Mixed Topic Worksheet Grades 8/9: Day 089
- 1
Question 1. A class 10 < x ≤ 30 has frequency 50. Work out its frequency density.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: class width = 20
- A1: dfrac5020 = 2.5
Answer: 2.5[2 marks] - 2
Question 2. Simplify √72 + √18 into the form a√2
Simplifying Surds▶ Show worked answerHide worked answer
- M1: 6√2 or 3√2 seen
- A1: 9√2
Answer: 9√2[2 marks] - 3
Question 3. Amir translates the graph of y = f(x) by the vector beginpmatrix 4 -3 endpmatrix and writes the new equation as y = f(x + 4) - 3 Explain his mistake and write down the correct equation
Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- B1: a move of 4 to the right is f(x - 4), not f(x + 4)
- B1: y = f(x - 4) - 3
Answer: y = f(x - 4) - 3[2 marks] - 4
Question 4. y is directly proportional to the square of x and inversely proportional to z.
x is increased by 10%.
z is decreased by 20%.
Work out the percentage change in y.Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y is multiplied by (110 ÷ 100)² ÷ (80 ÷ 100)
- M1: 1.21 ÷ 0.8 = 1.5125
- A1: 51.25% increase
Answer: 51.25% increase[3 marks] - 5
Question 5. The diagram shows a right-angled triangle.
The shorter sides are x cm and (x + 7) cm. The hypotenuse is less than 13 cm.
Work out the possible values of x.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x² + (x + 7)² < 13²
- M1: 2x² + 14x + 49 < 169 so x²+7x-60 < 0
- M1: (x + 12)(x - 5) < 0 so -12 < x < 5
- A1: 0 < x < 5 because x is a length
Answer: 0 < x < 5[4 marks]
Mixed Topic Worksheet Grades 8/9: Day 089
- 1
Question 1. A class 10 < x ≤ 30 has frequency 50. Work out its frequency density.
[2 marks]Sketching Histograms▶ Show worked answerHide worked answer
- M1: class width = 20
- A1: dfrac5020 = 2.5
Answer: 2.5 - 2
Question 2. Simplify √72 + √18 into the form a√2
[2 marks]Simplifying Surds▶ Show worked answerHide worked answer
- M1: 6√2 or 3√2 seen
- A1: 9√2
Answer: 9√2 - 3
Question 3. Amir translates the graph of y = f(x) by the vector beginpmatrix 4 -3 endpmatrix and writes the new equation as y = f(x + 4) - 3 Explain his mistake and write down the correct equation
[2 marks]Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- B1: a move of 4 to the right is f(x - 4), not f(x + 4)
- B1: y = f(x - 4) - 3
Answer: y = f(x - 4) - 3 - 4
Question 4. y is directly proportional to the square of x and inversely proportional to z.
[3 marks]
x is increased by 10%.
z is decreased by 20%.
Work out the percentage change in y.Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y is multiplied by (110 ÷ 100)² ÷ (80 ÷ 100)
- M1: 1.21 ÷ 0.8 = 1.5125
- A1: 51.25% increase
Answer: 51.25% increase - 5
Question 5. The diagram shows a right-angled triangle.
[4 marks]
The shorter sides are x cm and (x + 7) cm. The hypotenuse is less than 13 cm.
Work out the possible values of x.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x² + (x + 7)² < 13²
- M1: 2x² + 14x + 49 < 169 so x²+7x-60 < 0
- M1: (x + 12)(x - 5) < 0 so -12 < x < 5
- A1: 0 < x < 5 because x is a length
Answer: 0 < x < 5
Mixed Topic Worksheet Grades 8/9: Day 089
- 1
Question 1. A class 10 < x ≤ 30 has frequency 50. Work out its frequency density.
Sketching Histograms▶ Show worked answerHide worked answer
- M1: class width = 20
- A1: dfrac5020 = 2.5
Answer: 2.5[2 marks] - 2
Question 2. Simplify √72 + √18 into the form a√2
Simplifying Surds▶ Show worked answerHide worked answer
- M1: 6√2 or 3√2 seen
- A1: 9√2
Answer: 9√2[2 marks] - 3
Question 3. Amir translates the graph of y = f(x) by the vector beginpmatrix 4 -3 endpmatrix and writes the new equation as y = f(x + 4) - 3 Explain his mistake and write down the correct equation
Translations Along the x- & y-Axes▶ Show worked answerHide worked answer
- B1: a move of 4 to the right is f(x - 4), not f(x + 4)
- B1: y = f(x - 4) - 3
Answer: y = f(x - 4) - 3[2 marks] - 4
Question 4. y is directly proportional to the square of x and inversely proportional to z.
x is increased by 10%.
z is decreased by 20%.
Work out the percentage change in y.Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: y is multiplied by (110 ÷ 100)² ÷ (80 ÷ 100)
- M1: 1.21 ÷ 0.8 = 1.5125
- A1: 51.25% increase
Answer: 51.25% increase[3 marks] - 5
Question 5. The diagram shows a right-angled triangle.
The shorter sides are x cm and (x + 7) cm. The hypotenuse is less than 13 cm.
Work out the possible values of x.Solving Quadratic Inequalities▶ Show worked answerHide worked answer
- M1: x² + (x + 7)² < 13²
- M1: 2x² + 14x + 49 < 169 so x²+7x-60 < 0
- M1: (x + 12)(x - 5) < 0 so -12 < x < 5
- A1: 0 < x < 5 because x is a length
Answer: 0 < x < 5[4 marks]