Mixed Topic Worksheet Grades 8/9: Day 052
- 1
Question 1. y = x² + 3x is reflected in the x-axis. Write down the equation of the image.
Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: y becomes -y
- A1: y = -x² - 3x
Answer: y = -x² - 3x[2 marks] - 2
Question 2. A garden centre has 45 shrubs and 75 herbs. 30 of the shrubs and 20 of the herbs are in flower. A plant in flower is chosen at random. Work out the probability that it is a shrub.
Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: plants in flower = 30 + 20 = 50
- A1: 30/50 = 3/5
Answer: 3/5[2 marks] - 3
Question 3. A cube has a face diagonal of 8 cm. Work out the length of a space diagonal of the cube. Give your answer correct to 3 significant figures.
3D Pythagoras▶ Show worked answerHide worked answer
- M1: edge = 8 ÷ √2 = 4√2
- M1: space diagonal = √3 × 4√2
- A1: 9.80 cm
Answer: 9.80 cm[3 marks] - 4
Question 4. The volume of a cuboid is 40 cm³
Its sides are x cm, (x + 1) cm and (x + 3) cm
So x³ + 4x² + 3x - 40 = 0 has a solution between 2 and 3
Find this solution correct to 1 decimal placeChange of Signs▶ Show worked answerHide worked answer
- M1: f(x) = x³ + 4x² + 3x - 40, test values between 2 and 3
- M1: f(2.25) = -1.609... and f(2.3) = 0.227, sign change
- A1: 2.3
Answer: x = 2.3[3 marks] - 5
Question 5. Rationalise the denominator of dfrac43 - √5 and simplify
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: multiplies by dfrac3+√53+√5
- M1: denominator 9 - 5 = 4
- A1: 3 + √5
Answer: 3 + √5[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 052
- 1
Question 1. y = x² + 3x is reflected in the x-axis. Write down the equation of the image.
[2 marks]Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: y becomes -y
- A1: y = -x² - 3x
Answer: y = -x² - 3x - 2
Question 2. A garden centre has 45 shrubs and 75 herbs. 30 of the shrubs and 20 of the herbs are in flower. A plant in flower is chosen at random. Work out the probability that it is a shrub.
[2 marks]Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: plants in flower = 30 + 20 = 50
- A1: 30/50 = 3/5
Answer: 3/5 - 3
Question 3. A cube has a face diagonal of 8 cm. Work out the length of a space diagonal of the cube. Give your answer correct to 3 significant figures.
[3 marks]3D Pythagoras▶ Show worked answerHide worked answer
- M1: edge = 8 ÷ √2 = 4√2
- M1: space diagonal = √3 × 4√2
- A1: 9.80 cm
Answer: 9.80 cm - 4
Question 4. The volume of a cuboid is 40 cm³
[3 marks]
Its sides are x cm, (x + 1) cm and (x + 3) cm
So x³ + 4x² + 3x - 40 = 0 has a solution between 2 and 3
Find this solution correct to 1 decimal placeChange of Signs▶ Show worked answerHide worked answer
- M1: f(x) = x³ + 4x² + 3x - 40, test values between 2 and 3
- M1: f(2.25) = -1.609... and f(2.3) = 0.227, sign change
- A1: 2.3
Answer: x = 2.3 - 5
Question 5. Rationalise the denominator of dfrac43 - √5 and simplify
[3 marks]Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: multiplies by dfrac3+√53+√5
- M1: denominator 9 - 5 = 4
- A1: 3 + √5
Answer: 3 + √5
Mixed Topic Worksheet Grades 8/9: Day 052
- 1
Question 1. y = x² + 3x is reflected in the x-axis. Write down the equation of the image.
Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- M1: y becomes -y
- A1: y = -x² - 3x
Answer: y = -x² - 3x[2 marks] - 2
Question 2. A garden centre has 45 shrubs and 75 herbs. 30 of the shrubs and 20 of the herbs are in flower. A plant in flower is chosen at random. Work out the probability that it is a shrub.
Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: plants in flower = 30 + 20 = 50
- A1: 30/50 = 3/5
Answer: 3/5[2 marks] - 3
Question 3. A cube has a face diagonal of 8 cm. Work out the length of a space diagonal of the cube. Give your answer correct to 3 significant figures.
3D Pythagoras▶ Show worked answerHide worked answer
- M1: edge = 8 ÷ √2 = 4√2
- M1: space diagonal = √3 × 4√2
- A1: 9.80 cm
Answer: 9.80 cm[3 marks] - 4
Question 4. The volume of a cuboid is 40 cm³
Its sides are x cm, (x + 1) cm and (x + 3) cm
So x³ + 4x² + 3x - 40 = 0 has a solution between 2 and 3
Find this solution correct to 1 decimal placeChange of Signs▶ Show worked answerHide worked answer
- M1: f(x) = x³ + 4x² + 3x - 40, test values between 2 and 3
- M1: f(2.25) = -1.609... and f(2.3) = 0.227, sign change
- A1: 2.3
Answer: x = 2.3[3 marks] - 5
Question 5. Rationalise the denominator of dfrac43 - √5 and simplify
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: multiplies by dfrac3+√53+√5
- M1: denominator 9 - 5 = 4
- A1: 3 + √5
Answer: 3 + √5[3 marks]