10 Work out the value of w 1 mark WriteWork the out ABletter the of value each oftriangle w thatC has a right angleD . E WorkHowWrite muchout the the lettermoreA value ofdoes of each w it. hold? triangleB that has a right angle. XXXXHowShowWrite much the your letter more working. of doeseach ittriangle hold? that has a right angle. [2 marks]16a Show your working. w =cm 10 GiveWork your out answer the value in millilitres. of w 1 mark 2 marks WriteGive the your letter answer of each in millilitres. triangle that has a right angle. How much more does it hold? 16a 13.19 (a) AShow triangle your has working. three equal sides. T 16a KS3/04/Ma/Tier WriteWrite 5–7/P2 the the letter letter of of each each triangle triangle that that has hastwo aequal right sides. angle. T Give your answer in millilitres. 10 1 mark [Extra] Write the sizes of the angles in this triangle. 1 mark T 16a 19 Write the letter of each triangle that has a right angle. 16a Write the letter of each triangle that has two equal sides. millilitres 1 mark millilitres 1 mark 1 mark 1 mark 15 ° ° ° XXXXWrite the letter of each triangle that, has wtwo=cm equal, sides . millilitres [2[2 marks]16amarks] XXXX [2 1marks] mark w =cm 2 marks 1 mark 15 Write the letter of each triangle that has two equal sides. 2 marks 13.7 (a) AHeight triangle in metreshas three Height equal in metressides. Height metres Height in metres [2 marks] KS3/04/Ma/Tier19 XXXXWrite 5–7/P2 the letter of each triangle that has wtwo=cm equal sides. [2 marks]16b 13.KS3/04/Ma/Tier19 (a) A triangle 5–7/P2 has three equal sides. 10 [Extra] 10 2 marks [Extra] Write the sizes of the angles in this triangle. 1 mark 7 [Extra] (b) WriteWrite A right-angled the the letter sizes of of triangle eachthe angles triangle has twoin thisthat equal triangle. has sides two. equal sides. 19 13.KS3/04/Ma/Tier197 (a) A triangle 5–7/P2 has three equal sides. 16b 19 [216b marks] WriteWrite the the sizes letter of ofthe each angles triangle in this that triangle.10 has two equal sides. [Extra] Write the sizes of the angles in this triangle. 1 mark 1 mark 197 ° ° ° [216b marks] °, °, ° [2 marks] Write the letter of each triangle that has two equal sides. 16b , , 1 mark 1 mark ° ° ° 1 mark °, °, ° 1[2 mark marks] 5 , , 1 mark [2116b markmarks] [2 marks] (b) A right-angled triangle has two equal sides. (b) A right-angled triangle has two equal sides. 1 mark Write the sizes of the angles in this triangle. [2 marks] KS3/07/Ma/TierWrite 4–6/P2 the sizes of the angles in this 13triangle. (b) A right-angled triangle has two equal sides.
Write the sizes of the angles in this triangle. 17 Total out of 4 ° ° ° 2275663_p2_46.indd75663_p2_46.indd 1313 °, °, ° 115/11/065/11/06 10:20:4610:20:46 ppmm , , 1 mark 10 17 Total out of 4 1 mark 17 ° ° Total out° of 4 [2[2 marks]marks] , , [2 marks] 1 mark 17 Total out of 4 KS3/07/Ma/Tier 4–6/P2 13 [2 marks] KS3/07/Ma/Tier 4–6/P2 17 13 Total out of 4
KS3/07/Ma/Tier 4–6/P2 13 17 Total out of 4 2275663_p2_46.indd75663_p2_46.indd 1313 115/11/065/11/06 10:20:4610:20:46 ppmm 2275663_p2_46.indd75663_p2_46.indd 1313 cm 115/11/065/11/06 10:20:4610:20:46 ppmm
2275663_p2_46.indd1575663_p2_46.indd 1313 115/11/065/11/06 10:20:4610:20:46 ppmm
cm cm
cm p1_46FINAL_4pp.qxd 21/01/2004 16:44 Page 9 p1_46FINAL_4pp.qxd 21/01/2004 16:44 Page 9
Triangle statement T Triangle statement T 8 Look at the triangle ABC, drawn on a square grid. 8 Look8 at Lookthe triangle at the triangle ABC, ABC, drawn drawn on aon square a square grid. grid. [Extra] 8 6 6
5 5 5 4 C B 4 C B 3 3
2 A 2 10 A 1 1
0 0 0123456 0123456
15 Here areHere some are some statements statements about about triangle triangle ABC.ABC. Here are some statements about triangle ABC. For eachFor eachstatement statement tick tick ( ( ) True)True or or False. False. For each statement tick ( ) True or False. True False True False The triangle is isosceles. The triangle is isosceles. The triangle has only one line of symmetry. The triangle has only one line of symmetry. The triangle is right-angled. The triangle is right-angled. The coordinates of A are (2, 3) 2 marks The coordinates of A are (2, 3) 2 marks [2 marks]
Y8/Ma/Levels 4–6/P1 9 Y8/Ma/Levels 4–6/P1 9 24 Part of this number line is shaded.
012
Circle all the numbers below that belong in the shaded part of the number line.
1 1 24 1.1 1.4 1 1 3 5 1 mark
259 Jamie draws a triangle. [2007] 9 He says,
‘Two of the three angles in my triangle are obtuse’.
Explain why Jamie cannot be correct.
25
1 mark
[1 mark]
10 21 Here are four statements. 22 [2005] 10 For each statement put a tick ( ) if it is possible. Put a cross ( ) if it is impossible.
KKS2S2 MMathsTestA_275355.inddath1sTes2tA_27 35355 4.indd 5 2222 6 7 8 9 10 11 12 13 14 15 16 17 18 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3666/2/07/2 /0377 5:19:455:19:45 ppmm
A triangle can have 2 acute angles.
A triangle can have 2 obtuse angles.
A triangle can have 2 parallel sides.
21i
A triangle can have 2 perpendicular sides. 21ii
2 marks [2 marks]
22 Write these fractions in order of size starting with the smallest.
3 3 9 17 4 5 10 20
22
smallest 1 mark
18 t
A2_5PP_0801.qxd 22/01/2004 15:40 Page 16
Drawing triangles
16 (a) Tina measures the angles in a triangle. 11 TheTina sketch measures shows the angles her results. in a triangle. 19 A packet contains 1.5 kilograms of guinea pig food. [Extra] The sketch shows her results. 11 Remi feeds her guinea pig 30 grams of food each day.
Not drawn accurately
5
How can you tell that Tina has made a mistake? How can you tell that Tina has made a mistake? How many days does the packet of food last?
10
1 mark
19i Height in metres Height in metres Height metres Height in metres (b) Draw a triangle with one angle of 35° and one angle ofdays 45° 19ii
2 marks 15 Use the line below as one side of the triangle, [1 mark] and draw the triangle accurately. 2012 An isosceles triangle has a perimeter of 12cm. [2003] One of its sides is 5cm. 12
What could the length of each of the other two sides be?
Two different answers are possible.
Give both answers.
2 marks cm and cm 20i cm and cm Y7/Ma/Levels 4–6/P2 16 20ii 2 marks [2 marks]
16 6M7b M003985_axehead – 8 December 2015 4:29 PM – Version 4
1217 Here are five triangles on a square grid. 13 Here are five triangles on a square grid. [2016] 12 [2016] 13
A
Possible? B 5 23. (a) Is it possible to draw a triangle with angles 150°, 10° and 10°?
Yes No
D Explain your answer. E C
10
Four of the triangles have the same area. Four of the triangles have the same area. T Which triangle has a different area? Which triangle has a different area? 1 mark
[1 mark] 15 XXXX 1 mark M003985 14 (b) Is it possible to draw a triangle with sides 150cm, 10cm and 10cm? [1 mark] [Extra] Yes No 14
Explain your answer.
1 mark
E00080A01924 Page 19 of 24 KS2 item template version 1.1 [1 mark]
Y9/Ma/Tier 4–6/P2 24
112009_p2.46.indd 24 07/12/2009 12:40:58 20 7. 4 8 . 1 9 . 4 1 0
Which two of these numbers, when multiplied together, have the answer closest to 70?
and 20
1 mark
2115 Here is an isosceles triangle. [2005] 15
Not to scale
110˚
Calculate the size of angle x.
Do not use a protractor (angle measurer).
265280 Ma KS3 4-6.qxp 20/6/05 9:55 am Page 21 T ° x = 21
1 mark
Angle p [1 mark]
22. 16This shapeThis shapehas been has beenmade made from from two two congruent congruent isosceles triangles.triangles. [Extra] 16 17 Total out of 4
35˚
Not drawn accurately
35˚
What is the size of angle p?
º What is the size of angle p? [2 marks]
p = ° 2 marks
KS3/05/Ma/Tier 4–6/P1 21
3736 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 2317 Look at this diagram. [2002] 17
Not to scale
Calculate the size of angle x and angle y.
Do not use a protractor (angle measurer).
O x = 23a 1 markT O 23b M01451_calcangley = – 25 February 2013 8:37 AM – Version 2 1 mark
3 The diagram shows an isosceles triangle and a square on a [2 marks] straight line. 18 The diagram shows an isosceles triangle and a square on a straight line. [Extra] 18 1 2 24 Which is larger, or ? 3 5 34° Not to scale a Explain how you know.
......
Calculate angle a. Calculate...... angle a. 24 ...... 1 mark
[2 marks] Show your method 18 Total
°
2 marks
M01451_calcangle L5 S 06 T
Angle k, Terms
20. Look at the diagram. 19 Look at the diagram. Not drawn [Extra] k accurately 19
130º 85º A B
AB is a straight line. AB is a straight line. Work out the size of angle k Work out the size of angle k
º
[2 marks]
205 The diagram shows two shaded equilateral triangles. [2001] ° 20 k = 2 marks
Not to scale
21. Look at the sequence below.
To get the next term in the sequence, subtract 90 from the term before.
500 410 320 …
Write the first two terms of the sequence that are less than zero.
Calculate the size of the angle x and angle y.
Do not use a protractor (angle measurer). 5a
1 mark
OO x = y = 5b , 1 mark 2 marks [2 marks] Y9/Ma/Tier 4–6/P1 20
072009_p1.46.indd6 20 Find the value of u in this equation. 07/12/2009 12:38:57
7+4u =70–3u
Show your method. You may get a mark.
6
2 marks
4 Same area
8. (a) The square and the rectangle below have the same area.
Not drawn accurately
Work out the value of y T
y =cm 1 mark
21 (b)The The triangle triangle and and the therectangle rectangle below below has the have same the area same. area. [Extra] Not drawn 21 accurately
Work out the value of w. Work out the value of w Show your working.
T
M01958_shaded triangle – 15 November 2013 11:32 AM – Version 2
w =cm [2 marks] 11 The diagram shows a shaded triangle inside a rectangle. 2 marks
KS3/04/Ma/Tier22 The 5–7/P2diagram shows a shaded triangle inside a rectangle. 10 [Extra] 10cm 22
6cm Not actual size
4cm
What is the area of the shaded triangle? What is the area of the shaded triangle?
cm2
[2 marks] Show your working
cm2
2 marks
M01958_shaded triangle S S5/S4e L6
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