Mixed Topic Worksheet Grades 8/9: Day 069
- 1
Question 1. Here is the graph of y = sin x for 0^° ≤ x ≤ 360^°. Use the graph to write down the value of
(a) sin 90^° [1]
(b) sin 270^° [1]Calculating Values of Trig Functions Using Graphs▶ Show worked answerHide worked answer
- (a) B1: 1
- (b) B1: -1
Answer: (a) 1; (b) -1[2 marks] - 2
Question 2. A cuboid has a 4 cm by 7 cm base and a space diagonal of 9 cm. Work out its height.
3D Pythagoras▶ Show worked answerHide worked answer
- M1: h² = 9² - 4² - 7²
- A1: h = 4 cm
Answer: 4 cm[2 marks] - 3
Question 3. Four raffle tickets have consecutive positive whole numbers on them.
Lena adds the four numbers together.
Prove that Lena's total can never be a multiple of 4.Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: n + (n + 1) + (n + 2) + (n + 3)
- A1: 4n + 6
- C1: 4(n + 1) + 2, which is 2 more than a multiple of 4
Answer: 4(n + 1) + 2[3 marks] - 4
Question 4. ABCD is a cyclic quadrilateral and AC is a diameter. Angle BAC = 35° and angle CAD = 20°. Work out the size of angle BCD. Give reasons.
Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: angle ABC = 90° (angle in a semicircle) so angle ACB = 55°
- M1: angle ACD = 70° in the same way
- A1: 55 + 70 = 125°
Answer: 125°[3 marks] - 5
Question 5. Rationalise the denominator of dfrac65 - √13 giving your answer in its simplest form.
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac6(5 + √13)5² - 13
- A1: dfrac5 + √132
Answer: dfrac5 + √132[2 marks]
Mixed Topic Worksheet Grades 8/9: Day 069
- 1
Question 1. Here is the graph of y = sin x for 0^° ≤ x ≤ 360^°. Use the graph to write down the value of
[2 marks]
(a) sin 90^° [1]
(b) sin 270^° [1]Calculating Values of Trig Functions Using Graphs▶ Show worked answerHide worked answer
- (a) B1: 1
- (b) B1: -1
Answer: (a) 1; (b) -1 - 2
Question 2. A cuboid has a 4 cm by 7 cm base and a space diagonal of 9 cm. Work out its height.
[2 marks]3D Pythagoras▶ Show worked answerHide worked answer
- M1: h² = 9² - 4² - 7²
- A1: h = 4 cm
Answer: 4 cm - 3
Question 3. Four raffle tickets have consecutive positive whole numbers on them.
[3 marks]
Lena adds the four numbers together.
Prove that Lena's total can never be a multiple of 4.Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: n + (n + 1) + (n + 2) + (n + 3)
- A1: 4n + 6
- C1: 4(n + 1) + 2, which is 2 more than a multiple of 4
Answer: 4(n + 1) + 2 - 4
Question 4. ABCD is a cyclic quadrilateral and AC is a diameter. Angle BAC = 35° and angle CAD = 20°. Work out the size of angle BCD. Give reasons.
[3 marks]Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: angle ABC = 90° (angle in a semicircle) so angle ACB = 55°
- M1: angle ACD = 70° in the same way
- A1: 55 + 70 = 125°
Answer: 125° - 5
Question 5. Rationalise the denominator of dfrac65 - √13 giving your answer in its simplest form.
[2 marks]Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac6(5 + √13)5² - 13
- A1: dfrac5 + √132
Answer: dfrac5 + √132
Mixed Topic Worksheet Grades 8/9: Day 069
- 1
Question 1. Here is the graph of y = sin x for 0^° ≤ x ≤ 360^°. Use the graph to write down the value of
(a) sin 90^° [1]
(b) sin 270^° [1]Calculating Values of Trig Functions Using Graphs▶ Show worked answerHide worked answer
- (a) B1: 1
- (b) B1: -1
Answer: (a) 1; (b) -1[2 marks] - 2
Question 2. A cuboid has a 4 cm by 7 cm base and a space diagonal of 9 cm. Work out its height.
3D Pythagoras▶ Show worked answerHide worked answer
- M1: h² = 9² - 4² - 7²
- A1: h = 4 cm
Answer: 4 cm[2 marks] - 3
Question 3. Four raffle tickets have consecutive positive whole numbers on them.
Lena adds the four numbers together.
Prove that Lena's total can never be a multiple of 4.Proof with Consecutive Numbers▶ Show worked answerHide worked answer
- M1: n + (n + 1) + (n + 2) + (n + 3)
- A1: 4n + 6
- C1: 4(n + 1) + 2, which is 2 more than a multiple of 4
Answer: 4(n + 1) + 2[3 marks] - 4
Question 4. ABCD is a cyclic quadrilateral and AC is a diameter. Angle BAC = 35° and angle CAD = 20°. Work out the size of angle BCD. Give reasons.
Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: angle ABC = 90° (angle in a semicircle) so angle ACB = 55°
- M1: angle ACD = 70° in the same way
- A1: 55 + 70 = 125°
Answer: 125°[3 marks] - 5
Question 5. Rationalise the denominator of dfrac65 - √13 giving your answer in its simplest form.
Rationalising Denominators of the Form a ± √b▶ Show worked answerHide worked answer
- M1: dfrac6(5 + √13)5² - 13
- A1: dfrac5 + √132
Answer: dfrac5 + √132[2 marks]