Mixed Topic Worksheet Grades 4/5: Day 095
- 1
Question 1. A liquid has a density of 0.9 g/cm³.
A container holds 4000 cm³ of the liquid.
Work out the mass of the liquid in kg.Density, Mass & Volume Calculations▶ Show worked answerHide worked answer
- M1: 0.9 × 4000 = 3600 g
- M1: 3600 ÷ 1000
- A1: 3.6
Answer: 3.6 kg[3 marks] - 2
Question 2. Work out dfrac13 + dfrac14
Common Denominators▶ Show worked answerHide worked answer
- M1: dfrac13 = dfrac412 and dfrac14 = dfrac312
- A1: dfrac712
Answer: dfrac712[2 marks] - 3
Question 3. A frequency polygon is drawn for some times, t minutes.
The class 10 < t ≤ 20 has frequency 6.
The class 20 < t ≤ 30 has frequency 11.
Write down the coordinates of the points plotted for these two classes.Sketching Frequency Polygons▶ Show worked answerHide worked answer
- B1: the x-coordinates are the midpoints 15 and 25
- B1: (15, 6) and (25, 11)
Answer: (15, 6) and (25, 11)[2 marks] - 4
Question 4. Here is a statement.
"Every cube number is odd."
Give a counterexample to show that the statement is not true.Proof by Counterexample▶ Show worked answerHide worked answer
- M1: a cube number tested, 2³ = 8 and 8 is even
- A1: 8 stated as the counterexample, with 8 a cube number and an even number
Answer: 8 is a cube number (2³) and it is even[2 marks] - 5
Question 5. overrightarrowAB = mathbfa + 2mathbfb and overrightarrowCD = 3mathbfa + 6mathbfb. Write down two facts about the lines AB and CD.
Fundamentals of Vector Problems▶ Show worked answerHide worked answer
- B1: overrightarrowCD = 3overrightarrowAB, so AB and CD are parallel
- B1: CD is 3 times as long as AB
Answer: AB and CD are parallel, and CD is 3 times as long as AB[2 marks]
Mixed Topic Worksheet Grades 4/5: Day 095
- 1
Question 1. A liquid has a density of 0.9 g/cm³.
[3 marks]
A container holds 4000 cm³ of the liquid.
Work out the mass of the liquid in kg.Density, Mass & Volume Calculations▶ Show worked answerHide worked answer
- M1: 0.9 × 4000 = 3600 g
- M1: 3600 ÷ 1000
- A1: 3.6
Answer: 3.6 kg - 2
Question 2. Work out dfrac13 + dfrac14
[2 marks]Common Denominators▶ Show worked answerHide worked answer
- M1: dfrac13 = dfrac412 and dfrac14 = dfrac312
- A1: dfrac712
Answer: dfrac712 - 3
Question 3. A frequency polygon is drawn for some times, t minutes.
[2 marks]
The class 10 < t ≤ 20 has frequency 6.
The class 20 < t ≤ 30 has frequency 11.
Write down the coordinates of the points plotted for these two classes.Sketching Frequency Polygons▶ Show worked answerHide worked answer
- B1: the x-coordinates are the midpoints 15 and 25
- B1: (15, 6) and (25, 11)
Answer: (15, 6) and (25, 11) - 4
Question 4. Here is a statement.
[2 marks]
"Every cube number is odd."
Give a counterexample to show that the statement is not true.Proof by Counterexample▶ Show worked answerHide worked answer
- M1: a cube number tested, 2³ = 8 and 8 is even
- A1: 8 stated as the counterexample, with 8 a cube number and an even number
Answer: 8 is a cube number (2³) and it is even - 5
Question 5. overrightarrowAB = mathbfa + 2mathbfb and overrightarrowCD = 3mathbfa + 6mathbfb. Write down two facts about the lines AB and CD.
[2 marks]Fundamentals of Vector Problems▶ Show worked answerHide worked answer
- B1: overrightarrowCD = 3overrightarrowAB, so AB and CD are parallel
- B1: CD is 3 times as long as AB
Answer: AB and CD are parallel, and CD is 3 times as long as AB
Mixed Topic Worksheet Grades 4/5: Day 095
- 1
Question 1. A liquid has a density of 0.9 g/cm³.
A container holds 4000 cm³ of the liquid.
Work out the mass of the liquid in kg.Density, Mass & Volume Calculations▶ Show worked answerHide worked answer
- M1: 0.9 × 4000 = 3600 g
- M1: 3600 ÷ 1000
- A1: 3.6
Answer: 3.6 kg[3 marks] - 2
Question 2. Work out dfrac13 + dfrac14
Common Denominators▶ Show worked answerHide worked answer
- M1: dfrac13 = dfrac412 and dfrac14 = dfrac312
- A1: dfrac712
Answer: dfrac712[2 marks] - 3
Question 3. A frequency polygon is drawn for some times, t minutes.
The class 10 < t ≤ 20 has frequency 6.
The class 20 < t ≤ 30 has frequency 11.
Write down the coordinates of the points plotted for these two classes.Sketching Frequency Polygons▶ Show worked answerHide worked answer
- B1: the x-coordinates are the midpoints 15 and 25
- B1: (15, 6) and (25, 11)
Answer: (15, 6) and (25, 11)[2 marks] - 4
Question 4. Here is a statement.
"Every cube number is odd."
Give a counterexample to show that the statement is not true.Proof by Counterexample▶ Show worked answerHide worked answer
- M1: a cube number tested, 2³ = 8 and 8 is even
- A1: 8 stated as the counterexample, with 8 a cube number and an even number
Answer: 8 is a cube number (2³) and it is even[2 marks] - 5
Question 5. overrightarrowAB = mathbfa + 2mathbfb and overrightarrowCD = 3mathbfa + 6mathbfb. Write down two facts about the lines AB and CD.
Fundamentals of Vector Problems▶ Show worked answerHide worked answer
- B1: overrightarrowCD = 3overrightarrowAB, so AB and CD are parallel
- B1: CD is 3 times as long as AB
Answer: AB and CD are parallel, and CD is 3 times as long as AB[2 marks]