Area and perimeter L6 non calc 27 minutes 25 marks Page 1 of 21 Q1. L-shape What is the area of this L-shape? Show your working. ........................ cm2 2 marks Q2. Perimeters Jenny and Alan each have a rectangle made out of paper. One side is 10cm. The other side is n cm. Page 2 of 21 (a) They write expressions for the perimeter of the rectangle. Jenny writes 2n + 20 Alan writes 2(n + 10) Tick ( ) the true statement below. Jenny is correct and Alan is wrong. Jenny is wrong and Alan is correct. Both Jenny and Alan are correct. Both Jenny and Alan are wrong. 1 mark (b) Alan cuts his rectangle, then puts the two halves side by side. What is the perimeter of Alan’s new rectangle? Write your expression as simply as possible. 2 marks (c) Jenny cuts her rectangle a different way, and puts one half below the other. Page 3 of 21 What is the perimeter of Jenny’s new rectangle? Write your expression as simply as possible. 2 marks (d) What value of n would make the perimeter of Jenny’s new rectangle the same value as the perimeter of Alan’s new rectangle? 1 mark Q3. Areas algebraically (a) The diagram shows a rectangle. Its dimensions are 3a by 5b Write simplified expressions for the area and the perimeter of this rectangle. Area: ........................................ 1 mark Perimeter: ................................ 1 mark Page 4 of 21 (b) A different rectangle has area 12a 2 and perimeter 14a . What are the dimensions of this rectangle? Dimensions: ...................... by ........................... 1 mark Q4. Cuboids You can make only four different cuboids with 16 cubes. Dimensions (a) Cuboid A 1 1 16 Cuboid B 1 2 8 Cuboid C 1 4 4 Cuboid D 2 2 4 Which of the cuboids A and D has the larger surface area? Tick ( ) the correct answer below. Cuboid A Cuboid D Both the same 1 mark Page 5 of 21 Explain how you know. 1 mark (b) Which cuboid has the largest volume? Tick ( ) the correct answer below. Cuboid A Cuboid B Cuboid C Cuboid D All the same 1 mark (c) How many of cuboid D make a cube of dimensions 4 × 4 × 4? ............................... 1 mark Page 6 of 21 (d) You can make only six different cuboids with 24 cubes. Complete the table to show the dimensions. Two have been done for you. Dimensions Cuboid E 1 1 24 Cuboid F 1 2 12 Cuboid G Cuboid H Cuboid I Cuboid J 3 marks Q5. Square cut The diagram shows a square. Two straight lines cut the square into four rectangles. The area of one of the rectangles is shown. Not drawn accurately Page 7 of 21 Work out the area of the rectangle marked A. ......................... cm2 2 marks Q6. Circle working Kevin is working out the area of a circle with radius 4 He writes: Area = π × 8 Explain why Kevin’s working is wrong. 1 mark Page 8 of 21 Q7. Cube Look at the cube. The area of a face of the cube is 9x 2 Write an expression for the total surface area of the cube. Write your answer as simply as possible. .................... 1 mark Q8. Square tiles The diagram shows a square with a perimeter of 12cm. Not drawn accurately Six of these squares fit together to make a rectangle. Not drawn accurately Page 9 of 21 What is the area of the rectangle? You must give the correct unit with your answer. ............................. 2 marks Q9. Missing lengths Look at the rectangle. Not drawn accurately Page 10 of 21 The total area of the rectangle is 40cm2 Work out lengths x and y x = ....................... cm y = ....................... cm 2 marks Page 11 of 21 M1. 30 2 or Shows a complete correct method with no more than one computational error The most common correct methods: Calculate the area as 2 non-overlapping parts, A and B, as shown in the diagram • 4×6+3×2 • 24 + 6 • 4 × 6 = 28 (error), 28 + 6 = 34 Calculate the area as 2 non-overlapping parts, C and D, as shown in the diagram • 7×2+4×4 • 14 + 16 • 4 × 4 = 18 (error), 18 + 14 = 32 Calculate the area as 3 non-overlapping parts, E, F and G, as shown in the diagram • 4 × 4 + 4 × 2 +3 × 2 • 16 + 8 + 6 Page 12 of 21 Calculate the area as two parts that need to be subtracted, eg • 6×7–4×3 • 42 – 12 ! Do not accept conceptual error, eg • 6 × 4 + 7 × 2 (overlapping parts) • 6 × 4 × 7 × 2 (given lengths multiplied) Method not shown fully If there is no evidence of an incorrect method, accept the following: • 24 + error but not 14 (for A and B) • 14 + error but not 24 (for C and D) • 16 + 8 error but not 14 (for E, F, G) • 16 + error not 24 or 14 + 6 (for E, F, G) • Error but not 24 + 8 + 6 (for E, F, G) • 42 – error (subtraction method) • Error – 12 (subtraction method) 1 [2] M2. (a) Both correct, ie 1 (b) or or Correct simplified expression, eg • 4n + 10 • 4 (n + 2.5) • 2(2n + 5) • (2n + 5) × 2 For only 1 Correct expression seen, even if terms are not collected together, eg • 5+n+n+n+n+5 • 2n + 2n + 10 For only 1 An otherwise correct simplified expression, of 4n + k, (k ≠ 10), eg • 4n + (10 ÷ 2) • 4(n + 5) • 2(2n + 2) Page 13 of 21 ! ! ! Incorrect working follows correct response eg, for part (a) • 4n + 10 = 40n Mark as 1, 0 Correct answer preceded by incorrect working If the intended answer is unambiguous, ignore preceding work eg, for part (b), accept • 5 + 2n × 2 = 10 + 4n An otherwise correct simplified expression with the only error being that the brackets are omitted eg, for part (b) • 2n + 5 × 2 Mark as 1, 0 2 (c) or or Correct simplified expression, eg • 40 + n • 2(20 + ½ n) For only 1 Correct expression seen, even if terms are not collected together, eg • 10 × 4 + n • 40 + ½ n + ½ n • 2(n ÷ 2 + 20) For only 1 An otherwise correct simplified expression, of n + k, (k ≠ 40 but is a multiple of 10) eg • 2(n ÷ 2 + 10) ! Value for n substituted into an otherwise creditworthy response Ignore. 2 (d) 10 Accept 10 cm 1 [6] M3. (a) Gives a correct simplified expression for the area, eg • 15ab • 15 × a × b 1 Page 14 of 21 Gives a correct simplified expression for the perimeter, eg • 6a + 10b • 2(3a + 5b) • 6 × a + 10 × b • 2 × (3a + 5b) ! ! Partially simplified or unsimplified expressions eg, for the area • 3a5b eg, for the perimeter • 2(3a) + 2(5b) • 2 × (3 × a + 5 × b) If both expressions are correct but are partially simplified or unsimplified, mark as 0, 1, provided neither has subsequently been incorrectly simplified Expressions transposed but otherwise correct and simplified Mark as 0, 1 1 (b) Gives both correct dimensions in either order, ie 4a and 3a ! Correct dimensions embedded Accept provided both the area and perimeter have been considered, eg, accept • 12a² = 3a × 4a 14a = 2(3a + 4a) ! Dimensions labelled as length or width Ignore 1 [3] M4. (a) Indicates Cuboid A and gives a correct explanation The most common correct explanations: Show the correct surface area for both A and D eg • The surface area of A is 66, but D is 40 Consider the number of cube faces that are not visible eg • Each cube in D has 3 or 4 faces that cannot be seen but each cube in A has only 1 or 2 • Fewer faces of the cubes are touching each other in A Page 15 of 21 Consider the number of cube faces that are visible eg • In A the cubes show 4 or 5 faces, but in D it’s 2 or 3 • There are more cube faces facing out on A than on D ! Units inserted Ignore Accept minimally acceptable explanation eg, for the correct surface areas • 66 and 40 seen • 4 × 16 + 2 is bigger than 4 × 8 + 8 eg, for cube faces that are not visible • There are fewer hidden faces in A • D is more compact eg, for cube faces that are visible • Cubes in A show 4 or more faces, D shows less than 4 • A has more faces showing • A is more spread out ! Use of ‘sides’ for cube faces Condone eg, accept • More sides face out on A ! Descriptors of cube faces Note that pupils use a wide range of terms to describe the cube faces eg, for cube faces that are not visible • Hidden faces • Faces pointing inside • Faces touching eg, for cube faces that are visible • Faces facing out • Faces showing • Faces you can see Condone provided the pupil does not explicitly refer to the area of only one of the faces of each cuboid eg, do not accept • You can see 8 faces on D and 16 faces on A Do not accept use of ‘square’ for cube or cuboid eg • You can see more of each square’s surface in A than in D Do not accept explanation is simply a description of one or both of the cuboids eg • In A all 16 are in a line and not on top of each other • D is two cubes high Do not accept incorrect statement eg • Each cube in A shows 4 faces; D is 3 U1 Page 16 of 21 (b) Indicates All the same 1 (c) 4 1 (d) Shows, in any order, all four correct sets of dimensions eg • 1 1 2 2 3 4 2 3 8 6 6 4 3 or Shows three correct sets of dimensions 2 or Shows two correct sets of dimensions 1 ! Repeated sets of dimensions eg • 1 3 8 1 8 3(repeated) 2 2 6 6 2 2 (repeated) Ignore the repeats and mark as 1, 0, 0 Do not accept negative or non-integer dimensions used [6] M5. 42, with no evidence of an incorrect method Do not accept incorrect method eg • 12 + 2 = 14, 14 × 3 = 42 2 or Shows or implies that the square is a 9(cm) by 9(cm) square eg • 7 × 6 seen • • Area of square = 81 Page 17 of 21 or Shows or implies a correct method in which the only error is to use an incorrect value for the shorter horizontal side of rectangle A eg • 12 ÷ 2 = 8 (error), 8 + 3 = 11 11 – 2 = 9, 8 × 9 = 72 • Answer: 20 1 (U1) [2] M6. Gives a correct explanation The most common correct explanations: Show the correct working eg • It should be π × 16 not π × 8 • Needs to be π × radius2, not π × diameter Accept: minimally acceptable explanation eg • 16 • • 42 4×4 • r2 • πr2 Do not accept: incomplete explanation eg • The 8 is wrong Page 18 of 21 Address the misconception eg • He is finding the circumference not the area • He is using 2πr, not πr2 • He has done 4 × 2 instead of 42 Accept: minimally acceptable explanation eg • Circumference • It’s not 2πr [or πd] • He didn’t square the 4 • He didn’t square the radius ! Use of ‘perimeter’ for ‘circumference’ Condone Do not accept: incomplete explanation eg • He used the wrong formula • He used the diameter • He hasn’t used the radius • He doubled the radius Show that his working gives an incorrect answer eg • He gets 25.(…), but it should be 50.(…) • His answer is half as big as it should be Accept: minimally acceptable explanation eg • 50, not 25 • It should be his answer × 2 Do not accept: incomplete explanation eg • 50 • His answer is too small U1 [1] Page 19 of 21 54x 2 M7. Do not accept: unsimplified expression or unconventional notation eg • 9x2 × 6 • • 9x2 + 9x2 + 9x2 + 9x2 + 9x2 + 9x2 54xx [1] M8. Gives a correct value for the area of the rectangle eg • 54 • 5400 U1 Shows the correct unit for their area eg • cm² [with 54] • mm² [with 5400] ! Area incorrect or omitted, but units given If the mark for their correct area has not been awarded, condone cm² seen for the second mark 1 [2] M9. Gives both correct lengths, ie x = 10 and y = 3.9 or equivalent 2 or Gives y = 3.9 or equivalent or Gives the two values transposed, ie x = 3.9 or equivalent and y = 10 or Shows a complete correct method with not more than one computational error eg • x = 10, 10 – 6.1 = 4.9 (error) • 4 × 6.1 = 24.4, 40 – 24.4 = 16.6 (error) 16.6 ÷ 4 = 4.15, 4.15 + 6.1 = 10.25 • 40 ÷ 4 = 20 (error) 20 – 6.1 = 13.9 1 [2] Page 20 of 21 Page 21 of 21

© Copyright 2022 Paperzz