Mixed Topic Worksheet Grades 8/9: Day 017
- 1
Question 1. Without a calculator, work out the exact value of tan 135^° + sin 210^°
Calculating Values of Trig Functions Using Graphs▶ Show worked answerHide worked answer
- M1: tan 135^° = -1 and sin 210^° = -dfrac12
- A1: -dfrac32
Answer: -dfrac32[2 marks] - 2
Question 2. P(3, -5) lies on y = f(x)
Write down the image of P on y = -f(x), on y = f(-x) and on y = -f(-x)Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- B1: (3, 5) on y = -f(x)
- B1: (-3, -5) on y = f(-x)
- B1: (-3, 5) on y = -f(-x)
Answer: (3, 5); (-3, -5); (-3, 5)[3 marks] - 3
Question 3. A car travels dfracx² - 4x + 5 km in dfracx - 2x² + x - 20 hours
Find an expression for its average speed in km/h
Give your answer in its simplest formMultiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: speed = dfracx² - 4x + 5 ÷ dfracx - 2(x + 5)(x - 4)
- M1: dfrac(x - 2)(x + 2)x + 5 × dfrac(x + 5)(x - 4)x - 2
- A1: (x + 2)(x - 4)
Answer: (x + 2)(x - 4) km/h[3 marks] - 4
Question 4. The histogram shows the lengths, x cm, of some leaves.
Work out an estimate for the mean length.
Use the midpoint of each class.Interpreting Histograms▶ Show worked answerHide worked answer
- M1: 2 × 10, 1.5 × 20, 3 × 10, 1 × 20 (at least two correct)
- M1: 5 × 20 + 20 × 30 + 35 × 30 + 50 × 20
- M1: divide by 20 + 30 + 30 + 20
- A1: 27.5
Answer: 27.5 cm[4 marks] - 5
Question 5. In triangle OAB, overrightarrowOA=mathbfa and overrightarrowOB=mathbfb. P lies on AB with AP:PB=3:1. Find overrightarrowOP in terms of mathbfa and mathbfb.
Vector Ratio Problems▶ Show worked answerHide worked answer
- M1: overrightarrowAB=mathbfb-mathbfa
- M1: overrightarrowOP=mathbfa+3/4(mathbfb-mathbfa)
- A1: 1/4mathbfa+3/4mathbfb
Answer: overrightarrowOP=1/4mathbfa+3/4mathbfb[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 017
- 1
Question 1. Without a calculator, work out the exact value of tan 135^° + sin 210^°
[2 marks]Calculating Values of Trig Functions Using Graphs▶ Show worked answerHide worked answer
- M1: tan 135^° = -1 and sin 210^° = -dfrac12
- A1: -dfrac32
Answer: -dfrac32 - 2
Question 2. P(3, -5) lies on y = f(x)
[3 marks]
Write down the image of P on y = -f(x), on y = f(-x) and on y = -f(-x)Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- B1: (3, 5) on y = -f(x)
- B1: (-3, -5) on y = f(-x)
- B1: (-3, 5) on y = -f(-x)
Answer: (3, 5); (-3, -5); (-3, 5) - 3
Question 3. A car travels dfracx² - 4x + 5 km in dfracx - 2x² + x - 20 hours
[3 marks]
Find an expression for its average speed in km/h
Give your answer in its simplest formMultiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: speed = dfracx² - 4x + 5 ÷ dfracx - 2(x + 5)(x - 4)
- M1: dfrac(x - 2)(x + 2)x + 5 × dfrac(x + 5)(x - 4)x - 2
- A1: (x + 2)(x - 4)
Answer: (x + 2)(x - 4) km/h - 4
Question 4. The histogram shows the lengths, x cm, of some leaves.
[4 marks]
Work out an estimate for the mean length.
Use the midpoint of each class.Interpreting Histograms▶ Show worked answerHide worked answer
- M1: 2 × 10, 1.5 × 20, 3 × 10, 1 × 20 (at least two correct)
- M1: 5 × 20 + 20 × 30 + 35 × 30 + 50 × 20
- M1: divide by 20 + 30 + 30 + 20
- A1: 27.5
Answer: 27.5 cm - 5
Question 5. In triangle OAB, overrightarrowOA=mathbfa and overrightarrowOB=mathbfb. P lies on AB with AP:PB=3:1. Find overrightarrowOP in terms of mathbfa and mathbfb.
[3 marks]Vector Ratio Problems▶ Show worked answerHide worked answer
- M1: overrightarrowAB=mathbfb-mathbfa
- M1: overrightarrowOP=mathbfa+3/4(mathbfb-mathbfa)
- A1: 1/4mathbfa+3/4mathbfb
Answer: overrightarrowOP=1/4mathbfa+3/4mathbfb
Mixed Topic Worksheet Grades 8/9: Day 017
- 1
Question 1. Without a calculator, work out the exact value of tan 135^° + sin 210^°
Calculating Values of Trig Functions Using Graphs▶ Show worked answerHide worked answer
- M1: tan 135^° = -1 and sin 210^° = -dfrac12
- A1: -dfrac32
Answer: -dfrac32[2 marks] - 2
Question 2. P(3, -5) lies on y = f(x)
Write down the image of P on y = -f(x), on y = f(-x) and on y = -f(-x)Reflections in the x- & y-Axes▶ Show worked answerHide worked answer
- B1: (3, 5) on y = -f(x)
- B1: (-3, -5) on y = f(-x)
- B1: (-3, 5) on y = -f(-x)
Answer: (3, 5); (-3, -5); (-3, 5)[3 marks] - 3
Question 3. A car travels dfracx² - 4x + 5 km in dfracx - 2x² + x - 20 hours
Find an expression for its average speed in km/h
Give your answer in its simplest formMultiplying & Dividing Algebraic Fractions▶ Show worked answerHide worked answer
- M1: speed = dfracx² - 4x + 5 ÷ dfracx - 2(x + 5)(x - 4)
- M1: dfrac(x - 2)(x + 2)x + 5 × dfrac(x + 5)(x - 4)x - 2
- A1: (x + 2)(x - 4)
Answer: (x + 2)(x - 4) km/h[3 marks] - 4
Question 4. The histogram shows the lengths, x cm, of some leaves.
Work out an estimate for the mean length.
Use the midpoint of each class.Interpreting Histograms▶ Show worked answerHide worked answer
- M1: 2 × 10, 1.5 × 20, 3 × 10, 1 × 20 (at least two correct)
- M1: 5 × 20 + 20 × 30 + 35 × 30 + 50 × 20
- M1: divide by 20 + 30 + 30 + 20
- A1: 27.5
Answer: 27.5 cm[4 marks] - 5
Question 5. In triangle OAB, overrightarrowOA=mathbfa and overrightarrowOB=mathbfb. P lies on AB with AP:PB=3:1. Find overrightarrowOP in terms of mathbfa and mathbfb.
Vector Ratio Problems▶ Show worked answerHide worked answer
- M1: overrightarrowAB=mathbfb-mathbfa
- M1: overrightarrowOP=mathbfa+3/4(mathbfb-mathbfa)
- A1: 1/4mathbfa+3/4mathbfb
Answer: overrightarrowOP=1/4mathbfa+3/4mathbfb[3 marks]