Mathematics Grade 10 Gauteng March Test 2023 Paper & Memo

Downloaded from Stanmorephysics.com REPUBLIC OF SOUTH AFRICA SEER: ecncncooremmen —— DEPARTMENT OF EDUCATION SEKHUKHUNE SOUTH DISTRICT GRADE 10 MATHEMATICS TEST 1 MARGH. 2023 MARKS : 50 MARKS DURATION: 1 HOUR. This question paper consist of 4 pages including cover page.

Rawnlaadedafrom Stanmoreps&ysics.com March 2023 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions . 1. This question paper consists of 2 questions. 2. Answer all the questions. 3. Clearly show all the calculations, diagrams, graphs, et cetera that you have used in determining your answers. 4, Answers only will not necessarily be awarded full marks. 5. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 6. If necessary, round your answers off to two decimal places, unless stated otherwise. 7. Number your answers correctly according to the numbering system used in this question paper. 8. It is in your best interest to write neatly and legibly. Page 2 of 4

Rawnlaadedafrom Stanmoreps&ysics.com March 2023 QUESTION 1 1.1 Ifx = V2 and y = —2, decide whether the following expressions are rational, irrational or no real 11.1 > xy (1) 1.1.22 (1) x 1.1.3 x? (1) 114 fy (1) 1.2 Expand the following expressions: 1.21 (a—2)(a?+2a+4) (2) 1.2.2 -(2x—5)? (2) 1.2.3 (5 +1 ) (¢ _ 1) (2) 1.3. Simplify completely 13.1 y= 3 — Se_ 4 (4) 2-x x-2 1.3.2 s7choyet (4) 18Y .gy-t 1.3.3 22nte—g2nta (3) qnet 1.4 Factorise the following: 14.1 8x3 +1 (2) 14.2 2x?-x-6 (2) 14.3. a?—2ab— 2b*+ab (3) [28] Page 3 of 4

Rawnlaadedafrom Stanmoreps&ysics.com March 2023 QUESTION 2 2.1 Solve for x : 211 > x%=5x (3) 21.2 p_ we (3) 3S 21.30 (1X1 (3) (3) =27 2.1.4 3(2 — 3x) 215 (4) 2.2. Solve for a and b simultaneously: a+b=12 and4a+ 2b = 44 (5) 2.3. George is 7 times as old as his son. In 25 years’ time he will be twice as old as his son. Calculate his son’s present age. HINT: variable x may be used to develop equations. (4) [22] TOTAL : 50 Page 4 of 4

Downloaded from Stanmorephysics.com REPUBLIC OF SOUTH AFRICA —— DEPARTMENT OF EDUCATION SEKHUKHUNE SOUTH DISTRICT GRADE 10 MATHEMATICS MEMORANDUM MARCH 2023 MARKS: 50 MARKS DURATION: 1 HOUR. This memorandum consist of 6 pages including cover page.

Pawnloadedefxom Stanmorephysics.com March 2023 QUESTION 1 1.1 1.1.1 | Irrational v Irrational (1) 1.1.2 | Irrational v Irrational (1) 1.1.3 | Rational v Rational () 1.1.4 | Non-real v Non-real qd) 1.2 1.2.1 | (a—2)(a? + 2a+4) = a?-8 va v -8 (2) 1.2.2 | —(2x — 5)? = —(4x? — 20x + 25) ¥ 4x? — 20x +25 = —4x? + 20x — 25 v Answer (2) 1.23 y @ 4 a a _@ 2 (F+1)(-1)=9-1 v -1 @ 1.3 13.1 ]),—3 - 58 42, _ 5x-6 _ 4 x—3 lox x2 3+ x-2 0 x-2 __ X(x-2)—-3 (x-2)+5x-6-4 Y LCD: (x _ 2) aa : 2 _ —6—. = xo -2x — 6-4 v Simplifying _ x4 ~~ x=2 _ (&@—2)(x +2) v_ Factors ~ x-2 v =~xy42 Answer (4) Page 2 of 6

Pawnleadedicfnom Stanmorephysics.com March 2023 1.3.2 42Y-1 gVtt (22)? (32)"** v prime bases 187.8Y72 (2.32) (23)7-4 L 24-2 g2yt2 v simplifying ™~ 2y 32¥,23¥-3 = 24Y-2-y-3y +3 32yt2-2y = 2! 32 Y 21,32 v answer =18 (4) 1.3.3 22nt2 _ panti 4nt1 = 222? ~ 2?n20 v prime bases ~ 22n 22 _ 22"( 22-2) = ange ¥ common factor: 22” =*2 ‘ v answer a =5 (3) 1.4 1.4.1 | 8x3 +1 = (2x + 1)(4x? - 2x +1) y 2xt1 Y 4x7-2x41 (2) 1.4.2 | 2x2 —x—6 = (2x + 3)(x — 2) ¥—2x+3 Yix-2 (2) Page 3 of 6

Pawnloadedefxom Stanmorephysics.com March 2023 1.4.3 a* — 2ab — 2b? + ab = (a — 2b) + b(a — 2b) ¥ a(a—2b) ¥ b(a—2b) = (a+ b)(a— 2b) ¥ answer (3) [28] QUESTION 2 2.1 | 2.1.1 |x? =5x x?-— 5x =0 ¥ x?-5x=0 x(x—5)=0 VY x(x-5) =0 x=Oorx=5 Y both x values (3) 2.1.2 2 pal 3S 3RS = 2Vx v multiplying by 3S 3RS Y dividing by 2 = Vx 2 9R?S2 v answer x= 3) 2.1.3 net () 27 (3°1)*"7 = 33 v simplifying 3-*+1 — 33 -x+1=3 ¥-x+1=3 x=-2 v answer (3) Page 4 of 6

Pawnloadedefxom Stanmorephysics.com March 2023 2.1.4 | 3(2—3x) = 15 6—9x 215 simplifying —-9x 29 9x >9 x<-1 -_ answer -1 number line OR 2-3x 25 —3x >3 (4) x<-l 2.2 AtbD=12.. ce (1) 4a + 2b = 44........ (2) From (1) :a=12-—b 4(12 — b) + 2b = 44 48 — 4b + 2b = 44 —2b =—4 OR From (1).....b =12—a 4a + 2(12 — a) = 44 4a+24—2a= 44 2a = 20 a=12-b 4(12 —b) + 2b = 44 48 — 4b + 2b = 44 b=2 a=10 or b=12-a 4a+2(12—a)+ 2b = 44 4a +24—-2a=44 Page 5 of 6

Pawnloadedefxom Stanmorephysics.com March 2023 a=10 Y a=10 b=2 ¥ b=2 (5) 2.3 Son George Now x 7x In 25 years x+25 7x+25 ¥ x+25 Y 7x+25 Equation: 7x +25 = 2(x +25) ¥ 7x +25 =2x+50 7x +25 = 2x+50 ¥ 5x =25 5x = 25 x=5 vy Answer His son is 5 years old . (4) [22] TOTAL: 50 Page 6 of 6