Mixed Topic Worksheet Grades 6/7: Day 088
- 1
Question 1. Here is a cylinder. Work out the volume of the cylinder.
Give your answer to 1 decimal place.Volume of Cylinders▶ Show worked answerHide worked answer
- M1: 7 ÷ 2 = 3.5
- M1: π × 3.5² × 12
- A1: 461.8
Answer: 461.8[3 marks] - 2
Question 2. Is √81 rational or irrational? Give a reason.
Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: √81 = 9
- A1: rational, because 9 can be written as a fraction of two integers
Answer: Rational. √81 = 9 = dfrac91.[2 marks] - 3
Question 3. A photograph is mounted in a frame. The outer edge of the frame is a rectangle (n + 8) cm by (n + 5) cm. The photograph is a rectangle (n + 4) cm by (n + 1) cm, where n is a positive integer. Prove that the area of the frame not covered by the photograph is a multiple of 4 cm².
Proof with Multiples▶ Show worked answerHide worked answer
- M1: outer area (n + 8)(n + 5) = n² + 13n + 40
- M1: photograph area (n + 4)(n + 1) = n² + 5n + 4
- M1: n² + 13n + 40 - (n² + 5n + 4) = 8n + 36
- C1: 8n + 36 = 4(2n + 9), a multiple of 4
Answer: 4(2n + 9) cm², a multiple of 4[4 marks] - 4
Question 4. Here is a speed-time graph for a train.
The total distance travelled is 600 metres.
The diagram is not drawn accurately.
Work out the top speed of the train.Calculating Total Distance Travelled Using Speed-Time Graphs▶ Show worked answerHide worked answer
- M1: ½ × (40 + 20) × v = 600
- M1: 30v = 600
- A1: 20 m/s
Answer: 20 m/s[3 marks] - 5
Question 5. Triangle PQR is isosceles.
PQ = PR = 7.5 cm
Angle QPR = 110^°
Work out the area of triangle PQR.
Give your answer to 1 decimal place.Using the Area Rule with Isosceles Triangles▶ Show worked answerHide worked answer
- M1: 1/2 × 7.5 × 7.5 × sin 110^°
- A1: 26.4
Answer: 26.4 cm²[2 marks]
Mixed Topic Worksheet Grades 6/7: Day 088
- 1
Question 1. Here is a cylinder. Work out the volume of the cylinder.
[3 marks]
Give your answer to 1 decimal place.Volume of Cylinders▶ Show worked answerHide worked answer
- M1: 7 ÷ 2 = 3.5
- M1: π × 3.5² × 12
- A1: 461.8
Answer: 461.8 - 2
Question 2. Is √81 rational or irrational? Give a reason.
[2 marks]Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: √81 = 9
- A1: rational, because 9 can be written as a fraction of two integers
Answer: Rational. √81 = 9 = dfrac91. - 3
Question 3. A photograph is mounted in a frame. The outer edge of the frame is a rectangle (n + 8) cm by (n + 5) cm. The photograph is a rectangle (n + 4) cm by (n + 1) cm, where n is a positive integer. Prove that the area of the frame not covered by the photograph is a multiple of 4 cm².
[4 marks]Proof with Multiples▶ Show worked answerHide worked answer
- M1: outer area (n + 8)(n + 5) = n² + 13n + 40
- M1: photograph area (n + 4)(n + 1) = n² + 5n + 4
- M1: n² + 13n + 40 - (n² + 5n + 4) = 8n + 36
- C1: 8n + 36 = 4(2n + 9), a multiple of 4
Answer: 4(2n + 9) cm², a multiple of 4 - 4
Question 4. Here is a speed-time graph for a train.
[3 marks]
The total distance travelled is 600 metres.
The diagram is not drawn accurately.
Work out the top speed of the train.Calculating Total Distance Travelled Using Speed-Time Graphs▶ Show worked answerHide worked answer
- M1: ½ × (40 + 20) × v = 600
- M1: 30v = 600
- A1: 20 m/s
Answer: 20 m/s - 5
Question 5. Triangle PQR is isosceles.
[2 marks]
PQ = PR = 7.5 cm
Angle QPR = 110^°
Work out the area of triangle PQR.
Give your answer to 1 decimal place.Using the Area Rule with Isosceles Triangles▶ Show worked answerHide worked answer
- M1: 1/2 × 7.5 × 7.5 × sin 110^°
- A1: 26.4
Answer: 26.4 cm²
Mixed Topic Worksheet Grades 6/7: Day 088
- 1
Question 1. Here is a cylinder. Work out the volume of the cylinder.
Give your answer to 1 decimal place.Volume of Cylinders▶ Show worked answerHide worked answer
- M1: 7 ÷ 2 = 3.5
- M1: π × 3.5² × 12
- A1: 461.8
Answer: 461.8[3 marks] - 2
Question 2. Is √81 rational or irrational? Give a reason.
Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: √81 = 9
- A1: rational, because 9 can be written as a fraction of two integers
Answer: Rational. √81 = 9 = dfrac91.[2 marks] - 3
Question 3. A photograph is mounted in a frame. The outer edge of the frame is a rectangle (n + 8) cm by (n + 5) cm. The photograph is a rectangle (n + 4) cm by (n + 1) cm, where n is a positive integer. Prove that the area of the frame not covered by the photograph is a multiple of 4 cm².
Proof with Multiples▶ Show worked answerHide worked answer
- M1: outer area (n + 8)(n + 5) = n² + 13n + 40
- M1: photograph area (n + 4)(n + 1) = n² + 5n + 4
- M1: n² + 13n + 40 - (n² + 5n + 4) = 8n + 36
- C1: 8n + 36 = 4(2n + 9), a multiple of 4
Answer: 4(2n + 9) cm², a multiple of 4[4 marks] - 4
Question 4. Here is a speed-time graph for a train.
The total distance travelled is 600 metres.
The diagram is not drawn accurately.
Work out the top speed of the train.Calculating Total Distance Travelled Using Speed-Time Graphs▶ Show worked answerHide worked answer
- M1: ½ × (40 + 20) × v = 600
- M1: 30v = 600
- A1: 20 m/s
Answer: 20 m/s[3 marks] - 5
Question 5. Triangle PQR is isosceles.
PQ = PR = 7.5 cm
Angle QPR = 110^°
Work out the area of triangle PQR.
Give your answer to 1 decimal place.Using the Area Rule with Isosceles Triangles▶ Show worked answerHide worked answer
- M1: 1/2 × 7.5 × 7.5 × sin 110^°
- A1: 26.4
Answer: 26.4 cm²[2 marks]