question 3
1. a)
In the diagram Shown above, the Universal set, (U), represents all the students in a class. The set M represents the students who take Music. The Set D represents the students who take Drama. If 24 students take Music, calculate
i. the number of students who take BOTH Music and Drama ii. the number of students who take Drama ONLY. (4 marks)
b) A straight line passes through the point P(‑3, 5) and has a gradient of i. Write down the equation of this line in the form y = mx + c. (5 marks) ii. Show that this line is parallel to the line 2x – 3y = 0. (2 marks)
Total 11 marks
2. a) Given the formula, express u in terms of v, s, and t. (3 marks)
b) On a certain day, 300 customers visited a bakery that sells bread and cakes.
70 customers bought cakes only
80 customers bought neither bread nor cakes
2x customers bought bread only x customers bought both bread and cakes
i. U represents the set of customers visiting the bakery on that day, B represents the set of customers who bought bread, and C represents the set of customers who bought cake. Copy and complete the Venn diagram to illustrate the information. (3 marks) ii. Write an expression in x to represent the TOTAL number of customers who visited the bakery on that day. (2 marks) iii. Calculate the number of customers who bought bread ONLY. (3 marks)
Total 11 marks
3. a) In the quadrilateral KLMN, not drawn to scale, LM = LN = LK, KLM = 140o, and LKN = 40o.
Giving the reason for each step of your answer, calculate the size of i. LNK (2 marks) ii. NLM (2 marks) iii. KNM (2 marks)
b) In a survey of 39 students, it was found that 18 can ride a bicycle,
15 can drive a car, x can ride a bicycle and drive a car,
3x can do neither.
B is the set of students in the survey who can ride a bicycle, and C the set of students who can drive a car.
i. Copy and complete the Venn diagram to represent the information.
In the diagram Shown above, the Universal set, (U), represents all the students in a class. The set M represents the students who take Music. The Set D represents the students who take Drama. If 24 students take Music, calculate
i. the number of students who take BOTH Music and Drama ii. the number of students who take Drama ONLY. (4 marks)
b) A straight line passes through the point P(‑3, 5) and has a gradient of i. Write down the equation of this line in the form y = mx + c. (5 marks) ii. Show that this line is parallel to the line 2x – 3y = 0. (2 marks)
Total 11 marks
2. a) Given the formula, express u in terms of v, s, and t. (3 marks)
b) On a certain day, 300 customers visited a bakery that sells bread and cakes.
70 customers bought cakes only
80 customers bought neither bread nor cakes
2x customers bought bread only x customers bought both bread and cakes
i. U represents the set of customers visiting the bakery on that day, B represents the set of customers who bought bread, and C represents the set of customers who bought cake. Copy and complete the Venn diagram to illustrate the information. (3 marks) ii. Write an expression in x to represent the TOTAL number of customers who visited the bakery on that day. (2 marks) iii. Calculate the number of customers who bought bread ONLY. (3 marks)
Total 11 marks
3. a) In the quadrilateral KLMN, not drawn to scale, LM = LN = LK, KLM = 140o, and LKN = 40o.
Giving the reason for each step of your answer, calculate the size of i. LNK (2 marks) ii. NLM (2 marks) iii. KNM (2 marks)
b) In a survey of 39 students, it was found that 18 can ride a bicycle,
15 can drive a car, x can ride a bicycle and drive a car,
3x can do neither.
B is the set of students in the survey who can ride a bicycle, and C the set of students who can drive a car.
i. Copy and complete the Venn diagram to represent the information.