Mixed Topic Worksheet Grades 4/5: Day 099
- 1
Question 1. Rahul has pens and pencils.
number of pens : number of pencils = 3 : 7
Rahul has 21 pencils.
Work out the number of pens Rahul has.Scaling Up Ratios▶ Show worked answerHide worked answer
- M1: 21 ÷ 7 = 3
- A1: 9
Answer: 9[2 marks] - 2
Question 2. AB is a line of length 10 cm.
Mia wants to construct the perpendicular bisector of AB.
She sets her compasses to 4 cm.
She draws an arc above AB from A and an arc above AB from B.
Her two arcs do not cross.
Explain why her arcs do not cross.Drawing Perpendicular Bisectors▶ Show worked answerHide worked answer
- M1: half of AB is 10 ÷ 2 = 5 cm, which is more than 4 cm
- A1: arcs of 4 cm from A and B cannot reach each other, so the radius must be more than 5 cm
Answer: Her radius of 4 cm is less than half of AB (5 cm), so the arcs cannot meet. She needs a radius greater than 5 cm.[2 marks] - 3
Question 3. Write 64 000 in standard form.
Standard Form Conversions▶ Show worked answerHide worked answer
- M1: Moves the decimal point to give a number between 1 and 10, with the number of places moved as the power of 10
- A1: 6.4 × 10⁴
Answer: 6.4 × 10⁴[2 marks] - 4
Question 4. xi=1, 2, 3, ldots, 10, A=1, 2, 3, 4, 5 and B=2, 4, 6, 8, 10. Work out n(A' cap B).
Fundamentals of Set Notation▶ Show worked answerHide worked answer
- M1: A'=6, 7, 8, 9, 10
- A1: A' cap B=6, 8, 10, so 3
Answer: 3[2 marks] - 5
Question 5. Mo labels crates with numbers.
The first four labels are
3 qquad 8 qquad 13 qquad 18 qquad ldots
The labels carry on in the same way.
Is 102 one of the labels? You must show your working.Deciding If a Term Is in a Sequence▶ Show worked answerHide worked answer
- M1: labels go up by 5 (8 - 3), so the nth term is 5n - 2
- M1: 5n - 2 = 102, so n = 104 ÷ 5 = 20.8
- A1: No, because 20.8 is not a whole number
Answer: No: the nth term is 5n - 2 and 5n - 2 = 102 gives n = 20.8[3 marks]
Mixed Topic Worksheet Grades 4/5: Day 099
- 1
Question 1. Rahul has pens and pencils.
[2 marks]
number of pens : number of pencils = 3 : 7
Rahul has 21 pencils.
Work out the number of pens Rahul has.Scaling Up Ratios▶ Show worked answerHide worked answer
- M1: 21 ÷ 7 = 3
- A1: 9
Answer: 9 - 2
Question 2. AB is a line of length 10 cm.
[2 marks]
Mia wants to construct the perpendicular bisector of AB.
She sets her compasses to 4 cm.
She draws an arc above AB from A and an arc above AB from B.
Her two arcs do not cross.
Explain why her arcs do not cross.Drawing Perpendicular Bisectors▶ Show worked answerHide worked answer
- M1: half of AB is 10 ÷ 2 = 5 cm, which is more than 4 cm
- A1: arcs of 4 cm from A and B cannot reach each other, so the radius must be more than 5 cm
Answer: Her radius of 4 cm is less than half of AB (5 cm), so the arcs cannot meet. She needs a radius greater than 5 cm. - 3
Question 3. Write 64 000 in standard form.
[2 marks]Standard Form Conversions▶ Show worked answerHide worked answer
- M1: Moves the decimal point to give a number between 1 and 10, with the number of places moved as the power of 10
- A1: 6.4 × 10⁴
Answer: 6.4 × 10⁴ - 4
Question 4. xi=1, 2, 3, ldots, 10, A=1, 2, 3, 4, 5 and B=2, 4, 6, 8, 10. Work out n(A' cap B).
[2 marks]Fundamentals of Set Notation▶ Show worked answerHide worked answer
- M1: A'=6, 7, 8, 9, 10
- A1: A' cap B=6, 8, 10, so 3
Answer: 3 - 5
Question 5. Mo labels crates with numbers.
[3 marks]
The first four labels are
3 qquad 8 qquad 13 qquad 18 qquad ldots
The labels carry on in the same way.
Is 102 one of the labels? You must show your working.Deciding If a Term Is in a Sequence▶ Show worked answerHide worked answer
- M1: labels go up by 5 (8 - 3), so the nth term is 5n - 2
- M1: 5n - 2 = 102, so n = 104 ÷ 5 = 20.8
- A1: No, because 20.8 is not a whole number
Answer: No: the nth term is 5n - 2 and 5n - 2 = 102 gives n = 20.8
Mixed Topic Worksheet Grades 4/5: Day 099
- 1
Question 1. Rahul has pens and pencils.
number of pens : number of pencils = 3 : 7
Rahul has 21 pencils.
Work out the number of pens Rahul has.Scaling Up Ratios▶ Show worked answerHide worked answer
- M1: 21 ÷ 7 = 3
- A1: 9
Answer: 9[2 marks] - 2
Question 2. AB is a line of length 10 cm.
Mia wants to construct the perpendicular bisector of AB.
She sets her compasses to 4 cm.
She draws an arc above AB from A and an arc above AB from B.
Her two arcs do not cross.
Explain why her arcs do not cross.Drawing Perpendicular Bisectors▶ Show worked answerHide worked answer
- M1: half of AB is 10 ÷ 2 = 5 cm, which is more than 4 cm
- A1: arcs of 4 cm from A and B cannot reach each other, so the radius must be more than 5 cm
Answer: Her radius of 4 cm is less than half of AB (5 cm), so the arcs cannot meet. She needs a radius greater than 5 cm.[2 marks] - 3
Question 3. Write 64 000 in standard form.
Standard Form Conversions▶ Show worked answerHide worked answer
- M1: Moves the decimal point to give a number between 1 and 10, with the number of places moved as the power of 10
- A1: 6.4 × 10⁴
Answer: 6.4 × 10⁴[2 marks] - 4
Question 4. xi=1, 2, 3, ldots, 10, A=1, 2, 3, 4, 5 and B=2, 4, 6, 8, 10. Work out n(A' cap B).
Fundamentals of Set Notation▶ Show worked answerHide worked answer
- M1: A'=6, 7, 8, 9, 10
- A1: A' cap B=6, 8, 10, so 3
Answer: 3[2 marks] - 5
Question 5. Mo labels crates with numbers.
The first four labels are
3 qquad 8 qquad 13 qquad 18 qquad ldots
The labels carry on in the same way.
Is 102 one of the labels? You must show your working.Deciding If a Term Is in a Sequence▶ Show worked answerHide worked answer
- M1: labels go up by 5 (8 - 3), so the nth term is 5n - 2
- M1: 5n - 2 = 102, so n = 104 ÷ 5 = 20.8
- A1: No, because 20.8 is not a whole number
Answer: No: the nth term is 5n - 2 and 5n - 2 = 102 gives n = 20.8[3 marks]