Mixed Topic Worksheet Grades 8/9: Day 014
- 1
Question 1. The curve y = x² + bx + c has its minimum point at (-3, -7)
Work out the value of b and the value of cSolving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: y = (x + 3)² - 7
- M1: x² + 6x + 9 - 7
- A1: b = 6 and c = 2
Answer: b = 6, c = 2[3 marks] - 2
Question 2. A cuboid has a rectangular base 12 cm by 5 cm. The angle between a space diagonal and the base is 38°. Work out the height of the cuboid. Give your answer correct to 3 significant figures.
3D Trigonometry▶ Show worked answerHide worked answer
- M1: base diagonal = √12² + 5² = 13
- M1: h = 13tan 38°
- A1: 10.2 cm
Answer: 10.2 cm[3 marks] - 3
Question 3. Show that the equation x³ + 3x - 7 = 0 has a solution between x = 1.4 and x = 1.5
Change of Signs▶ Show worked answerHide worked answer
- M1: 1.4³ + 3(1.4) - 7 = -0.056
- M1: 1.5³ + 3(1.5) - 7 = 0.875
- A1: there is a change of sign, so there is a solution between x = 1.4 and x = 1.5
Answer: -0.056 < 0 and 0.875 > 0: a change of sign, so a solution lies between 1.4 and 1.5[3 marks] - 4
Question 4. Here is information about the times, t minutes, that 80 people waited.
0 < t ≤ 5: 12 people quad 5 < t ≤ 15: 30 people
15 < t ≤ 20: 18 people quad 20 < t ≤ 40: 20 people
Work out the frequency density for each class.Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency divided by class width for at least one class
- A1: two correct
- A1: three correct
- A1: 2.4, 3, 3.6, 1
Answer: 2.4, 3, 3.6, 1[4 marks] - 5
Question 5. Find the value of dfrac3 + 2√23 - 2√2 + dfrac3 - 2√23 + 2√2, giving your answer as an integer.
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac(3 + 2√2)² + (3 - 2√2)²(3 - 2√2)(3 + 2√2)
- M1: dfrac(17 + 12√2) + (17 - 12√2)1
- A1: 34
Answer: 34[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 014
- 1
Question 1. The curve y = x² + bx + c has its minimum point at (-3, -7)
[3 marks]
Work out the value of b and the value of cSolving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: y = (x + 3)² - 7
- M1: x² + 6x + 9 - 7
- A1: b = 6 and c = 2
Answer: b = 6, c = 2 - 2
Question 2. A cuboid has a rectangular base 12 cm by 5 cm. The angle between a space diagonal and the base is 38°. Work out the height of the cuboid. Give your answer correct to 3 significant figures.
[3 marks]3D Trigonometry▶ Show worked answerHide worked answer
- M1: base diagonal = √12² + 5² = 13
- M1: h = 13tan 38°
- A1: 10.2 cm
Answer: 10.2 cm - 3
Question 3. Show that the equation x³ + 3x - 7 = 0 has a solution between x = 1.4 and x = 1.5
[3 marks]Change of Signs▶ Show worked answerHide worked answer
- M1: 1.4³ + 3(1.4) - 7 = -0.056
- M1: 1.5³ + 3(1.5) - 7 = 0.875
- A1: there is a change of sign, so there is a solution between x = 1.4 and x = 1.5
Answer: -0.056 < 0 and 0.875 > 0: a change of sign, so a solution lies between 1.4 and 1.5 - 4
Question 4. Here is information about the times, t minutes, that 80 people waited.
[4 marks]
0 < t ≤ 5: 12 people quad 5 < t ≤ 15: 30 people
15 < t ≤ 20: 18 people quad 20 < t ≤ 40: 20 people
Work out the frequency density for each class.Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency divided by class width for at least one class
- A1: two correct
- A1: three correct
- A1: 2.4, 3, 3.6, 1
Answer: 2.4, 3, 3.6, 1 - 5
Question 5. Find the value of dfrac3 + 2√23 - 2√2 + dfrac3 - 2√23 + 2√2, giving your answer as an integer.
[3 marks]Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac(3 + 2√2)² + (3 - 2√2)²(3 - 2√2)(3 + 2√2)
- M1: dfrac(17 + 12√2) + (17 - 12√2)1
- A1: 34
Answer: 34
Mixed Topic Worksheet Grades 8/9: Day 014
- 1
Question 1. The curve y = x² + bx + c has its minimum point at (-3, -7)
Work out the value of b and the value of cSolving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: y = (x + 3)² - 7
- M1: x² + 6x + 9 - 7
- A1: b = 6 and c = 2
Answer: b = 6, c = 2[3 marks] - 2
Question 2. A cuboid has a rectangular base 12 cm by 5 cm. The angle between a space diagonal and the base is 38°. Work out the height of the cuboid. Give your answer correct to 3 significant figures.
3D Trigonometry▶ Show worked answerHide worked answer
- M1: base diagonal = √12² + 5² = 13
- M1: h = 13tan 38°
- A1: 10.2 cm
Answer: 10.2 cm[3 marks] - 3
Question 3. Show that the equation x³ + 3x - 7 = 0 has a solution between x = 1.4 and x = 1.5
Change of Signs▶ Show worked answerHide worked answer
- M1: 1.4³ + 3(1.4) - 7 = -0.056
- M1: 1.5³ + 3(1.5) - 7 = 0.875
- A1: there is a change of sign, so there is a solution between x = 1.4 and x = 1.5
Answer: -0.056 < 0 and 0.875 > 0: a change of sign, so a solution lies between 1.4 and 1.5[3 marks] - 4
Question 4. Here is information about the times, t minutes, that 80 people waited.
0 < t ≤ 5: 12 people quad 5 < t ≤ 15: 30 people
15 < t ≤ 20: 18 people quad 20 < t ≤ 40: 20 people
Work out the frequency density for each class.Sketching Histograms▶ Show worked answerHide worked answer
- M1: frequency divided by class width for at least one class
- A1: two correct
- A1: three correct
- A1: 2.4, 3, 3.6, 1
Answer: 2.4, 3, 3.6, 1[4 marks] - 5
Question 5. Find the value of dfrac3 + 2√23 - 2√2 + dfrac3 - 2√23 + 2√2, giving your answer as an integer.
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac(3 + 2√2)² + (3 - 2√2)²(3 - 2√2)(3 + 2√2)
- M1: dfrac(17 + 12√2) + (17 - 12√2)1
- A1: 34
Answer: 34[3 marks]