Mixed Topic Worksheet Grades 6/7: Day 081
- 1
Question 1. Solve x² + 6x = 0
Solving Quadratics by Factorising When c = 0▶ Show worked answerHide worked answer
- M1: factorise: x(x + 6) = 0
- M1: x = 0 or x + 6 = 0
- A1: x = 0 or x = -6
Answer: x = 0 or x = -6[3 marks] - 2
Question 2. A square rug has an area of 11 m². A room is 3 m wide. Will the rug fit across the width of the room? Use square numbers to give a reason for your answer.
Estimating Roots▶ Show worked answerHide worked answer
- M1: 3² = 9
- M1: 9 < 11, so the side of the rug is more than 3 m
- B1: No
Answer: No. 3² = 9, which is less than 11, so the side of the rug is more than 3 m[3 marks] - 3
Question 3. Triangle T is drawn on the grid.
Enlarge triangle T by scale factor -2 with centre of enlargement (0, 0).
Label the image U.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- M1: multiply coordinates by −2 for at least two vertices
- M1: three vertices found: (−2, −2), (−4, −2), (−2, −4)
- A1: image U correctly drawn and labelled
Answer: Image U has vertices (−2, −2), (−4, −2), (−2, −4)[3 marks] - 4
Question 4. A = (7, 2) B = (1, -2) C = (-3, 4)
Show that AB is perpendicular to BC.Properties of Perpendicular Lines▶ Show worked answerHide worked answer
- M1: gradient of AB = 2 - (-2)/7 - 1 = 2/3
- M1: gradient of BC = 4 - (-2)/-3 - 1 = -3/2
- A1: 2/3 × -3/2 = -1
- C1: so AB is perpendicular to BC
Answer: product of the gradients = -1[4 marks] - 5
Question 5. In a sale, all prices are reduced by 30%.
The sale price of a pair of shoes is £63.
Kai says, "The normal price is 63 × 1.3 = £81.90."
Is Kai correct?
You must show your working.Finding the Initial Amount▶ Show worked answerHide worked answer
- M1: 100 - 30 = 70%
- M1: 63 ÷ 0.7
- A1: 90
- C1: Kai is not correct because the 30% was taken off the normal price, not off the sale price
Answer: No. The normal price is £90[4 marks]
Mixed Topic Worksheet Grades 6/7: Day 081
- 1
Question 1. Solve x² + 6x = 0
[3 marks]Solving Quadratics by Factorising When c = 0▶ Show worked answerHide worked answer
- M1: factorise: x(x + 6) = 0
- M1: x = 0 or x + 6 = 0
- A1: x = 0 or x = -6
Answer: x = 0 or x = -6 - 2
Question 2. A square rug has an area of 11 m². A room is 3 m wide. Will the rug fit across the width of the room? Use square numbers to give a reason for your answer.
[3 marks]Estimating Roots▶ Show worked answerHide worked answer
- M1: 3² = 9
- M1: 9 < 11, so the side of the rug is more than 3 m
- B1: No
Answer: No. 3² = 9, which is less than 11, so the side of the rug is more than 3 m - 3
Question 3. Triangle T is drawn on the grid.
[3 marks]
Enlarge triangle T by scale factor -2 with centre of enlargement (0, 0).
Label the image U.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- M1: multiply coordinates by −2 for at least two vertices
- M1: three vertices found: (−2, −2), (−4, −2), (−2, −4)
- A1: image U correctly drawn and labelled
Answer: Image U has vertices (−2, −2), (−4, −2), (−2, −4) - 4
Question 4. A = (7, 2) B = (1, -2) C = (-3, 4)
[4 marks]
Show that AB is perpendicular to BC.Properties of Perpendicular Lines▶ Show worked answerHide worked answer
- M1: gradient of AB = 2 - (-2)/7 - 1 = 2/3
- M1: gradient of BC = 4 - (-2)/-3 - 1 = -3/2
- A1: 2/3 × -3/2 = -1
- C1: so AB is perpendicular to BC
Answer: product of the gradients = -1 - 5
Question 5. In a sale, all prices are reduced by 30%.
[4 marks]
The sale price of a pair of shoes is £63.
Kai says, "The normal price is 63 × 1.3 = £81.90."
Is Kai correct?
You must show your working.Finding the Initial Amount▶ Show worked answerHide worked answer
- M1: 100 - 30 = 70%
- M1: 63 ÷ 0.7
- A1: 90
- C1: Kai is not correct because the 30% was taken off the normal price, not off the sale price
Answer: No. The normal price is £90
Mixed Topic Worksheet Grades 6/7: Day 081
- 1
Question 1. Solve x² + 6x = 0
Solving Quadratics by Factorising When c = 0▶ Show worked answerHide worked answer
- M1: factorise: x(x + 6) = 0
- M1: x = 0 or x + 6 = 0
- A1: x = 0 or x = -6
Answer: x = 0 or x = -6[3 marks] - 2
Question 2. A square rug has an area of 11 m². A room is 3 m wide. Will the rug fit across the width of the room? Use square numbers to give a reason for your answer.
Estimating Roots▶ Show worked answerHide worked answer
- M1: 3² = 9
- M1: 9 < 11, so the side of the rug is more than 3 m
- B1: No
Answer: No. 3² = 9, which is less than 11, so the side of the rug is more than 3 m[3 marks] - 3
Question 3. Triangle T is drawn on the grid.
Enlarge triangle T by scale factor -2 with centre of enlargement (0, 0).
Label the image U.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- M1: multiply coordinates by −2 for at least two vertices
- M1: three vertices found: (−2, −2), (−4, −2), (−2, −4)
- A1: image U correctly drawn and labelled
Answer: Image U has vertices (−2, −2), (−4, −2), (−2, −4)[3 marks] - 4
Question 4. A = (7, 2) B = (1, -2) C = (-3, 4)
Show that AB is perpendicular to BC.Properties of Perpendicular Lines▶ Show worked answerHide worked answer
- M1: gradient of AB = 2 - (-2)/7 - 1 = 2/3
- M1: gradient of BC = 4 - (-2)/-3 - 1 = -3/2
- A1: 2/3 × -3/2 = -1
- C1: so AB is perpendicular to BC
Answer: product of the gradients = -1[4 marks] - 5
Question 5. In a sale, all prices are reduced by 30%.
The sale price of a pair of shoes is £63.
Kai says, "The normal price is 63 × 1.3 = £81.90."
Is Kai correct?
You must show your working.Finding the Initial Amount▶ Show worked answerHide worked answer
- M1: 100 - 30 = 70%
- M1: 63 ÷ 0.7
- A1: 90
- C1: Kai is not correct because the 30% was taken off the normal price, not off the sale price
Answer: No. The normal price is £90[4 marks]