Mixed Topic Worksheet Grades 6/7: Day 041
- 1
Question 1. A right-angled triangle has a hypotenuse of length 35 cm.
The angle x in the triangle has sin x = dfrac35.
Work out the length of the side opposite angle x.Fundamentals of SOH, CAH, TOA▶ Show worked answerHide worked answer
- M1: opposite = 35 × 3/5
- A1: 21
Answer: 21 cm[2 marks] - 2
Question 2. A cafe sells 5 types of sandwich and 4 types of drink.
A lunch deal is one sandwich and one drink.
Work out the number of different lunch deals.Calculating Combinations▶ Show worked answerHide worked answer
- M1: 5 × 4
- A1: 20
Answer: 20[2 marks] - 3
Question 3. Every length of a picture frame is increased by 30%.
Work out the percentage increase in the area of the picture frame.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: 1 + dfrac30100
- M1: 1.3² = 1.69
- A1: 69
Answer: 69%[3 marks] - 4
Question 4. A=x: 3<x≤ 8, x is an integer. Work out n(A).
Sets & Inequalities▶ Show worked answerHide worked answer
- M1: A=4,5,6,7,8
- A1: 5
Answer: 5[2 marks] - 5
Question 5. f(x) = x + 7
g(x) = x - 3
Decide whether fg(x) and gf(x) are the same function.
You must show your working.Composite Functions▶ Show worked answerHide worked answer
- M1: fg(x) = (x - 3) + 7
- M1: gf(x) = (x + 7) - 3
- A1: both are x + 4, so they are the same
Answer: Yes, both are x + 4[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 041
- 1
Question 1. A right-angled triangle has a hypotenuse of length 35 cm.
[2 marks]
The angle x in the triangle has sin x = dfrac35.
Work out the length of the side opposite angle x.Fundamentals of SOH, CAH, TOA▶ Show worked answerHide worked answer
- M1: opposite = 35 × 3/5
- A1: 21
Answer: 21 cm - 2
Question 2. A cafe sells 5 types of sandwich and 4 types of drink.
[2 marks]
A lunch deal is one sandwich and one drink.
Work out the number of different lunch deals.Calculating Combinations▶ Show worked answerHide worked answer
- M1: 5 × 4
- A1: 20
Answer: 20 - 3
Question 3. Every length of a picture frame is increased by 30%.
[3 marks]
Work out the percentage increase in the area of the picture frame.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: 1 + dfrac30100
- M1: 1.3² = 1.69
- A1: 69
Answer: 69% - 4
Question 4. A=x: 3<x≤ 8, x is an integer. Work out n(A).
[2 marks]Sets & Inequalities▶ Show worked answerHide worked answer
- M1: A=4,5,6,7,8
- A1: 5
Answer: 5 - 5
Question 5. f(x) = x + 7
[3 marks]
g(x) = x - 3
Decide whether fg(x) and gf(x) are the same function.
You must show your working.Composite Functions▶ Show worked answerHide worked answer
- M1: fg(x) = (x - 3) + 7
- M1: gf(x) = (x + 7) - 3
- A1: both are x + 4, so they are the same
Answer: Yes, both are x + 4
Mixed Topic Worksheet Grades 6/7: Day 041
- 1
Question 1. A right-angled triangle has a hypotenuse of length 35 cm.
The angle x in the triangle has sin x = dfrac35.
Work out the length of the side opposite angle x.Fundamentals of SOH, CAH, TOA▶ Show worked answerHide worked answer
- M1: opposite = 35 × 3/5
- A1: 21
Answer: 21 cm[2 marks] - 2
Question 2. A cafe sells 5 types of sandwich and 4 types of drink.
A lunch deal is one sandwich and one drink.
Work out the number of different lunch deals.Calculating Combinations▶ Show worked answerHide worked answer
- M1: 5 × 4
- A1: 20
Answer: 20[2 marks] - 3
Question 3. Every length of a picture frame is increased by 30%.
Work out the percentage increase in the area of the picture frame.Similar Areas & Volumes▶ Show worked answerHide worked answer
- M1: 1 + dfrac30100
- M1: 1.3² = 1.69
- A1: 69
Answer: 69%[3 marks] - 4
Question 4. A=x: 3<x≤ 8, x is an integer. Work out n(A).
Sets & Inequalities▶ Show worked answerHide worked answer
- M1: A=4,5,6,7,8
- A1: 5
Answer: 5[2 marks] - 5
Question 5. f(x) = x + 7
g(x) = x - 3
Decide whether fg(x) and gf(x) are the same function.
You must show your working.Composite Functions▶ Show worked answerHide worked answer
- M1: fg(x) = (x - 3) + 7
- M1: gf(x) = (x + 7) - 3
- A1: both are x + 4, so they are the same
Answer: Yes, both are x + 4[3 marks]