Mixed Topic Worksheet Grades 8/9: Day 013
- 1
Question 1. The graph of y = x² - 4x + 7 is translated 3 units to the right.
Find the equation of the translated graph in the form y = x² + bx + cTranslations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: y = (x - 3)² - 4(x - 3) + 7
- M1: x² - 6x + 9 - 4x + 12 + 7
- A1: y = x² - 10x + 28
Answer: y = x² - 10x + 28[3 marks] - 2
Question 2. Solve dfracx² - 9x² + x - 12 = dfrac12
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: dfrac(x - 3)(x + 3)(x + 4)(x - 3) = dfracx + 3x + 4
- M1: 2(x + 3) = x + 4
- A1: x = -2
Answer: x = -2[3 marks] - 3
Question 3. The graph of y = x² - 6x + 11 has a minimum point
Use completing the square to work out the coordinates of the minimum point.Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: y = (x - 3)² - 9 + 11
- A1: y = (x - 3)² + 2
- M1: minimum when (x - 3)² = 0, so x = 3
- A1: (3, 2)
Answer: (3, 2)[4 marks] - 4
Question 4. A car travels 150 m, correct to the nearest 10 m.
It takes 12 seconds, correct to the nearest second.
Work out the lower bound of the average speed of the car.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: lower bound of the distance is 145 m
- M1: upper bound of the time is 12.5 seconds
- M1: 145 ÷ 12.5
- A1: 11.6 m/s
Answer: 11.6 m/s[4 marks] - 5
Question 5. overrightarrowOA = mathbfa and overrightarrowOB = mathbfb
X is the point on AB such that AX : XB = 2 : 1
Find overrightarrowOX in terms of mathbfa and mathbfb.
Give your answer in its simplest form.Vector Ratio Problems▶ Show worked answerHide worked answer
- M1: overrightarrowAB = mathbfb - mathbfa
- M1: overrightarrowOX = mathbfa + dfrac23(mathbfb - mathbfa)
- A1: dfrac13mathbfa + dfrac23mathbfb
Answer: dfrac13mathbfa + dfrac23mathbfb[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 013
- 1
Question 1. The graph of y = x² - 4x + 7 is translated 3 units to the right.
[3 marks]
Find the equation of the translated graph in the form y = x² + bx + cTranslations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: y = (x - 3)² - 4(x - 3) + 7
- M1: x² - 6x + 9 - 4x + 12 + 7
- A1: y = x² - 10x + 28
Answer: y = x² - 10x + 28 - 2
Question 2. Solve dfracx² - 9x² + x - 12 = dfrac12
[3 marks]Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: dfrac(x - 3)(x + 3)(x + 4)(x - 3) = dfracx + 3x + 4
- M1: 2(x + 3) = x + 4
- A1: x = -2
Answer: x = -2 - 3
Question 3. The graph of y = x² - 6x + 11 has a minimum point
[4 marks]
Use completing the square to work out the coordinates of the minimum point.Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: y = (x - 3)² - 9 + 11
- A1: y = (x - 3)² + 2
- M1: minimum when (x - 3)² = 0, so x = 3
- A1: (3, 2)
Answer: (3, 2) - 4
Question 4. A car travels 150 m, correct to the nearest 10 m.
[4 marks]
It takes 12 seconds, correct to the nearest second.
Work out the lower bound of the average speed of the car.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: lower bound of the distance is 145 m
- M1: upper bound of the time is 12.5 seconds
- M1: 145 ÷ 12.5
- A1: 11.6 m/s
Answer: 11.6 m/s - 5
Question 5. overrightarrowOA = mathbfa and overrightarrowOB = mathbfb
[3 marks]
X is the point on AB such that AX : XB = 2 : 1
Find overrightarrowOX in terms of mathbfa and mathbfb.
Give your answer in its simplest form.Vector Ratio Problems▶ Show worked answerHide worked answer
- M1: overrightarrowAB = mathbfb - mathbfa
- M1: overrightarrowOX = mathbfa + dfrac23(mathbfb - mathbfa)
- A1: dfrac13mathbfa + dfrac23mathbfb
Answer: dfrac13mathbfa + dfrac23mathbfb
Mixed Topic Worksheet Grades 8/9: Day 013
- 1
Question 1. The graph of y = x² - 4x + 7 is translated 3 units to the right.
Find the equation of the translated graph in the form y = x² + bx + cTranslations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: y = (x - 3)² - 4(x - 3) + 7
- M1: x² - 6x + 9 - 4x + 12 + 7
- A1: y = x² - 10x + 28
Answer: y = x² - 10x + 28[3 marks] - 2
Question 2. Solve dfracx² - 9x² + x - 12 = dfrac12
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: dfrac(x - 3)(x + 3)(x + 4)(x - 3) = dfracx + 3x + 4
- M1: 2(x + 3) = x + 4
- A1: x = -2
Answer: x = -2[3 marks] - 3
Question 3. The graph of y = x² - 6x + 11 has a minimum point
Use completing the square to work out the coordinates of the minimum point.Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: y = (x - 3)² - 9 + 11
- A1: y = (x - 3)² + 2
- M1: minimum when (x - 3)² = 0, so x = 3
- A1: (3, 2)
Answer: (3, 2)[4 marks] - 4
Question 4. A car travels 150 m, correct to the nearest 10 m.
It takes 12 seconds, correct to the nearest second.
Work out the lower bound of the average speed of the car.Combining Upper & Lower Bounds▶ Show worked answerHide worked answer
- M1: lower bound of the distance is 145 m
- M1: upper bound of the time is 12.5 seconds
- M1: 145 ÷ 12.5
- A1: 11.6 m/s
Answer: 11.6 m/s[4 marks] - 5
Question 5. overrightarrowOA = mathbfa and overrightarrowOB = mathbfb
X is the point on AB such that AX : XB = 2 : 1
Find overrightarrowOX in terms of mathbfa and mathbfb.
Give your answer in its simplest form.Vector Ratio Problems▶ Show worked answerHide worked answer
- M1: overrightarrowAB = mathbfb - mathbfa
- M1: overrightarrowOX = mathbfa + dfrac23(mathbfb - mathbfa)
- A1: dfrac13mathbfa + dfrac23mathbfb
Answer: dfrac13mathbfa + dfrac23mathbfb[3 marks]