Mixed Topic Worksheet Grades 6/7: Day 001
- 1
Question 1. Solve 5 < 2x - 1 and x + 4 < 12. Write down the values of x that satisfy both inequalities.
Solving Compound Inequalities▶ Show worked answerHide worked answer
- M1: 6 < 2x, so 3 < x
- M1: x < 12 - 4, so x < 8
- A1: 3 < x < 8
Answer: 3 < x < 8[3 marks] - 2
Question 2. Is √0.25 a rational number or an irrational number? You must show your working.
Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: √0.25 = 0.5
- A1: rational, because 0.5 = dfrac12
Answer: Rational, because √0.25 = 0.5 = dfrac12[2 marks] - 3
Question 3. Simplify fully dfrac4x+20x²+5x
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: 4(x+5) or x(x+5)
- M1: cancels the common factor (x+5)
- A1: dfrac4x
Answer: dfrac4x[3 marks] - 4
Question 4. Here is triangle PQR.
Write down an equation, using the sine rule, that could be used to find x.
Do not solve your equation.Fundamentals of the Sine Rule▶ Show worked answerHide worked answer
- M1: dfrac8sin 42^° (the known side with the angle opposite it)
- A1: dfracxsin 65^° = dfrac8sin 42^°
Answer: dfracxsin 65^° = dfrac8sin 42^°[2 marks] - 5
Question 5. The region R satisfies the inequalities
x + y ≤ 9 qquad y > 2x - 6 qquad y ≥ 1
Show that the point (4, 3) is in R.Shading Regions with Graphical Inequalities▶ Show worked answerHide worked answer
- B1: 4 + 3 = 7 ≤ 9
- B1: 2(4) - 6 = 2 and 3 > 2
- B1: 3 ≥ 1, so (4, 3) is in R
Answer: 7 ≤ 9, 3 > 2 and 3 ≥ 1, so (4, 3) is in R[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 001
- 1
Question 1. Solve 5 < 2x - 1 and x + 4 < 12. Write down the values of x that satisfy both inequalities.
[3 marks]Solving Compound Inequalities▶ Show worked answerHide worked answer
- M1: 6 < 2x, so 3 < x
- M1: x < 12 - 4, so x < 8
- A1: 3 < x < 8
Answer: 3 < x < 8 - 2
Question 2. Is √0.25 a rational number or an irrational number? You must show your working.
[2 marks]Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: √0.25 = 0.5
- A1: rational, because 0.5 = dfrac12
Answer: Rational, because √0.25 = 0.5 = dfrac12 - 3
Question 3. Simplify fully dfrac4x+20x²+5x
[3 marks]Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: 4(x+5) or x(x+5)
- M1: cancels the common factor (x+5)
- A1: dfrac4x
Answer: dfrac4x - 4
Question 4. Here is triangle PQR.
[2 marks]
Write down an equation, using the sine rule, that could be used to find x.
Do not solve your equation.Fundamentals of the Sine Rule▶ Show worked answerHide worked answer
- M1: dfrac8sin 42^° (the known side with the angle opposite it)
- A1: dfracxsin 65^° = dfrac8sin 42^°
Answer: dfracxsin 65^° = dfrac8sin 42^° - 5
Question 5. The region R satisfies the inequalities
[3 marks]
x + y ≤ 9 qquad y > 2x - 6 qquad y ≥ 1
Show that the point (4, 3) is in R.Shading Regions with Graphical Inequalities▶ Show worked answerHide worked answer
- B1: 4 + 3 = 7 ≤ 9
- B1: 2(4) - 6 = 2 and 3 > 2
- B1: 3 ≥ 1, so (4, 3) is in R
Answer: 7 ≤ 9, 3 > 2 and 3 ≥ 1, so (4, 3) is in R
Mixed Topic Worksheet Grades 6/7: Day 001
- 1
Question 1. Solve 5 < 2x - 1 and x + 4 < 12. Write down the values of x that satisfy both inequalities.
Solving Compound Inequalities▶ Show worked answerHide worked answer
- M1: 6 < 2x, so 3 < x
- M1: x < 12 - 4, so x < 8
- A1: 3 < x < 8
Answer: 3 < x < 8[3 marks] - 2
Question 2. Is √0.25 a rational number or an irrational number? You must show your working.
Rational & Irrational Numbers▶ Show worked answerHide worked answer
- M1: √0.25 = 0.5
- A1: rational, because 0.5 = dfrac12
Answer: Rational, because √0.25 = 0.5 = dfrac12[2 marks] - 3
Question 3. Simplify fully dfrac4x+20x²+5x
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: 4(x+5) or x(x+5)
- M1: cancels the common factor (x+5)
- A1: dfrac4x
Answer: dfrac4x[3 marks] - 4
Question 4. Here is triangle PQR.
Write down an equation, using the sine rule, that could be used to find x.
Do not solve your equation.Fundamentals of the Sine Rule▶ Show worked answerHide worked answer
- M1: dfrac8sin 42^° (the known side with the angle opposite it)
- A1: dfracxsin 65^° = dfrac8sin 42^°
Answer: dfracxsin 65^° = dfrac8sin 42^°[2 marks] - 5
Question 5. The region R satisfies the inequalities
x + y ≤ 9 qquad y > 2x - 6 qquad y ≥ 1
Show that the point (4, 3) is in R.Shading Regions with Graphical Inequalities▶ Show worked answerHide worked answer
- B1: 4 + 3 = 7 ≤ 9
- B1: 2(4) - 6 = 2 and 3 > 2
- B1: 3 ≥ 1, so (4, 3) is in R
Answer: 7 ≤ 9, 3 > 2 and 3 ≥ 1, so (4, 3) is in R[3 marks]