Mixed Topic Worksheet Grades 4/5: Day 039
- 1
Question 1. Work out dfrac54 ÷ dfrac76
Give your answer as a fraction in its simplest form.Dividing Fractions▶ Show worked answerHide worked answer
- M1: dfrac54 × dfrac67
- M1: 5 × 6 = 30 and 4 × 7 = 28
- A1: dfrac1514
Answer: dfrac1514[3 marks] - 2
Question 2. PX is constructed at right angles to the straight line APB.
Y is a point on the same side of APB as X.
Y lies between PX and PB.
Angle XPY = 27^°
Work out the size of angle YPB.Drawing a 90° Angle▶ Show worked answerHide worked answer
- B1: 90 - 27 = 63
Answer: 63[1 mark] - 3
Question 3. A spinner has 8 equal sections.
2 sections are red, 3 are blue and 3 are green.
Tia says, "The probability that the spinner lands on red is dfrac13 because there are three colours."
Is Tia correct?
Give a reason for your answer.Calculating Probabilities▶ Show worked answerHide worked answer
- M1: dfrac28, as 2 of the 8 equal sections are red
- A1: No, the probability is dfrac14, not dfrac13, because the three colours do not have the same number of sections
Answer: No. 2 of the 8 equal sections are red, so the probability of red is 2/8 = 1/4.[2 marks] - 4
Question 4. Mia works out the value of y when x = 2 for the graph y = x³ - 4 Here is her working.
2³ = 2 × 3 = 6
y = 6 - 4 = 2
Is Mia correct? You must give a reason for your answer.Plotting a Cubic▶ Show worked answerHide worked answer
- M1: 2³ = 2 × 2 × 2 = 8
- A1: No, y = 8 - 4 = 4
Answer: No, y = 4[2 marks] - 5
Question 5. Cone A has base radius 5 cm and slant height 12 cm.
Cone B has base radius 7 cm and slant height 8 cm.
Sam says that cone A has the larger total surface area because its slant height is larger.
Is Sam correct?
You must show your working.Surface Area of Cones▶ Show worked answerHide worked answer
- M1: π × 5 × (5 + 12) or 85π
- M1: π × 7 × (7 + 8) or 105π
- A1: A is 85π cm² and B is 105π cm², so Sam is not correct
Answer: No: cone A has 85π cm² and cone B has 105π cm²[3 marks]
Mixed Topic Worksheet Grades 4/5: Day 039
- 1
Question 1. Work out dfrac54 ÷ dfrac76
[3 marks]
Give your answer as a fraction in its simplest form.Dividing Fractions▶ Show worked answerHide worked answer
- M1: dfrac54 × dfrac67
- M1: 5 × 6 = 30 and 4 × 7 = 28
- A1: dfrac1514
Answer: dfrac1514 - 2
Question 2. PX is constructed at right angles to the straight line APB.
[1 mark]
Y is a point on the same side of APB as X.
Y lies between PX and PB.
Angle XPY = 27^°
Work out the size of angle YPB.Drawing a 90° Angle▶ Show worked answerHide worked answer
- B1: 90 - 27 = 63
Answer: 63 - 3
Question 3. A spinner has 8 equal sections.
[2 marks]
2 sections are red, 3 are blue and 3 are green.
Tia says, "The probability that the spinner lands on red is dfrac13 because there are three colours."
Is Tia correct?
Give a reason for your answer.Calculating Probabilities▶ Show worked answerHide worked answer
- M1: dfrac28, as 2 of the 8 equal sections are red
- A1: No, the probability is dfrac14, not dfrac13, because the three colours do not have the same number of sections
Answer: No. 2 of the 8 equal sections are red, so the probability of red is 2/8 = 1/4. - 4
Question 4. Mia works out the value of y when x = 2 for the graph y = x³ - 4 Here is her working.
[2 marks]
2³ = 2 × 3 = 6
y = 6 - 4 = 2
Is Mia correct? You must give a reason for your answer.Plotting a Cubic▶ Show worked answerHide worked answer
- M1: 2³ = 2 × 2 × 2 = 8
- A1: No, y = 8 - 4 = 4
Answer: No, y = 4 - 5
Question 5. Cone A has base radius 5 cm and slant height 12 cm.
[3 marks]
Cone B has base radius 7 cm and slant height 8 cm.
Sam says that cone A has the larger total surface area because its slant height is larger.
Is Sam correct?
You must show your working.Surface Area of Cones▶ Show worked answerHide worked answer
- M1: π × 5 × (5 + 12) or 85π
- M1: π × 7 × (7 + 8) or 105π
- A1: A is 85π cm² and B is 105π cm², so Sam is not correct
Answer: No: cone A has 85π cm² and cone B has 105π cm²
Mixed Topic Worksheet Grades 4/5: Day 039
- 1
Question 1. Work out dfrac54 ÷ dfrac76
Give your answer as a fraction in its simplest form.Dividing Fractions▶ Show worked answerHide worked answer
- M1: dfrac54 × dfrac67
- M1: 5 × 6 = 30 and 4 × 7 = 28
- A1: dfrac1514
Answer: dfrac1514[3 marks] - 2
Question 2. PX is constructed at right angles to the straight line APB.
Y is a point on the same side of APB as X.
Y lies between PX and PB.
Angle XPY = 27^°
Work out the size of angle YPB.Drawing a 90° Angle▶ Show worked answerHide worked answer
- B1: 90 - 27 = 63
Answer: 63[1 mark] - 3
Question 3. A spinner has 8 equal sections.
2 sections are red, 3 are blue and 3 are green.
Tia says, "The probability that the spinner lands on red is dfrac13 because there are three colours."
Is Tia correct?
Give a reason for your answer.Calculating Probabilities▶ Show worked answerHide worked answer
- M1: dfrac28, as 2 of the 8 equal sections are red
- A1: No, the probability is dfrac14, not dfrac13, because the three colours do not have the same number of sections
Answer: No. 2 of the 8 equal sections are red, so the probability of red is 2/8 = 1/4.[2 marks] - 4
Question 4. Mia works out the value of y when x = 2 for the graph y = x³ - 4 Here is her working.
2³ = 2 × 3 = 6
y = 6 - 4 = 2
Is Mia correct? You must give a reason for your answer.Plotting a Cubic▶ Show worked answerHide worked answer
- M1: 2³ = 2 × 2 × 2 = 8
- A1: No, y = 8 - 4 = 4
Answer: No, y = 4[2 marks] - 5
Question 5. Cone A has base radius 5 cm and slant height 12 cm.
Cone B has base radius 7 cm and slant height 8 cm.
Sam says that cone A has the larger total surface area because its slant height is larger.
Is Sam correct?
You must show your working.Surface Area of Cones▶ Show worked answerHide worked answer
- M1: π × 5 × (5 + 12) or 85π
- M1: π × 7 × (7 + 8) or 105π
- A1: A is 85π cm² and B is 105π cm², so Sam is not correct
Answer: No: cone A has 85π cm² and cone B has 105π cm²[3 marks]