Mixed Topic Worksheet Grades 8/9: Day 081
- 1
Question 1. Dan sketches the graph of y = cos x for 0^° ≤ x ≤ 360^°. Here is his sketch. Find Dan's mistake.
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- M1: finds the value of y when x = 0 for y = cos x, which is 1
- A1: Dan's curve passes through (0, 0), so he has drawn the graph of y = sin x
Answer: The graph of y = cos x passes through (0, 1) but Dan's curve passes through (0, 0) (he has drawn y = sin x)[2 marks] - 2
Question 2. Fatima draws a histogram using frequency as the bar height. The class 0 < t ≤ 10 has frequency 20 and the class 10 < t ≤ 40 has frequency 30. Work out the correct frequency densities and say which bar should be taller.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: 20÷10 and 30÷30
- A1: 2 and 1
- B1: the class 0 < t ≤ 10
Answer: Frequency densities 2 and 1; the bar for 0 < t ≤ 10 should be taller[3 marks] - 3
Question 3. s is directly proportional to t². When t=3, s=45. Work out the value of t when s=80. t>0.
Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: s=kt², 45=9k, k=5
- M1: 80=5t², t²=16
- A1: t=4
Answer: t=4[3 marks] - 4
Question 4. PA and PB are tangents to a circle with centre O, touching it at A and B. Prove that PA = PB.
Circle Theorems▶ Show worked answerHide worked answer
- B1: angles OAP and OBP are both 90°, OA = OB (radii)
- B1: OP is common to both triangles
- C1: triangles OAP and OBP are congruent (RHS), so PA = PB
Answer: Triangles OAP and OBP are congruent (RHS), so PA = PB[3 marks] - 5
Question 5. Solve 6x² - 7x - 20 > 0
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: (2x - 5)(3x + 4) > 0
- M1: critical values x = dfrac52 and x = -dfrac43
- A1: x < -dfrac43 or x > dfrac52
Answer: x < -dfrac43 or x > dfrac52[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 081
- 1
Question 1. Dan sketches the graph of y = cos x for 0^° ≤ x ≤ 360^°. Here is his sketch. Find Dan's mistake.
[2 marks]Sketching sin, cos & tan▶ Show worked answerHide worked answer
- M1: finds the value of y when x = 0 for y = cos x, which is 1
- A1: Dan's curve passes through (0, 0), so he has drawn the graph of y = sin x
Answer: The graph of y = cos x passes through (0, 1) but Dan's curve passes through (0, 0) (he has drawn y = sin x) - 2
Question 2. Fatima draws a histogram using frequency as the bar height. The class 0 < t ≤ 10 has frequency 20 and the class 10 < t ≤ 40 has frequency 30. Work out the correct frequency densities and say which bar should be taller.
[3 marks]Sketching Histograms▶ Show worked answerHide worked answer
- M1: 20÷10 and 30÷30
- A1: 2 and 1
- B1: the class 0 < t ≤ 10
Answer: Frequency densities 2 and 1; the bar for 0 < t ≤ 10 should be taller - 3
Question 3. s is directly proportional to t². When t=3, s=45. Work out the value of t when s=80. t>0.
[3 marks]Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: s=kt², 45=9k, k=5
- M1: 80=5t², t²=16
- A1: t=4
Answer: t=4 - 4
Question 4. PA and PB are tangents to a circle with centre O, touching it at A and B. Prove that PA = PB.
[3 marks]Circle Theorems▶ Show worked answerHide worked answer
- B1: angles OAP and OBP are both 90°, OA = OB (radii)
- B1: OP is common to both triangles
- C1: triangles OAP and OBP are congruent (RHS), so PA = PB
Answer: Triangles OAP and OBP are congruent (RHS), so PA = PB - 5
Question 5. Solve 6x² - 7x - 20 > 0
[3 marks]Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: (2x - 5)(3x + 4) > 0
- M1: critical values x = dfrac52 and x = -dfrac43
- A1: x < -dfrac43 or x > dfrac52
Answer: x < -dfrac43 or x > dfrac52
Mixed Topic Worksheet Grades 8/9: Day 081
- 1
Question 1. Dan sketches the graph of y = cos x for 0^° ≤ x ≤ 360^°. Here is his sketch. Find Dan's mistake.
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- M1: finds the value of y when x = 0 for y = cos x, which is 1
- A1: Dan's curve passes through (0, 0), so he has drawn the graph of y = sin x
Answer: The graph of y = cos x passes through (0, 1) but Dan's curve passes through (0, 0) (he has drawn y = sin x)[2 marks] - 2
Question 2. Fatima draws a histogram using frequency as the bar height. The class 0 < t ≤ 10 has frequency 20 and the class 10 < t ≤ 40 has frequency 30. Work out the correct frequency densities and say which bar should be taller.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: 20÷10 and 30÷30
- A1: 2 and 1
- B1: the class 0 < t ≤ 10
Answer: Frequency densities 2 and 1; the bar for 0 < t ≤ 10 should be taller[3 marks] - 3
Question 3. s is directly proportional to t². When t=3, s=45. Work out the value of t when s=80. t>0.
Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: s=kt², 45=9k, k=5
- M1: 80=5t², t²=16
- A1: t=4
Answer: t=4[3 marks] - 4
Question 4. PA and PB are tangents to a circle with centre O, touching it at A and B. Prove that PA = PB.
Circle Theorems▶ Show worked answerHide worked answer
- B1: angles OAP and OBP are both 90°, OA = OB (radii)
- B1: OP is common to both triangles
- C1: triangles OAP and OBP are congruent (RHS), so PA = PB
Answer: Triangles OAP and OBP are congruent (RHS), so PA = PB[3 marks] - 5
Question 5. Solve 6x² - 7x - 20 > 0
Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: (2x - 5)(3x + 4) > 0
- M1: critical values x = dfrac52 and x = -dfrac43
- A1: x < -dfrac43 or x > dfrac52
Answer: x < -dfrac43 or x > dfrac52[3 marks]