Tiêu đề 14. Math QandA grade 10-12.pdf ✅

Moonga Stephen 2011 (All rights reserved) 0975414998 1 1. (a) Evaluate. (i) 32 x 33 (ii) 70 x 74 x 7-2 (iii) 53 x 5-1 x 80 (iv) 962 – 16 (v) 52 + 51 (vi) ( ) 3 2 2 x ( ) 3 2 1 x ( ) 3 2 0 (b) Factorize completely 5 – 20x 2 (c) Solve for x, 2x = 8 SOLUTION (a) (i) 32 x 33 (ii) 70 x 74 x 7-2 (iii) 53 x 5-1 x 80 (iv) 962 – 16 = 32+3 = 70+4-2 = 53-1 x 80 = 9216 – 16 = 35 = 72 = 52x 1 = 9200 = 243 = 49 = 25 (v) 52 + 51 (vi) ( ) 3 2 2 x ( ) 3 2 1 x ( ) 3 2 0 = 52+1 = ( ) 3 2 2+1+0 = 53 = 125 = ( ) 3 2 3 = 27 8 (b) 5 – 20x 2 (c) 2x = 8 = 5(1 – 4x 2) 2x = 2 x 2 x2 = 5(1 – 2x)(1 + 2x) 2x = 23 ∴ x = 3 2. (a) Solve the equations, (i) x 2 = 1 5 (ii) 4y2 = 7y (iii) 4(m - 2) - 3 = -26 – m (iv) 3 2x + 4 1 = 8 (v) 2 3t −1 = 1 4 (vi) 2(2x – 5) + 2 = x + 7 (vii) 2x - 6 = 4 - 3(x – 5) (viii) 3 2 = 2r 9 (b) Solve the inequalities; (i) 1- 5 3x < 4 (ii) 3 x + 6 5 3x − 6 SOLUTION (a) (i) x 2 = 1 5 (cross multiply) (ii) 4y 2 = 7y 5x = 2 4y2 - 7y = 0 5 5x = 5 2 y (4y – 7) = 0 x = 5 2 y = 0 or 4y = 7 y = 0 or y = 4 7
Moonga Stephen 2011 (All rights reserved) 0975414998 2 (iii) 4(m - 2) - 3 = -26 – m (iv) 3 2x + 4 1 = 8 (v) 2 3t −1 = 1 4 4m – 8 - 3 = -26 – m 12 8x + 3 = 1 8 3t - 1 = 2 × 4 4m – 11 = -26 – m 8x + 3 = 12 × 8 3t - 1 = 8 4m + m = -26 + 11 8x + 3 = 96 3t = 8 + 1 5m = -15 8x = 96- 3 3t = 9 m = -3 8x = 93 t = 3 x = 8 93 (vi) 2(2x – 5) + 2 = x + 7 (vii) 2x - 6 = 4 - 3(x – 5) (viii) 3 2 = 2r 9 4x – 10 + 2 = x + 7 2x - 6 = 4 - 3x + 15 2 × 2r = 3 × 9 4x – 8 = x + 7 2x + 3x = 4 + 15 + 6 4r = 27 4x – x = 7 + 8 5x = 25 r = 4 27 3 3x = 15 x = 5 x = 5 (b) (i) 1- 5 3x < 4 (ii) 3 x + 6 5 3x − 6 1 1 - 5 3x < 1 4 3 x + 6 5 3x − 6 5 5 − 3x < 1 4 5(x + 6) 3(3x - 6) 5× ( 5 5 − 3x ) < 1 4 ×5 5x + 30 9x - 18 5- 3x < 20 5x - 9x -18 - 30 -3x < 20 – 5 -4x -48 -3x < 15 x 12 x < -5 3. Express each of the following as a fraction in its lowest term. (a) 0.586 (b) 0.06 (c) 0.05 SOLUTION (a) 0.586 (b) 0.06 (c) 0.05 = 1000 586 = 100 6 = 100 5 = 500 243 = 50 3 = 20 1
Moonga Stephen 2011 (All rights reserved) 0975414998 3 4. Express each of the following as a percentage; (a) 20 15 (b) 25 9 SOLUTION (a) = 20 15 (b) = 25 9 = 20 15 × 100% = 25 9 × 100% = 75% = 36% 5. Express each of the following as a single fraction. (a) 3 x + 5 - 4 x + 2 (b) 4 x - 7 x + 14 x (c) 2 7 p − - 1 5 p − (d) 2 3 5 x − - 5 1 x + (e) 2 3 - x x 4 1− 2 (f) 1 3 p − - 1− p 2 (g) 2 1 5 x − - 3 2 7 x − (h) 2 − x 1 - 4 2 x − (i) 3 x −1 - 5 2x − 3 SOLUTION (a) 3 x + 5 - 4 x + 2 (b) 4 x - 7 x + 14 x (c) 2 7 p − + 1 5 p − = 12 4(x + 5) − 3(x − 2) = 28 7x − 4x + 2x = ( 2)( 1 7( 1) 5( 2) − − − + − p p p p = 12 4x + 20 − 3x + 6 = 28 3x + 2x = ( 2)( 1) 7 7 5 10 − − − + − p p p p = 12 4x − 3x + 20 + 6 = 28 5x = ( 2)( 1) 7 5 10 7 − − + − − p p p p = 12 x + 26 = ( 2)( 1) 12 17 − − − p p p (d) 2 3 5 x − - 5 1 x + (e) 2 3 - x x 4 1− 2 (f) 1 3 p − - 1− p 2 = (2 3)( 5) 5( 5) 1(2 3) − + + − − x x x x = x x x 4 3(2 ) −1(1− 2 ) = ( 1)(1 ) 3(1 ) 2( 1) p p p p − − − − − = (2 3)( 5) 5 25 2 3 − + + − + x x x x = x x x 4 6 −1+ 2 = ( 1)(1 ) 3 3 2 2 p p p p − − − − + = (2 3)( 5) 5 2 3 25 − + − + + x x x x = x x x 4 6 + 2 −1 = ( 1)(1 ) 3 2 2 3 p p p p − − − − + + = (2 3)( 5) 3 28 − + + x x x = x x 4 8 −1 = ( 1)(1 ) 5 5 p p p − − − +