Mixed Topic Worksheet Grades 8/9: Day 021
- 1
Question 1. The graph of y = sin(x + a), where 0° < a < 90°, has a maximum point at (60°, 1). Work out the value of a.
Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: 60 + a = 90
- A1: a = 30
Answer: a = 30[2 marks] - 2
Question 2. 100 students each study French or Spanish. The two-way table shows the results.
One of the students who study French is chosen at random.
Work out the probability that this student is a girl.Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: 27 ÷ 45
- A1: 3/5
Answer: dfrac35[2 marks] - 3
Question 3. Pia says (4, 7) and (-4, -7) are the only solutions of
x² + y² = 65 and xy = 28
Is Pia correct? Show working.Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: 7² + 4² = 65
- M1: 7 × 4 = 28
- C1: No, (7, 4) also works
Answer: No, since (7, 4) is also a solution[3 marks] - 4
Question 4. The table shows the frequency densities of a histogram of 100 values. Estimate the upper quartile.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: cumulative frequencies 8, 30, 60, so need 15 of 40
- M1: 40+dfrac1540×20
- A1: 47.5
Answer: 47.5[3 marks] - 5
Question 5. Rationalise the denominator of dfrac3 + √52 + √5 giving your answer in its simplest form.
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac(3 + √5)(2 - √5)(2 + √5)(2 - √5)
- M1: dfrac1 - √5-1
- A1: √5 - 1
Answer: √5 - 1[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 021
- 1
Question 1. The graph of y = sin(x + a), where 0° < a < 90°, has a maximum point at (60°, 1). Work out the value of a.
[2 marks]Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: 60 + a = 90
- A1: a = 30
Answer: a = 30 - 2
Question 2. 100 students each study French or Spanish. The two-way table shows the results.
[2 marks]
One of the students who study French is chosen at random.
Work out the probability that this student is a girl.Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: 27 ÷ 45
- A1: 3/5
Answer: dfrac35 - 3
Question 3. Pia says (4, 7) and (-4, -7) are the only solutions of
[3 marks]
x² + y² = 65 and xy = 28
Is Pia correct? Show working.Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: 7² + 4² = 65
- M1: 7 × 4 = 28
- C1: No, (7, 4) also works
Answer: No, since (7, 4) is also a solution - 4
Question 4. The table shows the frequency densities of a histogram of 100 values. Estimate the upper quartile.
[3 marks]Median from a Histogram▶ Show worked answerHide worked answer
- M1: cumulative frequencies 8, 30, 60, so need 15 of 40
- M1: 40+dfrac1540×20
- A1: 47.5
Answer: 47.5 - 5
Question 5. Rationalise the denominator of dfrac3 + √52 + √5 giving your answer in its simplest form.
[3 marks]Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac(3 + √5)(2 - √5)(2 + √5)(2 - √5)
- M1: dfrac1 - √5-1
- A1: √5 - 1
Answer: √5 - 1
Mixed Topic Worksheet Grades 8/9: Day 021
- 1
Question 1. The graph of y = sin(x + a), where 0° < a < 90°, has a maximum point at (60°, 1). Work out the value of a.
Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- M1: 60 + a = 90
- A1: a = 30
Answer: a = 30[2 marks] - 2
Question 2. 100 students each study French or Spanish. The two-way table shows the results.
One of the students who study French is chosen at random.
Work out the probability that this student is a girl.Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: 27 ÷ 45
- A1: 3/5
Answer: dfrac35[2 marks] - 3
Question 3. Pia says (4, 7) and (-4, -7) are the only solutions of
x² + y² = 65 and xy = 28
Is Pia correct? Show working.Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: 7² + 4² = 65
- M1: 7 × 4 = 28
- C1: No, (7, 4) also works
Answer: No, since (7, 4) is also a solution[3 marks] - 4
Question 4. The table shows the frequency densities of a histogram of 100 values. Estimate the upper quartile.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: cumulative frequencies 8, 30, 60, so need 15 of 40
- M1: 40+dfrac1540×20
- A1: 47.5
Answer: 47.5[3 marks] - 5
Question 5. Rationalise the denominator of dfrac3 + √52 + √5 giving your answer in its simplest form.
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac(3 + √5)(2 - √5)(2 + √5)(2 - √5)
- M1: dfrac1 - √5-1
- A1: √5 - 1
Answer: √5 - 1[3 marks]