Mixed Topic Worksheet Grades 6/7: Day 060
- 1
Question 1. The table shows the favourite sport of each of 72 students.
Work out the angle for each sport on a pie chart. Write the angles in the table.Drawing Pie Charts▶ Show worked answerHide worked answer
- M1: 360 ÷ 72 = 5 degrees for each student
- A1: at least three correct angles
- A1: all five angles 105, 90, 75, 50 and 40
Answer: Football 105°, Netball 90°, Hockey 75°, Rugby 50°, Tennis 40°[3 marks] - 2
Question 2. Simplify fully dfrac3x² - 12x² + 4x + 4
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: 3(x² - 4)
- M1: 3(x - 2)(x + 2)
- M1: denominator (x + 2)²
- A1: dfrac3(x - 2)x + 2
Answer: dfrac3(x - 2)x + 2[4 marks] - 3
Question 3. ABCD is a parallelogram.
AB = 11 cm.
AD = 6 cm.
Angle DAB = 70^°.
Work out the area of the parallelogram.
Give your answer to 1 decimal place.Area of Triangles Using ½ab sin C▶ Show worked answerHide worked answer
- M1: the diagonal BD splits the parallelogram into two equal triangles
- M1: 2 × 1/2 × 11 × 6 × sin 70^°
- A1: 62.0
Answer: 62.0 cm²[3 marks] - 4
Question 4. Prove that 4n² + 12n + 9 is a square number for all integer values of n.
Proof with Square Numbers▶ Show worked answerHide worked answer
- M1: (2n + 3)(2n + 3) = 4n² + 6n + 6n + 9
- A1: 4n² + 12n + 9
- C1: the expression is (2n + 3)², a square number
Answer: (2n + 3)²[3 marks] - 5
Question 5. Here is triangle ABC.
Work out the area of triangle ABC.
Give your answer to 1 decimal place.Combining the Cosine Rule with Other Rules▶ Show worked answerHide worked answer
- M1: 10.6² = 7.4² + 9.1² - 2 × 7.4 × 9.1 × cos B
- A1: B = 79.21^°
- M1: area = dfrac12 × 7.4 × 9.1 × sin B
- A1: 33.1
Answer: 33.1 cm²[4 marks]
Mixed Topic Worksheet Grades 6/7: Day 060
- 1
Question 1. The table shows the favourite sport of each of 72 students.
[3 marks]
Work out the angle for each sport on a pie chart. Write the angles in the table.Drawing Pie Charts▶ Show worked answerHide worked answer
- M1: 360 ÷ 72 = 5 degrees for each student
- A1: at least three correct angles
- A1: all five angles 105, 90, 75, 50 and 40
Answer: Football 105°, Netball 90°, Hockey 75°, Rugby 50°, Tennis 40° - 2
Question 2. Simplify fully dfrac3x² - 12x² + 4x + 4
[4 marks]Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: 3(x² - 4)
- M1: 3(x - 2)(x + 2)
- M1: denominator (x + 2)²
- A1: dfrac3(x - 2)x + 2
Answer: dfrac3(x - 2)x + 2 - 3
Question 3. ABCD is a parallelogram.
[3 marks]
AB = 11 cm.
AD = 6 cm.
Angle DAB = 70^°.
Work out the area of the parallelogram.
Give your answer to 1 decimal place.Area of Triangles Using ½ab sin C▶ Show worked answerHide worked answer
- M1: the diagonal BD splits the parallelogram into two equal triangles
- M1: 2 × 1/2 × 11 × 6 × sin 70^°
- A1: 62.0
Answer: 62.0 cm² - 4
Question 4. Prove that 4n² + 12n + 9 is a square number for all integer values of n.
[3 marks]Proof with Square Numbers▶ Show worked answerHide worked answer
- M1: (2n + 3)(2n + 3) = 4n² + 6n + 6n + 9
- A1: 4n² + 12n + 9
- C1: the expression is (2n + 3)², a square number
Answer: (2n + 3)² - 5
Question 5. Here is triangle ABC.
[4 marks]
Work out the area of triangle ABC.
Give your answer to 1 decimal place.Combining the Cosine Rule with Other Rules▶ Show worked answerHide worked answer
- M1: 10.6² = 7.4² + 9.1² - 2 × 7.4 × 9.1 × cos B
- A1: B = 79.21^°
- M1: area = dfrac12 × 7.4 × 9.1 × sin B
- A1: 33.1
Answer: 33.1 cm²
Mixed Topic Worksheet Grades 6/7: Day 060
- 1
Question 1. The table shows the favourite sport of each of 72 students.
Work out the angle for each sport on a pie chart. Write the angles in the table.Drawing Pie Charts▶ Show worked answerHide worked answer
- M1: 360 ÷ 72 = 5 degrees for each student
- A1: at least three correct angles
- A1: all five angles 105, 90, 75, 50 and 40
Answer: Football 105°, Netball 90°, Hockey 75°, Rugby 50°, Tennis 40°[3 marks] - 2
Question 2. Simplify fully dfrac3x² - 12x² + 4x + 4
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: 3(x² - 4)
- M1: 3(x - 2)(x + 2)
- M1: denominator (x + 2)²
- A1: dfrac3(x - 2)x + 2
Answer: dfrac3(x - 2)x + 2[4 marks] - 3
Question 3. ABCD is a parallelogram.
AB = 11 cm.
AD = 6 cm.
Angle DAB = 70^°.
Work out the area of the parallelogram.
Give your answer to 1 decimal place.Area of Triangles Using ½ab sin C▶ Show worked answerHide worked answer
- M1: the diagonal BD splits the parallelogram into two equal triangles
- M1: 2 × 1/2 × 11 × 6 × sin 70^°
- A1: 62.0
Answer: 62.0 cm²[3 marks] - 4
Question 4. Prove that 4n² + 12n + 9 is a square number for all integer values of n.
Proof with Square Numbers▶ Show worked answerHide worked answer
- M1: (2n + 3)(2n + 3) = 4n² + 6n + 6n + 9
- A1: 4n² + 12n + 9
- C1: the expression is (2n + 3)², a square number
Answer: (2n + 3)²[3 marks] - 5
Question 5. Here is triangle ABC.
Work out the area of triangle ABC.
Give your answer to 1 decimal place.Combining the Cosine Rule with Other Rules▶ Show worked answerHide worked answer
- M1: 10.6² = 7.4² + 9.1² - 2 × 7.4 × 9.1 × cos B
- A1: B = 79.21^°
- M1: area = dfrac12 × 7.4 × 9.1 × sin B
- A1: 33.1
Answer: 33.1 cm²[4 marks]