Mixed Topic Worksheet Grades 6/7: Day 024
- 1
Question 1. The population of a town falls from 8 000 to 7 600.
Work out the percentage decrease.Identifying Percentage Changes▶ Show worked answerHide worked answer
- M1: 8 000 - 7 600 = 400
- M1: 400 ÷ 8 000 × 100
- A1: 5%
Answer: 5%[3 marks] - 2
Question 2. Point P is (3, 4).
P is enlarged by scale factor -1 with centre of enlargement (5, 2).
Write down the x-coordinate of the image of P.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- M1: horizontal distance from the centre to P, 3 - 5 = -2
- A1: 7
Answer: 7[2 marks] - 3
Question 3. Two rugs are similar rectangles.
The smaller rug is 1.2 m long and costs £45.
The larger rug is 1.8 m long.
The cost of a rug is proportional to its area.
Work out the cost of the larger rug.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: 1.8 ÷ 1.2 = 1.5
- M1: 1.5² × 45
- A1: 101.25
Answer: £101.25[3 marks] - 4
Question 4. y is directly proportional to the square of x.
y = 45 when x = 3.
Find the value of y when x = 6.Algebraic Direct Proportion▶ Show worked answerHide worked answer
- M1: 45 = k × 3²
- M1: y = 5 × 6²
- A1: 180
Answer: 180[3 marks] - 5
Question 5. A sketch is to be drawn of the graph of y = x² - 2x - 8
Work out the coordinates of the points where the graph crosses the x-axis and the y-axis.Full Process for Sketching Quadratics▶ Show worked answerHide worked answer
- M1: (x + 2)(x - 4) = 0
- A1: (-2, 0) and (4, 0)
- B1: (0, -8)
Answer: (-2, 0), (4, 0) and (0, -8)[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 024
- 1
Question 1. The population of a town falls from 8 000 to 7 600.
[3 marks]
Work out the percentage decrease.Identifying Percentage Changes▶ Show worked answerHide worked answer
- M1: 8 000 - 7 600 = 400
- M1: 400 ÷ 8 000 × 100
- A1: 5%
Answer: 5% - 2
Question 2. Point P is (3, 4).
[2 marks]
P is enlarged by scale factor -1 with centre of enlargement (5, 2).
Write down the x-coordinate of the image of P.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- M1: horizontal distance from the centre to P, 3 - 5 = -2
- A1: 7
Answer: 7 - 3
Question 3. Two rugs are similar rectangles.
[3 marks]
The smaller rug is 1.2 m long and costs £45.
The larger rug is 1.8 m long.
The cost of a rug is proportional to its area.
Work out the cost of the larger rug.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: 1.8 ÷ 1.2 = 1.5
- M1: 1.5² × 45
- A1: 101.25
Answer: £101.25 - 4
Question 4. y is directly proportional to the square of x.
[3 marks]
y = 45 when x = 3.
Find the value of y when x = 6.Algebraic Direct Proportion▶ Show worked answerHide worked answer
- M1: 45 = k × 3²
- M1: y = 5 × 6²
- A1: 180
Answer: 180 - 5
Question 5. A sketch is to be drawn of the graph of y = x² - 2x - 8
[3 marks]
Work out the coordinates of the points where the graph crosses the x-axis and the y-axis.Full Process for Sketching Quadratics▶ Show worked answerHide worked answer
- M1: (x + 2)(x - 4) = 0
- A1: (-2, 0) and (4, 0)
- B1: (0, -8)
Answer: (-2, 0), (4, 0) and (0, -8)
Mixed Topic Worksheet Grades 6/7: Day 024
- 1
Question 1. The population of a town falls from 8 000 to 7 600.
Work out the percentage decrease.Identifying Percentage Changes▶ Show worked answerHide worked answer
- M1: 8 000 - 7 600 = 400
- M1: 400 ÷ 8 000 × 100
- A1: 5%
Answer: 5%[3 marks] - 2
Question 2. Point P is (3, 4).
P is enlarged by scale factor -1 with centre of enlargement (5, 2).
Write down the x-coordinate of the image of P.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- M1: horizontal distance from the centre to P, 3 - 5 = -2
- A1: 7
Answer: 7[2 marks] - 3
Question 3. Two rugs are similar rectangles.
The smaller rug is 1.2 m long and costs £45.
The larger rug is 1.8 m long.
The cost of a rug is proportional to its area.
Work out the cost of the larger rug.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: 1.8 ÷ 1.2 = 1.5
- M1: 1.5² × 45
- A1: 101.25
Answer: £101.25[3 marks] - 4
Question 4. y is directly proportional to the square of x.
y = 45 when x = 3.
Find the value of y when x = 6.Algebraic Direct Proportion▶ Show worked answerHide worked answer
- M1: 45 = k × 3²
- M1: y = 5 × 6²
- A1: 180
Answer: 180[3 marks] - 5
Question 5. A sketch is to be drawn of the graph of y = x² - 2x - 8
Work out the coordinates of the points where the graph crosses the x-axis and the y-axis.Full Process for Sketching Quadratics▶ Show worked answerHide worked answer
- M1: (x + 2)(x - 4) = 0
- A1: (-2, 0) and (4, 0)
- B1: (0, -8)
Answer: (-2, 0), (4, 0) and (0, -8)[3 marks]