Mathematics Grade 10 P1 November Mock 2026 Memo (English)

hlayiso mock exams Practice Series: Grade 10 Exam Preparation WWW.HLAYISO.COM NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 NOVEMBER EXAMINATION 2026 (MOCK) MARKING GUIDELINES MARKS: 100 These marking guidelines consist of 9 pages. Copyright reserved Please turn over

Mathematics/P1 2 Hlayiso/Mock 2026 NSC – Marking Guidelines NOTE: • If a candidate answers a question TWICE, only mark the FIRST attempt. • If a candidate has crossed out an attempt of a question and not redone the question, mark the crossed-out version. • Consistent accuracy (CA) applies in ALL aspects of the marking guidelines. Stop marking at the second calculation error. • Assuming answers/values in order to solve a problem is NOT acceptable. • The mark for substitution is awarded for substitution into the correct formula. QUESTION 1 √ √ √ √ √ 1.1 49 < 58 < 64 ✓ 49 and 64 √ 7√< 58 < 8 ✓ 7 and 8 (2) 58 lies between 7 and 8. 1.2.1 = 2x3 + 2x2 − 8x − 3x2 − 3x + 12 ✓ 2x3 + 2x2 − 8x = 2x3 − x2 − 11x + 12 ✓ −3x2 − 3x + 12 ✓ answer (3) (x − 3)(x + 3) 2(x − 2) 1.2.2 = × ✓ (x − 3)(x + 3) (x + 3)(x − 2) x−3 ✓ (x + 3)(x − 2) =2 ✓ 2(x − 2) ✓ answer (4) 3x .32 − 3x 1.2.3 = ✓ splitting the powers 4 . 3x .3−1 ✓ common factor 3x (9 − 1) 3x (9 − 1) = ✓ answer (3) 4 . 3x . 13 8 = 4 =6 3 1.3.1 (2x − 5)(x + 3) ✓ (2x − 5) ✓ (x + 3) (2) 1.3.2 = (x − 3)(x2 + 3x + 9) + 2(x − 3) ✓ (x − 3)(x2 + 3x + 9) = (x − 3)(x2 + 3x + 9 + 2) ✓ +2(x − 3) = (x − 3)(x2 + 3x + 11) ✓ answer (3) [17] Copyright reserved Please turn over

Mathematics/P1 3 Hlayiso/Mock 2026 NSC – Marking Guidelines QUESTION 2 2.1.1 3x2 − 5x − 2 = 0 ✓ standard form (3x + 1)(x − 2) = 0 ✓ factors 1 ✓ both answers (3) x=− or x = 2 3 4 1 2.1.2 5x+1 = = = 5−2 ✓ 25 1 100 25 x + 1 = −2 ✓ 5−2 / equating exponents x = −3 ✓ answer (3) 2.2 −4 − 2 < −3x ≤ 11 − 2 ✓ subtracting 2 −6 < −3x ≤ 9 ✓ dividing by −3 and 2 > x ≥ −3 reversing signs −3 ≤ x < 2 ✓ −3 ≤ x < 2 −4 −3 −2 −1 0 1 2 3 ✓ number line (closed dot at −3, open dot at 2) (4) 2.3 x = 14 + 4y …(1) ✓ x the subject 3(14 + 4y) + 2y = 7 ✓ substitution 42 + 12y + 2y = 7 14y = −35 5 ✓ y = − 25 y=− 2 ( ) ✓x=4 (4) 5 x = 14 + 4 − =4 2 OR (elimination): (1) × 2: 6x + 4y = 14; add to x − 4y = 14: 7x = 28 … [14] QUESTION 3 3.1.1 21 ; 25 ✓ both terms (1) 3.1.2 d=4 ✓ 4n Tn = 4n + 1 ✓ +1 (2) 3.1.3 T40 = 4(40) + 1 = 161 ✓ substitution ✓ answer (2) Copyright reserved Please turn over

Mathematics/P1 4 Hlayiso/Mock 2026 NSC – Marking Guidelines 3.1.4 4n + 1 = 297 ✓ equating 4n = 296 ✓ answer (2) n = 74 ∴ the 74th term 3.2.1 4 ; 7 ; 10 ; 13 ; 16 ✓ answer (1) Diagram 5 needs 16 matches. 3.2.2 d=3 ✓ 3n Tn = 3n + 1 ✓ +1 (2) 3.2.3 3n + 1 ≤ 150 ✓ 3n + 1 ≤ 150 (or = 150) 149 n≤ = 49,67 3 ✓ Diagram 49 Largest diagram: Diagram 49 T49 = 3(49) + 1 = 148 matches ✓ 2 matches (3) 150 − 148 = 2 matches left over [13] Copyright reserved Please turn over

Mathematics/P1 5 Hlayiso/Mock 2026 NSC – Marking Guidelines QUESTION 4 4.1.1 A = P(1 + ni) ✓ substitution A = 12 000(1 + 4 × 0,085) ✓ answer (2) A = R16 080 4.1.2 A = P(1 + i)n ✓ substitution A = 12 000(1 + 0,078)4 ✓ answer (2) A = R16 205,27 4.1.3 Option B, because it gives the greater amount after 4 ✓ option with reason (1) years (R125,27 more). 4.2 Deposit = 10% × 9 600 = R960 Balance = 9 600 − 960 = R8 640 ✓ R8 640 A = 8 640(1 + 3 × 0,14) = R12 268,80 ✓ substitution 12 268,80 ✓ R12 268,80 Monthly instalment = = R340,80 ✓ answer (4) 36 4.3 A = 32,99(1 + 0,052)4 ✓ substitution A = R40,41 ✓ answer (2) [11] Copyright reserved Please turn over

Mathematics/P1 6 Hlayiso/Mock 2026 NSC – Marking Guidelines QUESTION 5 5.1 TP B(0 ; 8): q = 8 ✓q=8 f (x) = ax2 + 8 Subst. A(4 ; 0): 0 = a(4)2 + 8 ✓ substitution of A 16a = −8 1 ✓ 16a = −8 (3) a=− 2 4−0 5.2 m= = −1; c=4 ✓ m = −1 0−4 ✓ c = 4 / equation (2) g(x) = −x + 4 1 5.3 − x2 + 8 = −x + 4 ✓ equating 2 ✓ standard form x2 − 2x − 8 = 0 ✓ x = −2 (x − 4)(x + 2) = 0 x = −2 (x = 4 at A) ✓y=6 (4) y = −(−2) + 4 = 6 E(−2 ; 6) 5.4 y ≤ 8 OR y ∈ (−∞ ; 8] ✓ answer (1) 5.5 x<0 OR x ∈ (−∞ ; 0) ✓ answer (1) 5.6 −2 ≤ x ≤ 4 ✓ critical values ✓ notation (2) 1 5.7.1 h(x) = − x2 + 5 ✓ answer (1) 2 5.7.2 y ≤ 5 OR y ∈ (−∞ ; 5] ✓ answer (1) [15] Copyright reserved Please turn over

Mathematics/P1 7 Hlayiso/Mock 2026 NSC – Marking Guidelines QUESTION 6 6.1 x=0 and y = 2 ✓x=0 ✓y=2 (2) 6 6.2 0= +2 ✓ f (x) = 0 x −2x = 6 ✓ (−3 ; 0) (2) x = −3 (−3 ; 0) 6.3 y ✓ horizontal asymptote y = 2 ✓ x-intercept (−3 ; 0) ✓ shape (both branches in correct quadrants relative to asymptotes) (3) y=2 x (−3 ; 0) O No y-intercept: the graph does not cut the y-axis. 6.4 x ∈ R, x ̸= 0 ✓ answer (1) [8] QUESTION 7 7.1 q = −3 ✓ answer (1) 7.2 Subst. P(2 ; 6): 6 = b2 − 3 ✓ substitution b2 = 9 ✓ b2 = 9 (2) b = 3 (b > 0) 7.3 0 = 3x − 3 ✓ 3x = 3 3x = 31 ✓ (1 ; 0) (2) x=1 (1 ; 0) Copyright reserved Please turn over

Mathematics/P1 8 Hlayiso/Mock 2026 NSC – Marking Guidelines 7.4 y > −3 OR y ∈ (−3 ; ∞) ✓ answer (1) ( )x 1 7.5 h(x) = 3−x − 3 OR h(x) = −3 ✓ answer (1) 3 [7] QUESTION 8 8.1.1 P(A or B) = P(A) + P(B) − P(A and B) ✓ substitution 0,75 = 0,35 + 0,4 − P(A and B) P(A and B) = 0 ✓ P(A and B) = 0 (2) ∴ A and B are mutually exclusive. 8.1.2 No. ✓ No P(A) + P(B) = 0,75 ̸= 1 (the events are not ✓ reason (2) exhaustive) 8.2.1 S ✓ x in the intersection T C ✓ 70 − x and 45 − x ✓ 25 outside the circles (3) 70 − x x 45 − x 25 8.2.2 (70 − x) + x + (45 − x) + 25 = 120 ✓ sum of regions = 120 140 − x = 120 ✓ 140 − x = 120 (2) x = 20 8.2.3(a) n(T only) = 70 − 20 = 50 ✓ 50 50 5 ✓ answer (2) P(T only) = = (or 0,42) 120 12 8.2.3(b) n(not choir) = 120 − 45 = 75 ✓ 75 75 5 ✓ answer (2) P(not choir) = = (or 0,625) 120 8 28 8.3.1 Relative frequency = = 0,35 ✓ answer (1) 80 Copyright reserved Please turn over

Mathematics/P1 9 Hlayiso/Mock 2026 NSC – Marking Guidelines 8.3.2 0,35 × 200 = 70 times ✓ answer (1) [15] TOTAL: 100 Copyright reserved