Mixed Topic Worksheet Grades 4/5: Day 003
- 1
Question 1. The lengths of two ribbons are in the ratio 14 : 21
Write the length of the shorter ribbon as a fraction of the length of the longer ribbon.
Give your fraction in its lowest terms.Writing Ratios as Fractions▶ Show worked answerHide worked answer
- M1: 14 ÷ 7 and 21 ÷ 7, or a common factor of 7
- A1: dfrac23
Answer: dfrac23[2 marks] - 2
Question 2. Mel says that the point (-2, 3) lies on the line 3x + 2y = 0.
Is Mel correct? You must show your working.Identifying If a Point Is on a Line▶ Show worked answerHide worked answer
- M1: substitute x = -2 and y = 3 into 3x + 2y
- A1: the total is 0, so Mel is correct
Answer: Yes. 3 × (-2) + 2 × 3 = -6 + 6 = 0[2 marks] - 3
Question 3. N = 2² × 3² × 5
Jo says that N is a multiple of 8.
Is Jo correct?
You must give a reason for your answer.Prime Factors & Prime Factorisation▶ Show worked answerHide worked answer
- M1: 8 = 2³ and N has 2² only, or N = 180 and 180 ÷ 8 = 22.5
- A1: No, with the reason
Answer: No, because N has only two factors of 2, and 8 = 2³ needs three[2 marks] - 4
Question 4. Here is a cylinder. Work out the volume of the cylinder.
Give your answer in terms of π.Volume of Cylinders▶ Show worked answerHide worked answer
- M1: π × 3² × 7
- A1: 63π
Answer: 63π[2 marks] - 5
Question 5. The angle of elevation of the top of a tower from a point 12 m from its base is 30^°.
The ground is level.
Work out the height of the tower.
Give your answer in the form a√3, where a is an integer.Applied Exact Trig Values Questions▶ Show worked answerHide worked answer
- M1: tan 30^° = dfrach12
- M1: h = 12 × dfrac√33
- A1: 4√3
Answer: 4√3[3 marks]
Mixed Topic Worksheet Grades 4/5: Day 003
- 1
Question 1. The lengths of two ribbons are in the ratio 14 : 21
[2 marks]
Write the length of the shorter ribbon as a fraction of the length of the longer ribbon.
Give your fraction in its lowest terms.Writing Ratios as Fractions▶ Show worked answerHide worked answer
- M1: 14 ÷ 7 and 21 ÷ 7, or a common factor of 7
- A1: dfrac23
Answer: dfrac23 - 2
Question 2. Mel says that the point (-2, 3) lies on the line 3x + 2y = 0.
[2 marks]
Is Mel correct? You must show your working.Identifying If a Point Is on a Line▶ Show worked answerHide worked answer
- M1: substitute x = -2 and y = 3 into 3x + 2y
- A1: the total is 0, so Mel is correct
Answer: Yes. 3 × (-2) + 2 × 3 = -6 + 6 = 0 - 3
Question 3. N = 2² × 3² × 5
[2 marks]
Jo says that N is a multiple of 8.
Is Jo correct?
You must give a reason for your answer.Prime Factors & Prime Factorisation▶ Show worked answerHide worked answer
- M1: 8 = 2³ and N has 2² only, or N = 180 and 180 ÷ 8 = 22.5
- A1: No, with the reason
Answer: No, because N has only two factors of 2, and 8 = 2³ needs three - 4
Question 4. Here is a cylinder. Work out the volume of the cylinder.
[2 marks]
Give your answer in terms of π.Volume of Cylinders▶ Show worked answerHide worked answer
- M1: π × 3² × 7
- A1: 63π
Answer: 63π - 5
Question 5. The angle of elevation of the top of a tower from a point 12 m from its base is 30^°.
[3 marks]
The ground is level.
Work out the height of the tower.
Give your answer in the form a√3, where a is an integer.Applied Exact Trig Values Questions▶ Show worked answerHide worked answer
- M1: tan 30^° = dfrach12
- M1: h = 12 × dfrac√33
- A1: 4√3
Answer: 4√3
Mixed Topic Worksheet Grades 4/5: Day 003
- 1
Question 1. The lengths of two ribbons are in the ratio 14 : 21
Write the length of the shorter ribbon as a fraction of the length of the longer ribbon.
Give your fraction in its lowest terms.Writing Ratios as Fractions▶ Show worked answerHide worked answer
- M1: 14 ÷ 7 and 21 ÷ 7, or a common factor of 7
- A1: dfrac23
Answer: dfrac23[2 marks] - 2
Question 2. Mel says that the point (-2, 3) lies on the line 3x + 2y = 0.
Is Mel correct? You must show your working.Identifying If a Point Is on a Line▶ Show worked answerHide worked answer
- M1: substitute x = -2 and y = 3 into 3x + 2y
- A1: the total is 0, so Mel is correct
Answer: Yes. 3 × (-2) + 2 × 3 = -6 + 6 = 0[2 marks] - 3
Question 3. N = 2² × 3² × 5
Jo says that N is a multiple of 8.
Is Jo correct?
You must give a reason for your answer.Prime Factors & Prime Factorisation▶ Show worked answerHide worked answer
- M1: 8 = 2³ and N has 2² only, or N = 180 and 180 ÷ 8 = 22.5
- A1: No, with the reason
Answer: No, because N has only two factors of 2, and 8 = 2³ needs three[2 marks] - 4
Question 4. Here is a cylinder. Work out the volume of the cylinder.
Give your answer in terms of π.Volume of Cylinders▶ Show worked answerHide worked answer
- M1: π × 3² × 7
- A1: 63π
Answer: 63π[2 marks] - 5
Question 5. The angle of elevation of the top of a tower from a point 12 m from its base is 30^°.
The ground is level.
Work out the height of the tower.
Give your answer in the form a√3, where a is an integer.Applied Exact Trig Values Questions▶ Show worked answerHide worked answer
- M1: tan 30^° = dfrach12
- M1: h = 12 × dfrac√33
- A1: 4√3
Answer: 4√3[3 marks]