Mixed Topic Worksheet Grades 8/9: Day 071
- 1
Question 1. Here is the graph of y = cos(bx) for 0^° ≤ x ≤ 360^°
(a) Write down b [1]
(b) Write down the period [1]Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- (a) B1: b = 4
- (b) B1: 90^°
Answer: (a) b = 4; (b) 90[2 marks] - 2
Question 2. Describe fully the single transformation that maps the graph of y = 3x onto the graph of y = 3⁻x
Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- B1: reflection
- B1: in the y-axis
Answer: Reflection in the y-axis[2 marks] - 3
Question 3. k is the smallest positive integer such that √540k is an integer.
Work out the value of k.Simplifying Surds▶ Show worked answerHide worked answer
- M1: 540 = 2² × 3³ × 5
- M1: k must supply the missing 3 and 5
- A1: k = 15
Answer: 15[3 marks] - 4
Question 4. On a histogram, 1 cm² of area represents 4 people. A bar is 2.5 cm wide and 3 cm tall. How many people does it represent?
Sketching Histograms▶ Show worked answerHide worked answer
- M1: area =2.5×3=7.5
- M1: 7.5×4
- A1: 30
Answer: 30 people[3 marks] - 5
Question 5. The number line shows the solution of x²+bx+c ≥ 0.
(a) Work out the value of b. [2]
(b) Work out the value of c. [1]Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- (a) M1: (x+3)(x-7) = x²-4x-21
- (a) A1: b = -4
- (b) B1: c = -21
Answer: (a) b = -4; (b) c = -21[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 071
- 1
Question 1. Here is the graph of y = cos(bx) for 0^° ≤ x ≤ 360^°
[2 marks]
(a) Write down b [1]
(b) Write down the period [1]Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- (a) B1: b = 4
- (b) B1: 90^°
Answer: (a) b = 4; (b) 90 - 2
Question 2. Describe fully the single transformation that maps the graph of y = 3x onto the graph of y = 3⁻x
[2 marks]Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- B1: reflection
- B1: in the y-axis
Answer: Reflection in the y-axis - 3
Question 3. k is the smallest positive integer such that √540k is an integer.
[3 marks]
Work out the value of k.Simplifying Surds▶ Show worked answerHide worked answer
- M1: 540 = 2² × 3³ × 5
- M1: k must supply the missing 3 and 5
- A1: k = 15
Answer: 15 - 4
Question 4. On a histogram, 1 cm² of area represents 4 people. A bar is 2.5 cm wide and 3 cm tall. How many people does it represent?
[3 marks]Sketching Histograms▶ Show worked answerHide worked answer
- M1: area =2.5×3=7.5
- M1: 7.5×4
- A1: 30
Answer: 30 people - 5
Question 5. The number line shows the solution of x²+bx+c ≥ 0.
[3 marks]
(a) Work out the value of b. [2]
(b) Work out the value of c. [1]Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- (a) M1: (x+3)(x-7) = x²-4x-21
- (a) A1: b = -4
- (b) B1: c = -21
Answer: (a) b = -4; (b) c = -21
Mixed Topic Worksheet Grades 8/9: Day 071
- 1
Question 1. Here is the graph of y = cos(bx) for 0^° ≤ x ≤ 360^°
(a) Write down b [1]
(b) Write down the period [1]Transforming Trigonometric Graphs▶ Show worked answerHide worked answer
- (a) B1: b = 4
- (b) B1: 90^°
Answer: (a) b = 4; (b) 90[2 marks] - 2
Question 2. Describe fully the single transformation that maps the graph of y = 3x onto the graph of y = 3⁻x
Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- B1: reflection
- B1: in the y-axis
Answer: Reflection in the y-axis[2 marks] - 3
Question 3. k is the smallest positive integer such that √540k is an integer.
Work out the value of k.Simplifying Surds▶ Show worked answerHide worked answer
- M1: 540 = 2² × 3³ × 5
- M1: k must supply the missing 3 and 5
- A1: k = 15
Answer: 15[3 marks] - 4
Question 4. On a histogram, 1 cm² of area represents 4 people. A bar is 2.5 cm wide and 3 cm tall. How many people does it represent?
Sketching Histograms▶ Show worked answerHide worked answer
- M1: area =2.5×3=7.5
- M1: 7.5×4
- A1: 30
Answer: 30 people[3 marks] - 5
Question 5. The number line shows the solution of x²+bx+c ≥ 0.
(a) Work out the value of b. [2]
(b) Work out the value of c. [1]Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- (a) M1: (x+3)(x-7) = x²-4x-21
- (a) A1: b = -4
- (b) B1: c = -21
Answer: (a) b = -4; (b) c = -21[3 marks]