Mixed Topic Worksheet Grades 6/7: Day 053
- 1
Question 1. A rope 16 m long is tied from the top of a pole to the ground.
The rope makes an angle of 60^° with the ground.
Work out the horizontal distance from the foot of the pole to the point where the rope meets the ground.Applied Exact Trig Values Questions▶ Show worked answerHide worked answer
- M1: 16 × cos 60^°
- A1: 8
Answer: 8[2 marks] - 2
Question 2. Shape A is drawn on the grid.
Enlarge shape A by scale factor -2 with centre of enlargement (0, 0).
Label the image B.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- B2: image B drawn with vertices (−2, −2), (−6, −2), (−2, −4) (one mark for the correct image on the wrong side of the centre, or for two correct vertices)
Answer: Image B has vertices (−2, −2), (−6, −2), (−2, −4)[2 marks] - 3
Question 3. A square photograph has an area of 440 cm²
The photograph is to be put into a square frame.
The inside of the frame is a square of side 22 cm.
Will the photograph fit inside the frame?
Use square numbers to give a reason for your answer.Estimating Roots▶ Show worked answerHide worked answer
- M1: 22² = 484
- M1: 440 < 484, so the side of the photograph is less than 22 cm
- C1: the photograph will fit inside the frame
Answer: Yes[3 marks] - 4
Question 4. f⁻¹(x) = dfracx + 85
Find f(x)Inverse Functions▶ Show worked answerHide worked answer
- M1: y = dfracx + 85, so 5y = x + 8
- M1: x = 5y - 8
- A1: f(x) = 5x - 8
Answer: 5x - 8[3 marks] - 5
Question 5. The region R is defined by the inequalities
x ≥ 1 y ≥ 2 x + y ≤ 5
Write down the coordinates of every point in R that has integer coordinates.Sketching Linear Inequalities▶ Show worked answerHide worked answer
- B3: (1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (3, 2) and no others (B2 for four or five correct with none wrong, B1 for two or three correct)
Answer: (1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (3, 2)[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 053
- 1
Question 1. A rope 16 m long is tied from the top of a pole to the ground.
[2 marks]
The rope makes an angle of 60^° with the ground.
Work out the horizontal distance from the foot of the pole to the point where the rope meets the ground.Applied Exact Trig Values Questions▶ Show worked answerHide worked answer
- M1: 16 × cos 60^°
- A1: 8
Answer: 8 - 2
Question 2. Shape A is drawn on the grid.
[2 marks]
Enlarge shape A by scale factor -2 with centre of enlargement (0, 0).
Label the image B.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- B2: image B drawn with vertices (−2, −2), (−6, −2), (−2, −4) (one mark for the correct image on the wrong side of the centre, or for two correct vertices)
Answer: Image B has vertices (−2, −2), (−6, −2), (−2, −4) - 3
Question 3. A square photograph has an area of 440 cm²
[3 marks]
The photograph is to be put into a square frame.
The inside of the frame is a square of side 22 cm.
Will the photograph fit inside the frame?
Use square numbers to give a reason for your answer.Estimating Roots▶ Show worked answerHide worked answer
- M1: 22² = 484
- M1: 440 < 484, so the side of the photograph is less than 22 cm
- C1: the photograph will fit inside the frame
Answer: Yes - 4
Question 4. f⁻¹(x) = dfracx + 85
[3 marks]
Find f(x)Inverse Functions▶ Show worked answerHide worked answer
- M1: y = dfracx + 85, so 5y = x + 8
- M1: x = 5y - 8
- A1: f(x) = 5x - 8
Answer: 5x - 8 - 5
Question 5. The region R is defined by the inequalities
[3 marks]
x ≥ 1 y ≥ 2 x + y ≤ 5
Write down the coordinates of every point in R that has integer coordinates.Sketching Linear Inequalities▶ Show worked answerHide worked answer
- B3: (1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (3, 2) and no others (B2 for four or five correct with none wrong, B1 for two or three correct)
Answer: (1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (3, 2)
Mixed Topic Worksheet Grades 6/7: Day 053
- 1
Question 1. A rope 16 m long is tied from the top of a pole to the ground.
The rope makes an angle of 60^° with the ground.
Work out the horizontal distance from the foot of the pole to the point where the rope meets the ground.Applied Exact Trig Values Questions▶ Show worked answerHide worked answer
- M1: 16 × cos 60^°
- A1: 8
Answer: 8[2 marks] - 2
Question 2. Shape A is drawn on the grid.
Enlarge shape A by scale factor -2 with centre of enlargement (0, 0).
Label the image B.Enlargements with Negative Integer Scale Factors▶ Show worked answerHide worked answer
- B2: image B drawn with vertices (−2, −2), (−6, −2), (−2, −4) (one mark for the correct image on the wrong side of the centre, or for two correct vertices)
Answer: Image B has vertices (−2, −2), (−6, −2), (−2, −4)[2 marks] - 3
Question 3. A square photograph has an area of 440 cm²
The photograph is to be put into a square frame.
The inside of the frame is a square of side 22 cm.
Will the photograph fit inside the frame?
Use square numbers to give a reason for your answer.Estimating Roots▶ Show worked answerHide worked answer
- M1: 22² = 484
- M1: 440 < 484, so the side of the photograph is less than 22 cm
- C1: the photograph will fit inside the frame
Answer: Yes[3 marks] - 4
Question 4. f⁻¹(x) = dfracx + 85
Find f(x)Inverse Functions▶ Show worked answerHide worked answer
- M1: y = dfracx + 85, so 5y = x + 8
- M1: x = 5y - 8
- A1: f(x) = 5x - 8
Answer: 5x - 8[3 marks] - 5
Question 5. The region R is defined by the inequalities
x ≥ 1 y ≥ 2 x + y ≤ 5
Write down the coordinates of every point in R that has integer coordinates.Sketching Linear Inequalities▶ Show worked answerHide worked answer
- B3: (1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (3, 2) and no others (B2 for four or five correct with none wrong, B1 for two or three correct)
Answer: (1, 2), (1, 3), (1, 4), (2, 2), (2, 3), (3, 2)[3 marks]