Mixed Topic Worksheet Grades 8/9: Day 038
- 1
Question 1. Work out the number of solutions of tan x = 2 for 0° ≤ x ≤ 540°.
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- M1: tan x repeats every 180°, with one solution in each repeat
- A1: 3
Answer: 3[2 marks] - 2
Question 2. The shorter sides of a right-angled triangle are 12 cm and 6 cm long. Work out the length of the hypotenuse, giving your answer in the form a√b where a and b are integers and b is as small as possible.
Simplifying Surds▶ Show worked answerHide worked answer
- M1: 12² + 6² = 180
- M1: √180 = √36 × 5
- A1: 6√5 cm
Answer: 6√5 cm[3 marks] - 3
Question 3. Of 90 students, 54 study French and the rest study Spanish. 25 of the French students and 15 of the Spanish students are boys. Show that the probability that a boy, chosen at random, studies French is 5/8.
Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: number of boys = 25 + 15 = 40
- M1: 25/40
- A1: = 5/8
Answer: 5/8 (shown)[3 marks] - 4
Question 4. A right-angled triangle has perpendicular sides of length x cm and (x + 4) cm
The area of the triangle is 20 cm²
Use completing the square to work out the value of x
Give your answer correct to 2 decimal places.Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: x(x + 4) = 40 so x² + 4x - 40 = 0
- M1: (x + 2)² - 4 - 40 = 0 so (x + 2)² = 44
- M1: x = -2 + √44 (rejects the negative root)
- A1: 4.63
Answer: 4.63[4 marks] - 5
Question 5. overrightarrowOA=mathbfa and overrightarrowOB=mathbfb. P is the midpoint of AB and overrightarrowOQ=2mathbfa+2mathbfb. Show that O, P and Q lie on a straight line.
Vectors Along a Straight Line▶ Show worked answerHide worked answer
- M1: overrightarrowOP=mathbfa+1/2(mathbfb-mathbfa)=1/2(mathbfa+mathbfb)
- M1: overrightarrowOQ=2(mathbfa+mathbfb)=4overrightarrowOP
- A1: parallel with common point O, so collinear
Answer: overrightarrowOQ=4overrightarrowOP, parallel with a common point O, so collinear[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 038
- 1
Question 1. Work out the number of solutions of tan x = 2 for 0° ≤ x ≤ 540°.
[2 marks]Sketching sin, cos & tan▶ Show worked answerHide worked answer
- M1: tan x repeats every 180°, with one solution in each repeat
- A1: 3
Answer: 3 - 2
Question 2. The shorter sides of a right-angled triangle are 12 cm and 6 cm long. Work out the length of the hypotenuse, giving your answer in the form a√b where a and b are integers and b is as small as possible.
[3 marks]Simplifying Surds▶ Show worked answerHide worked answer
- M1: 12² + 6² = 180
- M1: √180 = √36 × 5
- A1: 6√5 cm
Answer: 6√5 cm - 3
Question 3. Of 90 students, 54 study French and the rest study Spanish. 25 of the French students and 15 of the Spanish students are boys. Show that the probability that a boy, chosen at random, studies French is 5/8.
[3 marks]Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: number of boys = 25 + 15 = 40
- M1: 25/40
- A1: = 5/8
Answer: 5/8 (shown) - 4
Question 4. A right-angled triangle has perpendicular sides of length x cm and (x + 4) cm
[4 marks]
The area of the triangle is 20 cm²
Use completing the square to work out the value of x
Give your answer correct to 2 decimal places.Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: x(x + 4) = 40 so x² + 4x - 40 = 0
- M1: (x + 2)² - 4 - 40 = 0 so (x + 2)² = 44
- M1: x = -2 + √44 (rejects the negative root)
- A1: 4.63
Answer: 4.63 - 5
Question 5. overrightarrowOA=mathbfa and overrightarrowOB=mathbfb. P is the midpoint of AB and overrightarrowOQ=2mathbfa+2mathbfb. Show that O, P and Q lie on a straight line.
[3 marks]Vectors Along a Straight Line▶ Show worked answerHide worked answer
- M1: overrightarrowOP=mathbfa+1/2(mathbfb-mathbfa)=1/2(mathbfa+mathbfb)
- M1: overrightarrowOQ=2(mathbfa+mathbfb)=4overrightarrowOP
- A1: parallel with common point O, so collinear
Answer: overrightarrowOQ=4overrightarrowOP, parallel with a common point O, so collinear
Mixed Topic Worksheet Grades 8/9: Day 038
- 1
Question 1. Work out the number of solutions of tan x = 2 for 0° ≤ x ≤ 540°.
Sketching sin, cos & tan▶ Show worked answerHide worked answer
- M1: tan x repeats every 180°, with one solution in each repeat
- A1: 3
Answer: 3[2 marks] - 2
Question 2. The shorter sides of a right-angled triangle are 12 cm and 6 cm long. Work out the length of the hypotenuse, giving your answer in the form a√b where a and b are integers and b is as small as possible.
Simplifying Surds▶ Show worked answerHide worked answer
- M1: 12² + 6² = 180
- M1: √180 = √36 × 5
- A1: 6√5 cm
Answer: 6√5 cm[3 marks] - 3
Question 3. Of 90 students, 54 study French and the rest study Spanish. 25 of the French students and 15 of the Spanish students are boys. Show that the probability that a boy, chosen at random, studies French is 5/8.
Conditional Probability with Two-Way Tables▶ Show worked answerHide worked answer
- M1: number of boys = 25 + 15 = 40
- M1: 25/40
- A1: = 5/8
Answer: 5/8 (shown)[3 marks] - 4
Question 4. A right-angled triangle has perpendicular sides of length x cm and (x + 4) cm
The area of the triangle is 20 cm²
Use completing the square to work out the value of x
Give your answer correct to 2 decimal places.Solving Quadratics by Completing the Square (a = 1)▶ Show worked answerHide worked answer
- M1: x(x + 4) = 40 so x² + 4x - 40 = 0
- M1: (x + 2)² - 4 - 40 = 0 so (x + 2)² = 44
- M1: x = -2 + √44 (rejects the negative root)
- A1: 4.63
Answer: 4.63[4 marks] - 5
Question 5. overrightarrowOA=mathbfa and overrightarrowOB=mathbfb. P is the midpoint of AB and overrightarrowOQ=2mathbfa+2mathbfb. Show that O, P and Q lie on a straight line.
Vectors Along a Straight Line▶ Show worked answerHide worked answer
- M1: overrightarrowOP=mathbfa+1/2(mathbfb-mathbfa)=1/2(mathbfa+mathbfb)
- M1: overrightarrowOQ=2(mathbfa+mathbfb)=4overrightarrowOP
- A1: parallel with common point O, so collinear
Answer: overrightarrowOQ=4overrightarrowOP, parallel with a common point O, so collinear[3 marks]