Post on 08-Feb-2023
HIGHER MATHS
PRELIM REVISION
2019-20 Differentiation
Functions
Straight Line
Vectors
Polynomials
Quadratics
Differentiation Higher Maths Exam Questions Source: 2019 P1 Q1 Higher Maths (1)
Answers: π₯π₯ = 0 ππππππ 3
Source: 2019 P2 Q7b Higher Maths (2)
Answers: (ππ) β 6(π₯π₯ β 2)2 β 1 (ππ)
Source: 2018 P2 Q3 Higher Maths (3)
Answer:
Source: 2018 P2 Q9 Higher Maths (4)
Answer: ππππππππππππππ π£π£πππ£π£πππ£π£ ππππ ππ = 32
Source: 2017 P1 Q8 Higher Maths (5)
Answer: π₯π₯ = β 150
Source: 2017 P2 Q4 Higher Maths (6)
Answers: (ππ) 3(π₯π₯ + 4)2 + 2 (ππ) 3π₯π₯2 + 24π₯π₯ + 50 (c)
Source: 2017 P2 Q7 Higher Maths (7)
Answers: (ππ) π₯π₯ = 4 (ππ) πΊπΊπΊπΊπ£π£πππΊπΊπ£π£πΊπΊπΊπΊ = 8, πΏπΏπ£π£πππΊπΊπΊπΊ = 0
Source: 2016 P1 Q2 Higher Maths (8)
Answer: ππππππππ
= 36π₯π₯2 + 4π₯π₯β12
Source: 2016 P1 Q9 Higher Maths (9)
Answers: (ππ) π₯π₯ = β4, 2 (ππ) π₯π₯ < β4, π₯π₯ > 2
Source: 2015 P1 Q2 Higher Maths (10)
Answer: π¦π¦ = 24π₯π₯ + 35
Source: 2015 P1 Q7 Higher Maths (11)
Answer: 9 18
Source: Specimen P1 Q11 Higher Maths (12)
Answers: (ππ) ππ = ππβ²(π₯π₯) β₯ 0 (ππ)
Source: Exemplar P1 Q1 Higher Maths (13)
Answer: π¦π¦ β 12 = 6(π₯π₯ β 5)
Source: Exemplar P2 Q10 Higher Maths (14)
Answers:
Source: 2014 P2 Q2 Higher Maths (15)
Answer: π¦π¦ β 5 = 8(π₯π₯ β 2)
Optimisation Higher Maths Exam Questions
Source: 2019 P2 Q11 Higher Maths (1)
Answers: (ππ) ππππππππππ (ππ) ππππππππππππππ π£π£πππ£π£πππ£π£ ππππ π΄π΄ = 1200
Source: 2016 P2 Q7 Higher Maths (2)
Answers: (ππ) ππππππππππ (ππ) π₯π₯ = 4
Source: Specimen P2 Q8 Higher Maths (3)
Answers: (ππ) ππππππππππ (ππ) ππ = 2.20 ππ
Source: Exemplar P2 Q9 Higher Maths (4)
Answers: (ππ) π₯π₯ = 4 ππππ (ππ) ππππ ππππ Β£198 > Β£195
Source: 2010 P2 Q5 Higher Maths (5)
Answers: (ππ) (ππ) ππππ = 6 β π₯π₯2 (ππππ) ππππππππππ
(ππ) πππππ₯π₯ππππππππ πππππ£π£ππ = 8β2 (β 11.3) πππ π πππππππ£π£ πππππππ’π’ππ
Source: 2008 P2 Q6 Higher Maths (6)
Answers: (ππ) ππππππππππ
(ππ) ππ(32 , 3)
Source: 2004 P2 Q9 Higher Maths (7)
Answers: (ππ) ππππππππππ (ππ) π₯π₯ = β2 πππππππ’π’ππ
Source: 2003 P2 Q8 Higher Maths (8)
Answers: (ππ) ππππππππππ (ππ) π₯π₯ = 60
Source: 2002 P2 Q10 Higher Maths (9)
Answers:
(ππ) (ππ) ππππππππππ
(ππππ) ππ =35
(8 β ππ) π£π£π£π£ππππππππππ π’π’ππ π΄π΄ =34ππ
(8 β ππ)
(ππ) ππ = 4
Functions & Graphs Higher Maths Exam Questions
Source: 2019 P1 Q10 Higher Maths (1)
Answers: (ππ) ππ = 3 (ππ) ππ = β2
Source: 2019 P1 Q12 Higher Maths (2)
Answers: (ππ) 1οΏ½5βπ₯π₯
οΏ½πποΏ½ π₯π₯ β₯ 5
Source: 2019 P2 Q5 Higher Maths (3)
Answer:
Source: 2019 P2 Q12 Higher Maths (4)
Answers: ππ = 14
ππ = 64
Source: 2018 P1 Q2 Higher Maths (5)
Answer: ππβ1(π₯π₯) = 5(π₯π₯ + 4)
Source: 2018 P1 Q15 Higher Maths (6)
Answer:
Source: 2018 P2 Q6 Higher Maths (7)
Answers: (ππ) (ππ) 3 + ππππππ2π₯π₯ (ππππ) 2(3 + πππππππ₯π₯) (ππ) π₯π₯ = ππ
Source: 2017 P1 Q1 Higher Maths (8)
Answers: (ππ) 10 (ππ) 2ππππππ5π₯π₯
Source: 2017 P1 Q6 Higher Maths (9)
Answer: ββ1(π₯π₯) = βπ₯π₯ β 73 ππππ (π₯π₯ β 7)13
Source: 2016 P1 Q6 Higher Maths (10)
Answers: (ππ) ππβ1(π₯π₯) = π₯π₯β53
(ππ) ππβ1(7) = 2
Source: 2017 P1 Q15a Higher Maths (11)
Answers: (ππ) ππ = β5 ππ = 3 (ππ) 10 (ππ) β 6
Source: 2016 P1 Q10 Higher Maths (12)
Answer:
Source: 2016 P1 Q12 Higher Maths (13)
Answers: (ππ) ππππππππππ ( ππ) 2(π₯π₯ β 2)2 + 3
Source: 2015 P1 Q4 Higher Maths (14)
Answers: ππ = 3, ππ = 4, ππ = 1
Source: 2015 P1 Q5 Higher Maths (15)
Answers: (ππ) ππβ1(π₯π₯) = 6βπ₯π₯2
= 3 β π₯π₯2
= π₯π₯β6β2
(ππ) π₯π₯
Source: 2015 P2 Q2 Higher Maths (16)
Answers: (ππ)10 + (1 + π₯π₯)(3β π₯π₯) + 2 (ππ) β π₯π₯2 + 2π₯π₯ + 15 (ππ) 5 & β 3
Source: Specimen P1 Q8 Higher Maths (17)
Answers: (ππ) ππππππππππ (ππ) 2(π₯π₯ β 2)2 β 3 (ππ) (2,β3)
(ππ)
Polynomials & Quadratics Higher Maths Exam Questions
Source: 2019 P1 Q2 Higher Maths (1)
Answers: ππ = 3, 7
Source: 2019 P2 Q7 Higher Maths (2)
Answers: (ππ) β 6(π₯π₯ β 2)2 β 1
(ππ)
Source: 2019 P2 Q10 Higher Maths (3)
Answers: (ππ) ππππππ πππ π π π π π βπππ π ππππ πππππ£π£πππππππ£π£π π π π π£π£ ππβπ£π£ππ π π βππ πππππππππππ π ππππππ ππππππππππππ π§π§πππππ£π£
(ππ) (π₯π₯ + 3)(π₯π₯ β 1)(3π₯π₯2 + 4π₯π₯ + 2)
Source: 2018 P1 Q7 Higher Maths (4)
Answers: (ππ) ππ(0, 5) (ππ) π π = 2π₯π₯ + 5 (ππ) ππ(3, 11)
Source: 2018 P2 Q4 Higher Maths (5)
Answer: β3(π₯π₯ + 1)2 + 10
Source: 2018 P2 Q7a Higher Maths (6)
Answers: (ππ) (ππ) ππππππ πππ π π π π π βπππ π ππππ πππππ£π£πππππππ£π£π π π π π£π£ ππβπ£π£ππ πππππππππππ π ππππππ ππππππππππππ π§π§πππππ£π£
(ππππ) (π₯π₯ β 2)(2π₯π₯ β 1)(π₯π₯ + 1)
(ππ) 2ππ3 β 3ππ2 β ππ β 1
(ππ) (ππ) ππ = 12
(ππππ) πΏπΏ = β2
Source: 2018 P2 Q10 Higher Maths (7)
Answers: ππ < 1,ππ > 9 πππππ π β ππππ πππππππ π ππβ π£π£ππ π π ππππππππ π£π£ππ πππππππ π ππ
Source: 2017 P1 Q4 Higher Maths (8)
Answer: ππ = 9
Source: 2017 P2 Q2 Higher Maths (9)
Answers: (ππ) ππππππ πππ π π π π π βπππ π ππππ πππππ£π£πππππππ£π£π π π π π£π£ ππβπ£π£ππ πππππππππππ π ππππππ ππππππππππππ π§π§πππππ£π£
(ππ ) π₯π₯ = β12 , 1, 2
Source: 2016 P1 Q15 Higher Maths (10)
Answers: (ππ) ππ = 4, ππ = β5, ππ = β 112
(ππ) ππ > 9
Source: 2016 P2 Q2 Higher Maths (11)
Answer: ππ < 2
Source: 2016 P2 Q3 Higher Maths (12)
Answers: (ππ) (ππ) ππππππ πππ π π π π π βπππ π ππππ πππππ£π£πππππππ£π£π π π π π£π£ ππβπ£π£ππ πππππππππππ π ππππππ ππππππππππππ π§π§πππππ£π£ (ππππ) π₯π₯ = β1, 2, 3.5 (ππ) (ππ) π΄π΄ (β1, 0) π΅π΅ (2, 0) (ππππ) π΄π΄ππππππ = 27 πππ π πππ π ππ2
Source: 2015 P1 Q3 Higher Maths (13)
Answer: ππππππ πππ π π π π π βπππ π ππππ πππππ£π£πππππππ£π£π π π π π£π£ ππβπ£π£ππ πππππππππππ π ππππππ ππππππππππππ π§π§πππππ£π£ (π₯π₯ + 3)(π₯π₯ β 4)(π₯π₯ β 2)
Source: 2015 P1 Q8 Higher Maths (14)
Answer: 2 < π₯π₯ < 5
Source: Specimen P1 Q4 Higher Maths (15)
Answer: β4 < ππ < 12
Source: Specimen P1 Q7 Higher Maths (16)
Answer: (ππ) ππππππ πππ π π π π π βπππ π ππππ πππππ£π£πππππππ£π£π π π π π£π£ ππβπ£π£ππ πππππππππππ π ππππππ ππππππππππππ π§π§πππππ£π£
(ππ) (π₯π₯ + 1)(π₯π₯ + 3)(π₯π₯ β 4)
Source: Specimen P2 Q3 Higher Maths (17)
Answers: (ππ) ππ = 1, ππ = 4 (ππ) π π = 9(π₯π₯ β 1)
Source: Exemplar P2 Q3 Higher Maths (18)
Answer: β7 < ππ < 5
Source: Exemplar P1 Q2 Higher Maths (19)
Answers: ππ = 1, ππ = β2, ππ = β1
Source: Exemplar P1 Q5 Higher Maths (20)
Answers: (ππ) ππ = β7, ππ = 10 (ππ) π₯π₯ = 1, π₯π₯ = 5, π₯π₯ = β2
Straight Lines Higher Maths Exam Questions
Source: 2019 P1 Q5 Higher Maths (1)
Answers:
(ππ) π΄π΄π΄π΄οΏ½οΏ½οΏ½οΏ½οΏ½β = οΏ½3β63οΏ½ π΄π΄π΅π΅οΏ½οΏ½οΏ½οΏ½οΏ½β = οΏ½
4β84οΏ½ π΄π΄π΄π΄οΏ½οΏ½οΏ½οΏ½οΏ½β =
34π΄π΄π΅π΅οΏ½οΏ½οΏ½οΏ½οΏ½β .
π΄π΄π΄π΄ ππππ ππππππππππππππππ π‘π‘π‘π‘ π΄π΄π΅π΅ (πππ‘π‘πππππ‘π‘ππ πππππππππ‘π‘πππ‘π‘ππ) ππππππ π΄π΄ ππππ ππ πππ‘π‘πππππ‘π‘ππ πππ‘π‘πππππ‘π‘.
ππβπππππππππ‘π‘ππππ π΄π΄,π΄π΄ ππππππ π΅π΅ ππππππ πππ‘π‘ππππππππππππππ.
(ππ) π π πππ‘π‘πππ‘π‘ 3: 4
Source: 2019 P1 Q7 Higher Maths (2)
Answer: π¦π¦ = ββ3π₯π₯ β 4
Source: 2019 P2 Q1 Higher Maths (3)
Answers: (ππ) 3π¦π¦ = βπ₯π₯ β 13 (ππ) π¦π¦ = π₯π₯ β 7 (ππ) (2,β5)
Source: 2018 P1 Q1 Higher Maths (4)
Answer: π¦π¦ = 2π₯π₯
Source: 2018 P1 Q8 Higher Maths (5)
Answer: 60Β° π‘π‘ππ ππ3
Source: 2017 P1 Q7 Higher Maths (6)
Answer: π₯π₯ = 2
Source: 2017 P1 Q11 Higher Maths (7)
Answer: ππ = 10
Source: 2015 P1 Q9 Higher Maths (8)
Answer: ππππππ = ββ3 ππππππ ππππππ = β 1β3
π‘π‘βπππππππ‘π‘ππππ πππ‘π‘πππππ‘π‘ππ ππππππ πππ‘π‘π‘π‘ πππ‘π‘ππππππππππππππ
Source: 2018 P2 Q5a,b Higher Maths (9)
Answers: (ππ) π¦π¦ = π₯π₯ β 5 (ππ) π΅π΅(10, 5) (ππ) (π₯π₯ β 10)2 + (π¦π¦ β 5)2 = 50
Source: 2017 P2 Q1 Higher Maths (10)
Answers: (ππ) π¦π¦ = 3π₯π₯ β 19 (ππ) π¦π¦ = π₯π₯ β 3 (ππ) (8, 5)
Source: 2016 P1 Q1 Higher Maths (11)
Answer: π¦π¦ + 4π₯π₯ = β5
Source: 2016 P2 Q1 Higher Maths (12)
Answers: (ππ) (ππ) ππ(2, 4) (ππππ) π¦π¦ = 4π₯π₯ β 6 (ππ) π¦π¦ = βπ₯π₯ + 6 (ππ) πππ‘π‘βππππ πππππ‘π‘βπ‘π‘ππππ π£π£ππππππππ β ππππππ ππππππππππππππ ππππβππππππ
Source: 2015 P2 Q1 Higher Maths (13)
Answers: (ππ) πππππ‘π‘π‘π‘ππ (ππ) π¦π¦ = 2π₯π₯ β 3 (ππ) (1, β1)
Source: Specimen P1 Q2 Higher Maths (14)
Answers: (β1, 0) (0, 4) (3, 16)
Source: Specimen P1 Q5 Higher Maths (15)
Answers: (ππ) ππ = ββ3 (ππ) π΄π΄ππππππππ = 2ππ3
π‘π‘ππ 120Β°
Source: Specimen P1 Q9 Higher Maths (16)
Answers: (ππ) π¦π¦ β 10 = β3(π₯π₯ + 1) (ππ) π΄π΄ (3, β2)
Source: Exemplar P1 Q6 Higher Maths (17)
Answers: (ππ) π¦π¦ β 3 = 13
(π₯π₯ β 1) (ππ) π¦π¦ + 2 = β3(π₯π₯ β 1)
(ππ) π₯π₯ = β12
, π¦π¦ =52
(ππ)οΏ½52
=β10
2= β2.5
Vectors Higher Maths Exam Questions Source: 2019 P1 Q9 Higher Maths (1)
Answers: (ππ)(ππ) 2ππ2 + 16ππ + 30 (ππππ) ππ = β5 & β 3 (ππ) ππ = β32
Source: 2019 P2 Q3 Higher Maths (2)
Answers: (ππ) π΅π΅π΅π΅οΏ½οΏ½οΏ½οΏ½οΏ½β = βππ + ππ (ππ) π΅π΅πΈπΈοΏ½οΏ½οΏ½οΏ½οΏ½β = ππ β ππ + 34ππ ππππ ππππππππππππππππππππ
Source: 2019 P2 Q14 Higher Maths (3)
Answer: π΄π΄πππ΄π΄ππππ = 75.5Β° ππππ 1.31 ππππππππππππππ
Source: 2018 P1 Q5 Higher Maths (4)
Answers: (ππ) π π ππππππππ 4: 1 (ππ) ππ = 8
Source: 2018 P1 Q12 Higher Maths (5)
Answers: (ππ) οΏ½6β3
4 + πποΏ½ (ππ) ππ = β2, β6
Source: 2018 P1 Q9 Higher Maths (6)
Answers: (ππ) π΅π΅π΅π΅οΏ½οΏ½οΏ½οΏ½οΏ½β = βππ + ππ (ππ) πππποΏ½οΏ½οΏ½οΏ½οΏ½οΏ½β = β12ππ β 1
2ππ + ππ
Source: 2018 P2 Q2 Higher Maths (7)
Answers: (ππ) ππ.ππ = 24 (ππ) 66.38Β° ππππ 1.16 ππππππππππππππ
Source: 2017 P1 Q5 Higher Maths (8)
Answers: (ππ) ππ. ππ = 1 (ππ) ππ.π€π€ = 4.5
Source: 2016 P1 Q7 Higher Maths (9)
Answers: (ππ) ππ.ππ = 24 (ππ) 66.38Β° ππππ 1.16 ππππππππππππππ
Source: 2017 P2 Q5 Higher Maths (10)
Answers: (ππ) β 3ππ β 4ππ + 5ππ (ππ)ππππππππππ (ππ) 45.6Β° ππππ 0.795 ππππππππππππππ
Source: 2016 P1 Q11 Higher Maths (11)
Answers: (ππ) π΅π΅ (2, 1, 0) (ππ) ππ = 19
Source: 2016 P2 Q5 Higher Maths (12)
Answers: (ππ) π΄π΄π΅π΅οΏ½οΏ½οΏ½οΏ½οΏ½β = οΏ½β8162οΏ½ π΅π΅π΅π΅οΏ½οΏ½οΏ½οΏ½οΏ½β = οΏ½
β2β816οΏ½ (ππ) 104.3Β° ππππ 1.82 ππππππππππππππ
Source: 2015 P1 Q1 Higher Maths (13)
Answer: ππ = 9
Source: 2015 P2 Q6 Higher Maths (14)
Answers: (ππ) ππ. (ππ + ππ) = 4.5 (ππ) π΅π΅π΅π΅οΏ½οΏ½οΏ½οΏ½οΏ½β = βππ + ππ + ππ (ππ) 3β3ππππππ30
Source: Specimen P1 Q3 Higher Maths (15)
Answer: ππ (5, 25, β2)
Source: Specimen P2 Q1 Higher Maths (16)
Answers: (ππ) π΅π΅ (45, 45, 40) πΈπΈ (60, 40, 0) (ππ) π΅π΅πποΏ½οΏ½οΏ½οΏ½οΏ½οΏ½β .π΅π΅πΈπΈοΏ½οΏ½οΏ½οΏ½οΏ½β = β1750 (ππ) 154Β°
Source: Specimen P2 Q6 Higher Maths (17)
Answer: π₯π₯ = β3
Source: Exemplar P2 Q5 Higher Maths (18)
Answers: (ππ) πππ΅π΅οΏ½οΏ½οΏ½οΏ½οΏ½β = 4ππ + 4ππ (ππ) πππ΅π΅οΏ½οΏ½οΏ½οΏ½οΏ½οΏ½β = οΏ½22β6
οΏ½ πππποΏ½οΏ½οΏ½οΏ½οΏ½οΏ½β = οΏ½0β2β6
οΏ½ (ππ) 40.3Β° ππππ 0.703 ππππππππππππππ
Source: Exemplar P2 Q6 Higher Maths (19)
Answer: ππ. (ππ + ππ + ππ) = 272