Mixed Topic Worksheet Grades 4/5: Day 065
- 1
Question 1. Tom says that the lowest common multiple of 6 and 10 is 60
Is Tom correct?
You must give a reason for your answer.Finding the Lowest Common Multiple▶ Show worked answerHide worked answer
- M1: finds a common multiple of 6 and 10 smaller than 60, such as 30
- A1: No, the lowest common multiple is 30
Answer: No, because 30 is a smaller common multiple of 6 and 10 (30 = 6 × 5 = 10 × 3)[2 marks] - 2
Question 2. Two straight lines, QP and QR, meet at Q.
Draw the locus of all the points inside angle PQR that are the same distance from QP as from QR.Drawing a Locus of All Points▶ Show worked answerHide worked answer
- M1: arc centred on Q cutting QP and QR, then two arcs of equal radius from those points that cross inside the angle
- A1: line drawn from Q through the crossing, to within 2 degrees of the true bisector
Answer: The bisector of angle PQR.[2 marks] - 3
Question 3. A recipe for 8 cupcakes uses 120 g of flour.
Work out the amount of flour needed for 20 cupcakes.Direct Proportion Problems▶ Show worked answerHide worked answer
- M1: 120 ÷ 8 (flour for one cupcake)
- A1: 300 g
Answer: 300 g[2 marks] - 4
Question 4. Jo says that the graph of y = 4 - x² has a lowest point at (0, 4), because 4 is positive.
Jo is not correct.
Write down the correct statement about the turning point of the graph. Describe Jo's mistake.General Shape of a Quadratic▶ Show worked answerHide worked answer
- B1: the turning point is a highest point (maximum)
- B1: the sign of the x² term decides the shape, not the sign of the 4
Answer: The graph has a highest point at (0, 4); the x² term is negative, so the graph is an upside-down U, and Jo looked at the sign of the 4 instead[2 marks] - 5
Question 5. A plumber charges a call-out fee of £40 and £20 for each hour of work. Hana has £170 to spend. The plumber works for h whole hours. Work out the greatest possible value of h.
Solving Single Inequalities▶ Show worked answerHide worked answer
- M1: 40 + 20h ≤ 170
- M1: 20h ≤ 170 - 40, so h ≤ 6.5
- A1: h = 6
Answer: 6[3 marks]
Mixed Topic Worksheet Grades 4/5: Day 065
- 1
Question 1. Tom says that the lowest common multiple of 6 and 10 is 60
[2 marks]
Is Tom correct?
You must give a reason for your answer.Finding the Lowest Common Multiple▶ Show worked answerHide worked answer
- M1: finds a common multiple of 6 and 10 smaller than 60, such as 30
- A1: No, the lowest common multiple is 30
Answer: No, because 30 is a smaller common multiple of 6 and 10 (30 = 6 × 5 = 10 × 3) - 2
Question 2. Two straight lines, QP and QR, meet at Q.
[2 marks]
Draw the locus of all the points inside angle PQR that are the same distance from QP as from QR.Drawing a Locus of All Points▶ Show worked answerHide worked answer
- M1: arc centred on Q cutting QP and QR, then two arcs of equal radius from those points that cross inside the angle
- A1: line drawn from Q through the crossing, to within 2 degrees of the true bisector
Answer: The bisector of angle PQR. - 3
Question 3. A recipe for 8 cupcakes uses 120 g of flour.
[2 marks]
Work out the amount of flour needed for 20 cupcakes.Direct Proportion Problems▶ Show worked answerHide worked answer
- M1: 120 ÷ 8 (flour for one cupcake)
- A1: 300 g
Answer: 300 g - 4
Question 4. Jo says that the graph of y = 4 - x² has a lowest point at (0, 4), because 4 is positive.
[2 marks]
Jo is not correct.
Write down the correct statement about the turning point of the graph. Describe Jo's mistake.General Shape of a Quadratic▶ Show worked answerHide worked answer
- B1: the turning point is a highest point (maximum)
- B1: the sign of the x² term decides the shape, not the sign of the 4
Answer: The graph has a highest point at (0, 4); the x² term is negative, so the graph is an upside-down U, and Jo looked at the sign of the 4 instead - 5
Question 5. A plumber charges a call-out fee of £40 and £20 for each hour of work. Hana has £170 to spend. The plumber works for h whole hours. Work out the greatest possible value of h.
[3 marks]Solving Single Inequalities▶ Show worked answerHide worked answer
- M1: 40 + 20h ≤ 170
- M1: 20h ≤ 170 - 40, so h ≤ 6.5
- A1: h = 6
Answer: 6
Mixed Topic Worksheet Grades 4/5: Day 065
- 1
Question 1. Tom says that the lowest common multiple of 6 and 10 is 60
Is Tom correct?
You must give a reason for your answer.Finding the Lowest Common Multiple▶ Show worked answerHide worked answer
- M1: finds a common multiple of 6 and 10 smaller than 60, such as 30
- A1: No, the lowest common multiple is 30
Answer: No, because 30 is a smaller common multiple of 6 and 10 (30 = 6 × 5 = 10 × 3)[2 marks] - 2
Question 2. Two straight lines, QP and QR, meet at Q.
Draw the locus of all the points inside angle PQR that are the same distance from QP as from QR.Drawing a Locus of All Points▶ Show worked answerHide worked answer
- M1: arc centred on Q cutting QP and QR, then two arcs of equal radius from those points that cross inside the angle
- A1: line drawn from Q through the crossing, to within 2 degrees of the true bisector
Answer: The bisector of angle PQR.[2 marks] - 3
Question 3. A recipe for 8 cupcakes uses 120 g of flour.
Work out the amount of flour needed for 20 cupcakes.Direct Proportion Problems▶ Show worked answerHide worked answer
- M1: 120 ÷ 8 (flour for one cupcake)
- A1: 300 g
Answer: 300 g[2 marks] - 4
Question 4. Jo says that the graph of y = 4 - x² has a lowest point at (0, 4), because 4 is positive.
Jo is not correct.
Write down the correct statement about the turning point of the graph. Describe Jo's mistake.General Shape of a Quadratic▶ Show worked answerHide worked answer
- B1: the turning point is a highest point (maximum)
- B1: the sign of the x² term decides the shape, not the sign of the 4
Answer: The graph has a highest point at (0, 4); the x² term is negative, so the graph is an upside-down U, and Jo looked at the sign of the 4 instead[2 marks] - 5
Question 5. A plumber charges a call-out fee of £40 and £20 for each hour of work. Hana has £170 to spend. The plumber works for h whole hours. Work out the greatest possible value of h.
Solving Single Inequalities▶ Show worked answerHide worked answer
- M1: 40 + 20h ≤ 170
- M1: 20h ≤ 170 - 40, so h ≤ 6.5
- A1: h = 6
Answer: 6[3 marks]