Mixed Topic Worksheet Grades 4/5: Day 053
- 1
Question 1. ABCD is an isosceles trapezium.
AB is parallel to DC.
AD = BC
Work out the size of angle x.Angles in Quadrilaterals▶ Show worked answerHide worked answer
- M1: 360 - 108 - 108 (the angles in a quadrilateral add up to 360^°)
- M1: divide the remainder by 2 (angle BCD = angle ADC in an isosceles trapezium)
- A1: 72
Answer: 72[3 marks] - 2
Question 2. Dan and Eve share £4.80 in the ratio 3 : 5
Work out how much money Dan receives.Proportional Division▶ Show worked answerHide worked answer
- M1: 3 + 5 = 8 parts, so 480 ÷ 8 = 60 pence, or £0.60
- A1: £1.80
Answer: £1.80[2 marks] - 3
Question 3. Here are the first three patterns made with squares.
How many squares are in pattern 6?Position-to-Term Rules Using Patterns▶ Show worked answerHide worked answer
- M1: one more square each time (4 - 3), so pattern 6 has 3 + 5
- A1: 8
Answer: 8[2 marks] - 4
Question 4. A capsule is a cylinder with a hemisphere at each end.
The radius of the capsule is 2 cm.
The cylinder is 7 cm long.
Work out the total surface area of the capsule.
Give your answer in terms of π
(Surface area of a sphere = 4π r²)Surface Area of Composite Shapes▶ Show worked answerHide worked answer
- M1: curved surface of the cylinder = 2 × π × 2 × 7 = 28π
- M1: two hemispheres make a sphere: 4 × π × 2² = 16π
- A1: 44π
Answer: 44π cm²[3 marks] - 5
Question 5. The population of one country is 7.6 × 10⁶
The population of another country is 5.9 × 10⁶
Work out the total population of the two countries.
Give your answer in standard form.Adding & Subtracting in Standard Form▶ Show worked answerHide worked answer
- M1: Adds the numbers in front of the powers of ten: 7.6 + 5.9
- M1: Changes 13.5 × 10⁶ so that the number in front is between 1 and 10
- A1: 1.35 × 10⁷
Answer: 1.35 × 10⁷[3 marks]
Mixed Topic Worksheet Grades 4/5: Day 053
- 1
Question 1. ABCD is an isosceles trapezium.
[3 marks]
AB is parallel to DC.
AD = BC
Work out the size of angle x.Angles in Quadrilaterals▶ Show worked answerHide worked answer
- M1: 360 - 108 - 108 (the angles in a quadrilateral add up to 360^°)
- M1: divide the remainder by 2 (angle BCD = angle ADC in an isosceles trapezium)
- A1: 72
Answer: 72 - 2
Question 2. Dan and Eve share £4.80 in the ratio 3 : 5
[2 marks]
Work out how much money Dan receives.Proportional Division▶ Show worked answerHide worked answer
- M1: 3 + 5 = 8 parts, so 480 ÷ 8 = 60 pence, or £0.60
- A1: £1.80
Answer: £1.80 - 3
Question 3. Here are the first three patterns made with squares.
[2 marks]
How many squares are in pattern 6?Position-to-Term Rules Using Patterns▶ Show worked answerHide worked answer
- M1: one more square each time (4 - 3), so pattern 6 has 3 + 5
- A1: 8
Answer: 8 - 4
Question 4. A capsule is a cylinder with a hemisphere at each end.
[3 marks]
The radius of the capsule is 2 cm.
The cylinder is 7 cm long.
Work out the total surface area of the capsule.
Give your answer in terms of π
(Surface area of a sphere = 4π r²)Surface Area of Composite Shapes▶ Show worked answerHide worked answer
- M1: curved surface of the cylinder = 2 × π × 2 × 7 = 28π
- M1: two hemispheres make a sphere: 4 × π × 2² = 16π
- A1: 44π
Answer: 44π cm² - 5
Question 5. The population of one country is 7.6 × 10⁶
[3 marks]
The population of another country is 5.9 × 10⁶
Work out the total population of the two countries.
Give your answer in standard form.Adding & Subtracting in Standard Form▶ Show worked answerHide worked answer
- M1: Adds the numbers in front of the powers of ten: 7.6 + 5.9
- M1: Changes 13.5 × 10⁶ so that the number in front is between 1 and 10
- A1: 1.35 × 10⁷
Answer: 1.35 × 10⁷
Mixed Topic Worksheet Grades 4/5: Day 053
- 1
Question 1. ABCD is an isosceles trapezium.
AB is parallel to DC.
AD = BC
Work out the size of angle x.Angles in Quadrilaterals▶ Show worked answerHide worked answer
- M1: 360 - 108 - 108 (the angles in a quadrilateral add up to 360^°)
- M1: divide the remainder by 2 (angle BCD = angle ADC in an isosceles trapezium)
- A1: 72
Answer: 72[3 marks] - 2
Question 2. Dan and Eve share £4.80 in the ratio 3 : 5
Work out how much money Dan receives.Proportional Division▶ Show worked answerHide worked answer
- M1: 3 + 5 = 8 parts, so 480 ÷ 8 = 60 pence, or £0.60
- A1: £1.80
Answer: £1.80[2 marks] - 3
Question 3. Here are the first three patterns made with squares.
How many squares are in pattern 6?Position-to-Term Rules Using Patterns▶ Show worked answerHide worked answer
- M1: one more square each time (4 - 3), so pattern 6 has 3 + 5
- A1: 8
Answer: 8[2 marks] - 4
Question 4. A capsule is a cylinder with a hemisphere at each end.
The radius of the capsule is 2 cm.
The cylinder is 7 cm long.
Work out the total surface area of the capsule.
Give your answer in terms of π
(Surface area of a sphere = 4π r²)Surface Area of Composite Shapes▶ Show worked answerHide worked answer
- M1: curved surface of the cylinder = 2 × π × 2 × 7 = 28π
- M1: two hemispheres make a sphere: 4 × π × 2² = 16π
- A1: 44π
Answer: 44π cm²[3 marks] - 5
Question 5. The population of one country is 7.6 × 10⁶
The population of another country is 5.9 × 10⁶
Work out the total population of the two countries.
Give your answer in standard form.Adding & Subtracting in Standard Form▶ Show worked answerHide worked answer
- M1: Adds the numbers in front of the powers of ten: 7.6 + 5.9
- M1: Changes 13.5 × 10⁶ so that the number in front is between 1 and 10
- A1: 1.35 × 10⁷
Answer: 1.35 × 10⁷[3 marks]