Mixed Topic Worksheet Grades 8/9: Day 077
- 1
Question 1. Frequency densities: 0 < x ≤ 4 is 5, 4 < x ≤ 10 is 3, 10 < x ≤ 20 is 1. Work out an estimate for the lower quartile.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: frequencies 20, 18, 10; the 12th value lies in the first class
- A1: 12/20 × 4 = 2.4
Answer: 2.4[2 marks] - 2
Question 2. y = x² is translated by the vector beginpmatrix -3 2 endpmatrix. Write down the equation of the new graph.
Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: x replaced by x + 3
- A1: y = (x + 3)² + 2
Answer: y = (x + 3)² + 2[2 marks] - 3
Question 3. A and B are on a circle, centre O.
TAS is the tangent at A.
Angle OBA = 25^°
Work out angle TAB.
Give reasons for each stage.Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: 90 - 25
- A1: angle TAB = 65^°
- C1: OAB is isosceles (radii); the tangent meets the radius at 90^°
Answer: 65^°[3 marks] - 4
Question 4. Solve
x + y = 6
x² - y = 24Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: x² - (6 - x) = 24 so x² + x - 30 = 0
- M1: (x + 6)(x - 5) = 0
- A2: x = 5, y = 1 and x = -6, y = 12
Answer: x = 5, y = 1 or x = -6, y = 12[4 marks] - 5
Question 5. Rationalise the denominator of dfrac5√6 - 1 giving your answer in its simplest form.
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac5(√6 + 1)(√6 - 1)(√6 + 1)
- A1: √6 + 1
Answer: √6 + 1[2 marks]
Mixed Topic Worksheet Grades 8/9: Day 077
- 1
Question 1. Frequency densities: 0 < x ≤ 4 is 5, 4 < x ≤ 10 is 3, 10 < x ≤ 20 is 1. Work out an estimate for the lower quartile.
[2 marks]Median from a Histogram▶ Show worked answerHide worked answer
- M1: frequencies 20, 18, 10; the 12th value lies in the first class
- A1: 12/20 × 4 = 2.4
Answer: 2.4 - 2
Question 2. y = x² is translated by the vector beginpmatrix -3 2 endpmatrix. Write down the equation of the new graph.
[2 marks]Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: x replaced by x + 3
- A1: y = (x + 3)² + 2
Answer: y = (x + 3)² + 2 - 3
Question 3. A and B are on a circle, centre O.
[3 marks]
TAS is the tangent at A.
Angle OBA = 25^°
Work out angle TAB.
Give reasons for each stage.Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: 90 - 25
- A1: angle TAB = 65^°
- C1: OAB is isosceles (radii); the tangent meets the radius at 90^°
Answer: 65^° - 4
Question 4. Solve
[4 marks]
x + y = 6
x² - y = 24Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: x² - (6 - x) = 24 so x² + x - 30 = 0
- M1: (x + 6)(x - 5) = 0
- A2: x = 5, y = 1 and x = -6, y = 12
Answer: x = 5, y = 1 or x = -6, y = 12 - 5
Question 5. Rationalise the denominator of dfrac5√6 - 1 giving your answer in its simplest form.
[2 marks]Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac5(√6 + 1)(√6 - 1)(√6 + 1)
- A1: √6 + 1
Answer: √6 + 1
Mixed Topic Worksheet Grades 8/9: Day 077
- 1
Question 1. Frequency densities: 0 < x ≤ 4 is 5, 4 < x ≤ 10 is 3, 10 < x ≤ 20 is 1. Work out an estimate for the lower quartile.
Median from a Histogram▶ Show worked answerHide worked answer
- M1: frequencies 20, 18, 10; the 12th value lies in the first class
- A1: 12/20 × 4 = 2.4
Answer: 2.4[2 marks] - 2
Question 2. y = x² is translated by the vector beginpmatrix -3 2 endpmatrix. Write down the equation of the new graph.
Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: x replaced by x + 3
- A1: y = (x + 3)² + 2
Answer: y = (x + 3)² + 2[2 marks] - 3
Question 3. A and B are on a circle, centre O.
TAS is the tangent at A.
Angle OBA = 25^°
Work out angle TAB.
Give reasons for each stage.Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: 90 - 25
- A1: angle TAB = 65^°
- C1: OAB is isosceles (radii); the tangent meets the radius at 90^°
Answer: 65^°[3 marks] - 4
Question 4. Solve
x + y = 6
x² - y = 24Solving Quadratic Simultaneous Equations▶ Show worked answerHide worked answer
- M1: x² - (6 - x) = 24 so x² + x - 30 = 0
- M1: (x + 6)(x - 5) = 0
- A2: x = 5, y = 1 and x = -6, y = 12
Answer: x = 5, y = 1 or x = -6, y = 12[4 marks] - 5
Question 5. Rationalise the denominator of dfrac5√6 - 1 giving your answer in its simplest form.
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac5(√6 + 1)(√6 - 1)(√6 + 1)
- A1: √6 + 1
Answer: √6 + 1[2 marks]