Mixed Topic Worksheet Grades 8/9: Day 091
- 1
Question 1. In a histogram, the bar for the class 14 < m ≤ k has a frequency density of 2.5.
The frequency of this class is 30.
Work out the value of k.Sketching Histograms▶ Show worked answerHide worked answer
- M1: 30 ÷ 2.5
- A1: 26
Answer: 26[2 marks] - 2
Question 2. The point (3, -2) lies on y = f(x). Write down a point that lies on y = f(x - 4) + 5.
Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: shifts 4 right and 5 up
- A1: (7, 3)
Answer: (7, 3)[2 marks] - 3
Question 3. Simplify fully dfrac3x²+12xx²+x-12
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: 3x(x+4)
- M1: (x+4)(x-3)
- A1: dfrac3xx-3
Answer: dfrac3xx-3[3 marks] - 4
Question 4. y is directly proportional to the cube root of x.
y = 6 when x = 27.
Find the value of x when y = 10.Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y = ksqrt[3]x, 6 = 3k so k = 2
- M1: 10 = 2sqrt[3]x, so sqrt[3]x = 5
- A1: x = 125
Answer: 125[3 marks] - 5
Question 5. The equation x² + kx + (k + 3) = 0 has two distinct real roots.
Work out the possible values of kSolving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: k² - 4(k + 3) > 0
- M1: k²-4k-12 > 0
- M1: (k - 6)(k + 2) > 0
- A1: k < -2 or k > 6
Answer: k < -2 or k > 6[4 marks]
Mixed Topic Worksheet Grades 8/9: Day 091
- 1
Question 1. In a histogram, the bar for the class 14 < m ≤ k has a frequency density of 2.5.
[2 marks]
The frequency of this class is 30.
Work out the value of k.Sketching Histograms▶ Show worked answerHide worked answer
- M1: 30 ÷ 2.5
- A1: 26
Answer: 26 - 2
Question 2. The point (3, -2) lies on y = f(x). Write down a point that lies on y = f(x - 4) + 5.
[2 marks]Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: shifts 4 right and 5 up
- A1: (7, 3)
Answer: (7, 3) - 3
Question 3. Simplify fully dfrac3x²+12xx²+x-12
[3 marks]Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: 3x(x+4)
- M1: (x+4)(x-3)
- A1: dfrac3xx-3
Answer: dfrac3xx-3 - 4
Question 4. y is directly proportional to the cube root of x.
[3 marks]
y = 6 when x = 27.
Find the value of x when y = 10.Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y = ksqrt[3]x, 6 = 3k so k = 2
- M1: 10 = 2sqrt[3]x, so sqrt[3]x = 5
- A1: x = 125
Answer: 125 - 5
Question 5. The equation x² + kx + (k + 3) = 0 has two distinct real roots.
[4 marks]
Work out the possible values of kSolving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: k² - 4(k + 3) > 0
- M1: k²-4k-12 > 0
- M1: (k - 6)(k + 2) > 0
- A1: k < -2 or k > 6
Answer: k < -2 or k > 6
Mixed Topic Worksheet Grades 8/9: Day 091
- 1
Question 1. In a histogram, the bar for the class 14 < m ≤ k has a frequency density of 2.5.
The frequency of this class is 30.
Work out the value of k.Sketching Histograms▶ Show worked answerHide worked answer
- M1: 30 ÷ 2.5
- A1: 26
Answer: 26[2 marks] - 2
Question 2. The point (3, -2) lies on y = f(x). Write down a point that lies on y = f(x - 4) + 5.
Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- M1: shifts 4 right and 5 up
- A1: (7, 3)
Answer: (7, 3)[2 marks] - 3
Question 3. Simplify fully dfrac3x²+12xx²+x-12
Algebraic Fractions Involving Factorising▶ Show worked answerHide worked answer
- M1: 3x(x+4)
- M1: (x+4)(x-3)
- A1: dfrac3xx-3
Answer: dfrac3xx-3[3 marks] - 4
Question 4. y is directly proportional to the cube root of x.
y = 6 when x = 27.
Find the value of x when y = 10.Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y = ksqrt[3]x, 6 = 3k so k = 2
- M1: 10 = 2sqrt[3]x, so sqrt[3]x = 5
- A1: x = 125
Answer: 125[3 marks] - 5
Question 5. The equation x² + kx + (k + 3) = 0 has two distinct real roots.
Work out the possible values of kSolving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: k² - 4(k + 3) > 0
- M1: k²-4k-12 > 0
- M1: (k - 6)(k + 2) > 0
- A1: k < -2 or k > 6
Answer: k < -2 or k > 6[4 marks]