Mixed Topic Worksheet Grades 8/9: Day 041
- 1
Question 1. sin 20^° = k. Write sin 200^° - sin 160^° in terms of k.
Calculating Values of Trig Functions Using Graphs▶ Show worked answerHide worked answer
- M1: sin 200^° = -k and sin 160^° = k
- A1: -k - k = -2k
Answer: -2k[2 marks] - 2
Question 2. a is a positive integer.
dfracx²+ax-21x²-9 simplifies to dfracx+7x+3.
Work out the value of a.Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: x²-9=(x-3)(x+3)
- M1: the top is (x+7)(x-3)
- A1: a = 4
Answer: a = 4[3 marks] - 3
Question 3. On a histogram, 1 cm of height represents a frequency density of 0.5. The class 20 < x ≤ 30 has a frequency of 18. Work out the height of its bar.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency density =18÷10=1.8
- M1: height =1.8÷0.5
- A1: 3.6 cm
Answer: 3.6 cm[3 marks] - 4
Question 4. A ball is thrown upwards. Its height, h metres, after t seconds is given by h = 12t - 2t² for 0 ≤ t ≤ 6
Work out the values of t for which the ball is more than 10 metres above the ground.Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: forms 12t - 2t² > 10 and rearranges to t² - 6t + 5 < 0
- M1: factorises to (t - 1)(t - 5)
- M1: critical values t = 1 and t = 5, with the expression negative between them
- A1: 1 < t < 5
Answer: 1 < t < 5[4 marks] - 5
Question 5. overrightarrowOA = 2mathbfa + mathbfb and overrightarrowOB = 6mathbfa + 3mathbfb. Show that O, A and B lie on a straight line.
Fundamentals of Vector Problems▶ Show worked answerHide worked answer
- M1: overrightarrowOB = 3(2mathbfa + mathbfb) = 3overrightarrowOA
- C1: parallel vectors with a common point O, so O, A, B are in a line
Answer: overrightarrowOB = 3overrightarrowOA, so the vectors are parallel and share O[2 marks]
Mixed Topic Worksheet Grades 8/9: Day 041
- 1
Question 1. sin 20^° = k. Write sin 200^° - sin 160^° in terms of k.
[2 marks]Calculating Values of Trig Functions Using Graphs▶ Show worked answerHide worked answer
- M1: sin 200^° = -k and sin 160^° = k
- A1: -k - k = -2k
Answer: -2k - 2
Question 2. a is a positive integer.
[3 marks]
dfracx²+ax-21x²-9 simplifies to dfracx+7x+3.
Work out the value of a.Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: x²-9=(x-3)(x+3)
- M1: the top is (x+7)(x-3)
- A1: a = 4
Answer: a = 4 - 3
Question 3. On a histogram, 1 cm of height represents a frequency density of 0.5. The class 20 < x ≤ 30 has a frequency of 18. Work out the height of its bar.
[3 marks]Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency density =18÷10=1.8
- M1: height =1.8÷0.5
- A1: 3.6 cm
Answer: 3.6 cm - 4
Question 4. A ball is thrown upwards. Its height, h metres, after t seconds is given by h = 12t - 2t² for 0 ≤ t ≤ 6
[4 marks]
Work out the values of t for which the ball is more than 10 metres above the ground.Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: forms 12t - 2t² > 10 and rearranges to t² - 6t + 5 < 0
- M1: factorises to (t - 1)(t - 5)
- M1: critical values t = 1 and t = 5, with the expression negative between them
- A1: 1 < t < 5
Answer: 1 < t < 5 - 5
Question 5. overrightarrowOA = 2mathbfa + mathbfb and overrightarrowOB = 6mathbfa + 3mathbfb. Show that O, A and B lie on a straight line.
[2 marks]Fundamentals of Vector Problems▶ Show worked answerHide worked answer
- M1: overrightarrowOB = 3(2mathbfa + mathbfb) = 3overrightarrowOA
- C1: parallel vectors with a common point O, so O, A, B are in a line
Answer: overrightarrowOB = 3overrightarrowOA, so the vectors are parallel and share O
Mixed Topic Worksheet Grades 8/9: Day 041
- 1
Question 1. sin 20^° = k. Write sin 200^° - sin 160^° in terms of k.
Calculating Values of Trig Functions Using Graphs▶ Show worked answerHide worked answer
- M1: sin 200^° = -k and sin 160^° = k
- A1: -k - k = -2k
Answer: -2k[2 marks] - 2
Question 2. a is a positive integer.
dfracx²+ax-21x²-9 simplifies to dfracx+7x+3.
Work out the value of a.Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: x²-9=(x-3)(x+3)
- M1: the top is (x+7)(x-3)
- A1: a = 4
Answer: a = 4[3 marks] - 3
Question 3. On a histogram, 1 cm of height represents a frequency density of 0.5. The class 20 < x ≤ 30 has a frequency of 18. Work out the height of its bar.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency density =18÷10=1.8
- M1: height =1.8÷0.5
- A1: 3.6 cm
Answer: 3.6 cm[3 marks] - 4
Question 4. A ball is thrown upwards. Its height, h metres, after t seconds is given by h = 12t - 2t² for 0 ≤ t ≤ 6
Work out the values of t for which the ball is more than 10 metres above the ground.Sketching Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: forms 12t - 2t² > 10 and rearranges to t² - 6t + 5 < 0
- M1: factorises to (t - 1)(t - 5)
- M1: critical values t = 1 and t = 5, with the expression negative between them
- A1: 1 < t < 5
Answer: 1 < t < 5[4 marks] - 5
Question 5. overrightarrowOA = 2mathbfa + mathbfb and overrightarrowOB = 6mathbfa + 3mathbfb. Show that O, A and B lie on a straight line.
Fundamentals of Vector Problems▶ Show worked answerHide worked answer
- M1: overrightarrowOB = 3(2mathbfa + mathbfb) = 3overrightarrowOA
- C1: parallel vectors with a common point O, so O, A, B are in a line
Answer: overrightarrowOB = 3overrightarrowOA, so the vectors are parallel and share O[2 marks]