GR 10 MATHS EXAM MEMOS

Transcription

1 NATINAL EXEPLAR PAPER.. (m - n)(m - 6mn - n ).. m - 6m n - mn - m n + mn + n m - 8m n + mn + n ( + )( - + ) ( - + ) GR 0 ATHS EXA ES ( + )( - ) ( + ) ( + ) - ( - ) ( - )( + ).. a + a - ab - b a(a + ) - b(a + ) (a + )(a - b). 9 < < 6... i.e. lies between 9 and 6 â 7 < < 8 i.e.... taking the square root lies between 7 and 8. Let iii 0, â 0, ➊ % 000) â 000, ➋ ➋ - ➊: â 999 â i.e. can be epressed as a b where a & b Z â is a rational number.. - â â ( + )( - 7) 0 â + 0 or â ) â ( ) â ( ) â â 6 â 7.. Grade 0 aths Eam emos: Paper S R % S) â SR ) â SR Square: â 9 S R. 6q + 7p... ➊ q + p ➋ % : 6q + p ➊ - ➌: â p - â p - ➋: â q - â q 8 â q.. The st terms: () + ; () ; () - 7 â 0 ; 6 ;.. The difference is - â In T n an + b: a - & T 0 b... â T n - n +... ➋... ➌ the term before the st term Copright The Answer EXA ES: PAPER

2 Grade 0 Eam emos: Paper.. n? if T n < - â - n + < - â - n < - (- ) â n > â The th term. The even numbers: 6 ; ; 8... â The th even number % 6 78 R: The th even number the 6 th term of the pattern 6 % 78.. The amount of interest The total amount paid over the 8 months the loan amount R6 06,88 R 99 R67,88. 8, g is worth $978, R978, % 8,79 R8 99,6 â g is worth â kg is worth R8 99,6 8, 8 99,6 R % kg 000 g 8, l R0 7,6.. (a) n(l or S) â P(L or S) 0 (b) n(r and S)... â P(R and S) where R is the set of all right-handed people EXA ES: PAPER. P 00; i, 00 Copright The Answer 0,0; n 0 ; A? A P( + i) n 00( + 0,0), R 99,7.. The loan amount R R600 R 99 The accumulated amount, A P( + in) where P 99; i 8% 0,08; n ears; A? â A 99 + (0,08)( ) R6 06,88 â The monthl amount to be paid 6 06,88 8 R,9.. A B R: A and B.. A R: not A. Set B.. f the 0 learners, 7 are left-handed â 0-7 are right-handed.. f the 8 learners who pla soccer, are left-handed â learners who pla soccer are right-handed â The number of learners who are right-handed and DN'T pla soccer - 9 L 7 - n(class) S f : + -intercept ( 0): none -intercept ( 0): + 0 g : - - -intercept ( 0): - - â - â - -intercept ( 0): Note: We can onl know that the graphs intersect once Question 6. has been done! â - â - f

3 6. Asmptotes: & 0 (the -ais) 6. Domain of f : 0; R... (- ; 0) (0; ) 6. f() g() % ) â â â ( + )( + ) 0 â + 0 or + 0 â - â g() < â - Note: These are the -coordinates of the points of intersection of f and g: -- ; - & (-- ; -) â <... g() - - add : â - < 7 (-): â - > â - 7 < -... i.e. - < - R: 6.6 k() g() (- - ) â The equation of k: When one divides b a negative number, the direction of the 'inequalit' changes. the inequalit has been rewritten with the smaller value on the left â The -intercept of k: (0; -8)... - ; - ( means ecluding ; ] means including substitute intercept of g: (-; 0) & -intercept of h: (; 0) -intercept of g: (0; - ) & -intercept of h: (0; - ) Notice: The reflected points have the same -coordinate, but the -coordinates are opposite in sign. 7. C(-; 0)... smmetrical about the -ais 7. The equation of f: a( + )( - )... roots â a( - & - ) Subst. B -; : â a(-) - â a() ) â a â The equation of f: ( - ) â - 7. The -intercept of f is (0; -) â The range of f: - (-; 0) (; 0) (0; - ) R: [-; ) Graphs are easier than ou thought! The Answer Series offers ecellent material in several subjects for Gr 0 -. See our website g h Grade 0 Eam emos: Paper 7. The graph of h is obtained b f flipping f... -f() then, shifting down - units... - â The range of h: 0 R: (- ; 0] R: h() â h() â h() - â The range of h: 0 7. q -... range > - - is an asmptote â Equation of g: b - ; b > 0 Substitute A(; 0): 0 b - â b â b... b - ä b > 0 â Equation of g: g h â means therefore ä means because Copright The Answer f A(; 0) h - EXA ES: PAPER

4 Grade 0 Eam emos: Paper NATINAL EXEPLAR PAPER. 00 < (- ) + (- 8) ;. The mean, n i i n 99 9 l 8,89... total number of scores total number of das The sum of... the products of the frequenc and the mid-value for each interval. Estimated mean, X * The sum of the frequencies * + 8 % % 00 â - ; - G D(-; ) F(-; k) E(; -) (Q ) (Q ). ; ; ; 6; 7; 9; 0; ; 6; 6; 8; (Q ) ; 6; 60; 6; 6; 6; 66; 7 The median (Q ) 6. The lower quartile (Q ) 7 The upper quartile (Q ) l 8 908,9 kg. The estimated mean X n fi i i n fi i This value is at the centre of the set, whereas the modal class is an etreme situation in relation to the other intervals... DEFG will be a m if is the midpoint of EG too. & Since DEF ˆ 90º, DEFG will be a rectangle.... if one ø of a m is a right ø, then the m is a rectangle.. in value & a value DE ( + ) + (- - ) â DE 0 units G + G + (-) - and - % ) â G + - â G - - â G -7 â G 0 EXA ES: PAPER 0 Copright The Answer ur solutions are set out in such a wa as to promote thorough understanding and logic! We trust that this package will help ou grow in confidence as ou prepare for our eams. The Answer Series stud guides have been the ke to eam success for man learners. Visit our website to find appropriate resources for our success! Gradient of DE, m DE m EF k + -- k + - DEF ˆ 90º m EF + â k + - % (-) â k + - â k EF DE â G(-7; 0) R: The translation F to G equals that of E to D â G(- - 6; ) â G(-7; 0) R: The translation D to G equals that of E to F â G(- - ; - ) â G(-7; 0)

5 . CD ( - ) + ( + ) ( ) D(; ) Note: must be negative. â ( - ) + 9 But < 0 in the second quadrant â ( - ) â - ± â or - â -... onl the neg. value of is valid AB.. sin C AC.. cot A AB BC C(; -) Note: tan A BC AB ; cot A tan A.. sin θ cosec θ â cosec θ cos ) â cos.. tan, ( 0,6) â l,º... cos - â 9,98 º... tan -,9 ) â l,0º Grade 0 Eam emos: Paper.. DS DK SK,8 km 8 km 7,8 km.. tan ˆ JSD 6.. 7,8 â JSD ˆ l 0,º... tan - 7,8 correct to dec. place The epression %... 60º 0º º The denominator must be rationalised º.. sec + ) â sec 8 ) â sec â cos 60º... cos -.. ˆ JKD 8º... alternate ø's; lines - - (0º; 0) º (80º; 0) 70º (60º; 0)... %.. P units... : : Δ ; Pthagoras P(-; ) (-) θ â cos θ cos θ r R.. In ΔJDK: DK cot 8º... % ) â DK tan 8º, km 76,8 metres tan 8º l 77 metres... correct to the nearest metre tan 6.. a 90º 70º g() a sin g(90º) a sin 90º a 6.. The range of h: the values of Copright The Answer EXA ES: PAPER

6 Grade 0 Eam emos: Paper 7. 0,8 m 0,8 B G C H, D F m E 7.. AH 0,8 +,,89 A â AH l,7 m 0,8 m A 7.. : 8 : New volume riginal volume 7.. Volume of silver π(8 + ) - π(8) , l 908,97 mm π ( r) πr r r 8 The volume of silver covering the ball 9. In ΔDBA: diagonals of m BCDE is the midpt of BD... bisect each other & F is the midpt of AD... â F AB AE D... opp. sides of m ADE â AE B and F AB... proven above diagonals of m ADE bisect each other the line joining the midpoints of two sides of a Δ is to the rd side EXA ES: PAPER J, m H R: Pthag. triple: 8 : : 7 0,8 :, :,7 7.. Surface area of roof A % area of ΔABC % ()(,7),7 m B 0, m H m C 7.. Surface area of the walls % area of GFEC % ()(,), m â The total surface area of the tent 0, +,, m 7.. Volume πr π(8) l,66 mm Copright The Answer 8. Q cm ˆ PQ 90º ˆ QP 0º C â ˆ QPS 0º the longer diagonal of a kite bisects the shorter diagonal the diagonals of a kite intersect at right angles the longer diagonal of a kite bisects the (opposite) angles of a kite Hint: Use hiliters to mark the various ms and Δ s B Geometr is easier than ou thought! The Answer Series offers ecellent material (especiall Geometr) for Gr 0 -. See our website A D F 6 E The hilited Δ s (and their sides) refer to Question 9.. â E AB â ABE is a m... R: In m ADE: AE and D... But D and B... â AE and B â ABE is a m In Δ s AB and ED ) AB E... opposite sides of m ABE ) B D... proved in 9. ) A ED... opposite sides of m ADE â ΔAB ΔED... SSS both pairs of opposite sides are parallel opp. sides of m proved midpt of BD in 9. pr of opp. sides and