Mixed Topic Worksheet Grades 4/5: Day 078
- 1
Question 1. Mia's phone battery is 0.84 full. Dev's phone battery is 76% full. Write Mia's battery as a percentage. Work out how many percentage points more full Mia's battery is than Dev's battery.
Converting Decimals & Percentages▶ Show worked answerHide worked answer
- M1: 0.84 × 100 = 84%
- A1: 84 - 76 = 8
Answer: 84% then 8 percentage points[2 marks] - 2
Question 2. The graph of y = x² + 4x + c crosses the y-axis at the point (0, -11). Work out the value of c.
y-Intercepts of Quadratics▶ Show worked answerHide worked answer
- M1: -11 = 0² + 4 × 0 + c
- A1: c = -11
Answer: -11[2 marks] - 3
Question 3. Here is a line CD.
Use ruler and compasses to construct the locus of all the points that are the same distance from C as from D.
You must show all your construction lines.Drawing a Locus of All Points▶ Show worked answerHide worked answer
- M1: arcs of equal radius (more than half of CD) from C and from D, crossing above and below CD
- A1: a straight line through the two crossing points: the perpendicular bisector of CD
Answer: The perpendicular bisector of CD, with construction arcs[2 marks] - 4
Question 4. 240 people were asked about cars and bikes. 135 own a car, 96 own a bike and 63 own neither. One person is chosen at random. Work out the probability, as a percentage, that the person owns both.
Finding Probabilities with Venn Diagrams▶ Show worked answerHide worked answer
- M1: at least one =240-63=177, so both =135+96-177=54
- A1: 54/240=22.5%
Answer: 22.5%[2 marks] - 5
Question 5. A bag contains only 10p coins and 20p coins.
number of 10p coins : number of 20p coins = 4 : 3
The total value of the coins is £7.00
Work out the number of 20p coins in the bag.Expressing Ratios as Linear Equations▶ Show worked answerHide worked answer
- M1: 10 × 4k + 20 × 3k = 700, or 100k = 700
- M1: k = 7
- A1: 21
Answer: 21[3 marks]
Mixed Topic Worksheet Grades 4/5: Day 078
- 1
Question 1. Mia's phone battery is 0.84 full. Dev's phone battery is 76% full. Write Mia's battery as a percentage. Work out how many percentage points more full Mia's battery is than Dev's battery.
[2 marks]Converting Decimals & Percentages▶ Show worked answerHide worked answer
- M1: 0.84 × 100 = 84%
- A1: 84 - 76 = 8
Answer: 84% then 8 percentage points - 2
Question 2. The graph of y = x² + 4x + c crosses the y-axis at the point (0, -11). Work out the value of c.
[2 marks]y-Intercepts of Quadratics▶ Show worked answerHide worked answer
- M1: -11 = 0² + 4 × 0 + c
- A1: c = -11
Answer: -11 - 3
Question 3. Here is a line CD.
[2 marks]
Use ruler and compasses to construct the locus of all the points that are the same distance from C as from D.
You must show all your construction lines.Drawing a Locus of All Points▶ Show worked answerHide worked answer
- M1: arcs of equal radius (more than half of CD) from C and from D, crossing above and below CD
- A1: a straight line through the two crossing points: the perpendicular bisector of CD
Answer: The perpendicular bisector of CD, with construction arcs - 4
Question 4. 240 people were asked about cars and bikes. 135 own a car, 96 own a bike and 63 own neither. One person is chosen at random. Work out the probability, as a percentage, that the person owns both.
[2 marks]Finding Probabilities with Venn Diagrams▶ Show worked answerHide worked answer
- M1: at least one =240-63=177, so both =135+96-177=54
- A1: 54/240=22.5%
Answer: 22.5% - 5
Question 5. A bag contains only 10p coins and 20p coins.
[3 marks]
number of 10p coins : number of 20p coins = 4 : 3
The total value of the coins is £7.00
Work out the number of 20p coins in the bag.Expressing Ratios as Linear Equations▶ Show worked answerHide worked answer
- M1: 10 × 4k + 20 × 3k = 700, or 100k = 700
- M1: k = 7
- A1: 21
Answer: 21
Mixed Topic Worksheet Grades 4/5: Day 078
- 1
Question 1. Mia's phone battery is 0.84 full. Dev's phone battery is 76% full. Write Mia's battery as a percentage. Work out how many percentage points more full Mia's battery is than Dev's battery.
Converting Decimals & Percentages▶ Show worked answerHide worked answer
- M1: 0.84 × 100 = 84%
- A1: 84 - 76 = 8
Answer: 84% then 8 percentage points[2 marks] - 2
Question 2. The graph of y = x² + 4x + c crosses the y-axis at the point (0, -11). Work out the value of c.
y-Intercepts of Quadratics▶ Show worked answerHide worked answer
- M1: -11 = 0² + 4 × 0 + c
- A1: c = -11
Answer: -11[2 marks] - 3
Question 3. Here is a line CD.
Use ruler and compasses to construct the locus of all the points that are the same distance from C as from D.
You must show all your construction lines.Drawing a Locus of All Points▶ Show worked answerHide worked answer
- M1: arcs of equal radius (more than half of CD) from C and from D, crossing above and below CD
- A1: a straight line through the two crossing points: the perpendicular bisector of CD
Answer: The perpendicular bisector of CD, with construction arcs[2 marks] - 4
Question 4. 240 people were asked about cars and bikes. 135 own a car, 96 own a bike and 63 own neither. One person is chosen at random. Work out the probability, as a percentage, that the person owns both.
Finding Probabilities with Venn Diagrams▶ Show worked answerHide worked answer
- M1: at least one =240-63=177, so both =135+96-177=54
- A1: 54/240=22.5%
Answer: 22.5%[2 marks] - 5
Question 5. A bag contains only 10p coins and 20p coins.
number of 10p coins : number of 20p coins = 4 : 3
The total value of the coins is £7.00
Work out the number of 20p coins in the bag.Expressing Ratios as Linear Equations▶ Show worked answerHide worked answer
- M1: 10 × 4k + 20 × 3k = 700, or 100k = 700
- M1: k = 7
- A1: 21
Answer: 21[3 marks]