Mixed Topic Worksheet Grades 6/7: Day 057
- 1
Question 1. OABC is a trapezium.
overrightarrowOA = 8mathbfa overrightarrowOC = mathbfb overrightarrowCB = 3mathbfa
Write overrightarrowAB in terms of mathbfa and mathbfb, in its simplest form.Fundamentals of Vector Problems▶ Show worked answerHide worked answer
- M1: overrightarrowAB = overrightarrowAO + overrightarrowOC + overrightarrowCB
- M1: -8mathbfa + mathbfb + 3mathbfa
- A1: -5mathbfa + mathbfb
Answer: -5mathbfa + mathbfb[3 marks] - 2
Question 2. A bat survey ringed 48 bats in a cave and released them.
The next week, 30 bats were caught in the same cave.
4 of these 30 bats had a ring.
Work out an estimate for the number of bats in the cave.Capture-Recapture▶ Show worked answerHide worked answer
- M1: dfrac430 = dfrac48N or 48 × 30 ÷ 4
- A1: 360
Answer: 360[2 marks] - 3
Question 3. Simplify fully dfracx² - 3x - 10x² - 25
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: numerator (x - 5)(x + 2)
- M1: denominator (x - 5)(x + 5)
- A1: dfracx + 2x + 5
Answer: dfracx + 2x + 5[3 marks] - 4
Question 4. The number line shows a set A of real numbers.
Write A in set notation using inequalities.Sets & Inequalities▶ Show worked answerHide worked answer
- M1: lower end 2 is an open circle so x > 2, upper end 8 is closed so x ≤slant 8
- A1: x : 2 < x ≤slant 8
Answer: x : 2 < x ≤slant 8[2 marks] - 5
Question 5. Show that the points A(-6, 8) and B(8, -6) both lie on the circle x² + y² = 100 and that AB is not a diameter of the circle.
General Form of the Equation of a Circle▶ Show worked answerHide worked answer
- M1: (-6)² + 8² = 36 + 64 = 100
- M1: 8² + (-6)² = 64 + 36 = 100, so both points lie on the circle
- C1: the midpoint of AB is (1, 1), not the centre (0, 0) (or the other end of the diameter through A is (6, -8), not B), so AB is not a diameter
Answer: Both give 100; the midpoint of AB is (1, 1), not (0, 0), so AB is not a diameter[3 marks]
Mixed Topic Worksheet Grades 6/7: Day 057
- 1
Question 1. OABC is a trapezium.
[3 marks]
overrightarrowOA = 8mathbfa overrightarrowOC = mathbfb overrightarrowCB = 3mathbfa
Write overrightarrowAB in terms of mathbfa and mathbfb, in its simplest form.Fundamentals of Vector Problems▶ Show worked answerHide worked answer
- M1: overrightarrowAB = overrightarrowAO + overrightarrowOC + overrightarrowCB
- M1: -8mathbfa + mathbfb + 3mathbfa
- A1: -5mathbfa + mathbfb
Answer: -5mathbfa + mathbfb - 2
Question 2. A bat survey ringed 48 bats in a cave and released them.
[2 marks]
The next week, 30 bats were caught in the same cave.
4 of these 30 bats had a ring.
Work out an estimate for the number of bats in the cave.Capture-Recapture▶ Show worked answerHide worked answer
- M1: dfrac430 = dfrac48N or 48 × 30 ÷ 4
- A1: 360
Answer: 360 - 3
Question 3. Simplify fully dfracx² - 3x - 10x² - 25
[3 marks]Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: numerator (x - 5)(x + 2)
- M1: denominator (x - 5)(x + 5)
- A1: dfracx + 2x + 5
Answer: dfracx + 2x + 5 - 4
Question 4. The number line shows a set A of real numbers.
[2 marks]
Write A in set notation using inequalities.Sets & Inequalities▶ Show worked answerHide worked answer
- M1: lower end 2 is an open circle so x > 2, upper end 8 is closed so x ≤slant 8
- A1: x : 2 < x ≤slant 8
Answer: x : 2 < x ≤slant 8 - 5
Question 5. Show that the points A(-6, 8) and B(8, -6) both lie on the circle x² + y² = 100 and that AB is not a diameter of the circle.
[3 marks]General Form of the Equation of a Circle▶ Show worked answerHide worked answer
- M1: (-6)² + 8² = 36 + 64 = 100
- M1: 8² + (-6)² = 64 + 36 = 100, so both points lie on the circle
- C1: the midpoint of AB is (1, 1), not the centre (0, 0) (or the other end of the diameter through A is (6, -8), not B), so AB is not a diameter
Answer: Both give 100; the midpoint of AB is (1, 1), not (0, 0), so AB is not a diameter
Mixed Topic Worksheet Grades 6/7: Day 057
- 1
Question 1. OABC is a trapezium.
overrightarrowOA = 8mathbfa overrightarrowOC = mathbfb overrightarrowCB = 3mathbfa
Write overrightarrowAB in terms of mathbfa and mathbfb, in its simplest form.Fundamentals of Vector Problems▶ Show worked answerHide worked answer
- M1: overrightarrowAB = overrightarrowAO + overrightarrowOC + overrightarrowCB
- M1: -8mathbfa + mathbfb + 3mathbfa
- A1: -5mathbfa + mathbfb
Answer: -5mathbfa + mathbfb[3 marks] - 2
Question 2. A bat survey ringed 48 bats in a cave and released them.
The next week, 30 bats were caught in the same cave.
4 of these 30 bats had a ring.
Work out an estimate for the number of bats in the cave.Capture-Recapture▶ Show worked answerHide worked answer
- M1: dfrac430 = dfrac48N or 48 × 30 ÷ 4
- A1: 360
Answer: 360[2 marks] - 3
Question 3. Simplify fully dfracx² - 3x - 10x² - 25
Simplifying Algebraic Fractions▶ Show worked answerHide worked answer
- M1: numerator (x - 5)(x + 2)
- M1: denominator (x - 5)(x + 5)
- A1: dfracx + 2x + 5
Answer: dfracx + 2x + 5[3 marks] - 4
Question 4. The number line shows a set A of real numbers.
Write A in set notation using inequalities.Sets & Inequalities▶ Show worked answerHide worked answer
- M1: lower end 2 is an open circle so x > 2, upper end 8 is closed so x ≤slant 8
- A1: x : 2 < x ≤slant 8
Answer: x : 2 < x ≤slant 8[2 marks] - 5
Question 5. Show that the points A(-6, 8) and B(8, -6) both lie on the circle x² + y² = 100 and that AB is not a diameter of the circle.
General Form of the Equation of a Circle▶ Show worked answerHide worked answer
- M1: (-6)² + 8² = 36 + 64 = 100
- M1: 8² + (-6)² = 64 + 36 = 100, so both points lie on the circle
- C1: the midpoint of AB is (1, 1), not the centre (0, 0) (or the other end of the diameter through A is (6, -8), not B), so AB is not a diameter
Answer: Both give 100; the midpoint of AB is (1, 1), not (0, 0), so AB is not a diameter[3 marks]