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Year 10 Exam Revision 2 Groups of 4 Pupil A,B,C,D 1 point for each pupil

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Expand and simplify A 3(2x-1)+4(x+3) B 5(2x+3)+3(x+2) C 4(2x+1)-2(x+3) D 5(3X-1)-2(X-5)

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Expand and simplify ANSWERS A 3(2x-1)+4(x+3) 6X-3+4X+1210X+9 B 5(2x+3)+3(x+2) 10x+15+3x+613x+21 C 4(2x+1)-2(x+3) 8x + 4 - 2x -6 6x -2 D 5(3X-1)-2(X-5) 15x – 5 -2x + 10 13x + 5

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Nth term of a sequence Write down the 1 st, 2 nd and 3 rd terms 4n+1 4n+1 5n-2 5n-2 2n+7 2n+7 3n-2 3n-2

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Nth term of a sequence ANSWERS Write down the 1 st and 2 nd terms 4n+1 means x4 then +1 4n+1 means x4 then +1 N=1 1x4+1=5 N=1 1x4+1=5 N=2 2x4+1=9 N=2 2x4+1=9 5n-2 5n-2 N=1 1x5-2=3 N=1 1x5-2=3 N=2 2x5-2=8 N=2 2x5-2=8 2n+7 2n+7 N=1 1x2+7=9 N=1 1x2+7=9 N=2 2x2+7=9 N=2 2x2+7=9 3n-2 3n-2 N=1 1X3-2=1 N=1 1X3-2=1 N=2 2X3-2=6 N=2 2X3-2=6

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Simplify by collecting like terms 4a + 2b + 3a + 3b 4a + 2b + 3a + 3b 5x + 4y – 2x + 10y 5x + 4y – 2x + 10y 3x + 10y + 2x + y – x 3x + 10y + 2x + y – x 6a + 3b – a + b – 2a 6a + 3b – a + b – 2a

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Simplify by collecting like terms ANSWERS 4a + 2b + 3a + 3b 4a + 2b + 3a + 3b 7a + 5b 7a + 5b 5x + 4y – 2x + 10y 5x + 4y – 2x + 10y 3x + 14y 3x + 14y 3x + 10y + 2x + y – x 3x + 10y + 2x + y – x 4x + 11y 4x + 11y 6a + 3b – a + b – 2a 6a + 3b – a + b – 2a 3a + 4b 3a + 4b

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Factorise by putting back into brackets 2a + 10 2a + 10 5a + 30 5a + 30 y 2 + 3y y 2 + 3y b 2 – 7b b 2 – 7b

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Factorise by putting back into brackets ANSWERS 2a + 10 2a + 10 2(a + 5) 2(a + 5) 5a + 30 5a + 30 5(a + 6) 5(a + 6) y 2 + 3y y 2 + 3y y(y+3) y(y+3) b 2 – 7b b 2 – 7b b(b – 7) b(b – 7)

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Plot the following coordinates, join them up then find the coordinates of the mid-point (1,1) and (5,5) (1,1) and (5,5) (2,10) and (4,4) (2,10) and (4,4) (6,3) and (9,4) (6,3) and (9,4) (6,10) and (8,7) (6,10) and (8,7)

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Plot the following coordinates, join them up then find the coordinates of the mid-point ANSWERS (1,1) and (5,5) (3,3) (1,1) and (5,5) (3,3) (2,10) and (4,4) (3,7) (2,10) and (4,4) (3,7) (6,3) and (9,4) (7.5,3.5) (6,3) and (9,4) (7.5,3.5) (6,10) and (8,7) (7,8.5) (6,10) and (8,7) (7,8.5)

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Find the area of these shapes 6cm 6cm 2cm 2cm 4cm 4cm 7cm 7cm 6cm 6cm 12cm 12cm

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Find the area of these shapes ANSWERS 6cm 6cm 2cm 6x=12cm 2 2cm 6x=12cm 2 4cm 4x7=28 4cm 4x7=28 7cm 28÷2 = 14cm 2 7cm 28÷2 = 14cm 2 6cm 6x12=72 6cm 6x12=72 12cm 72÷2=36cm 2 12cm 72÷2=36cm 2

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Calculate the mean Age(years)Frequency 35 47 510 66 72

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Calculate the mean ANSWERS Age(years)Frequency Age x freq 3515 4728 51050 6636 7214 30 143 Mean = 143 ÷ 30 = 4.7

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Calculate the mean Height (cm) Frequency 10 h < 20 3 20 h < 30 7 30 h < 40 8 40 h < 50 2

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Calculate the mean ANSWERS Height (cm) Frequency Midpoint x freq 10 h < 20 315x3=45 20 h < 30 725x7=175 30 h < 40 835x8=280 40 h < 50 245x2=90 20 590 Mean = 590 ÷ 20 = 29.5 cm

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Expanding double brackets (x + 2)(x + 7) (x + 2)(x + 7) (x + 6)(x – 3) (x + 6)(x – 3) (x + 5) 2 (x + 5) 2 (x + 7) 2 (x + 7) 2

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Expanding double brackets ANSWERS (x + 2)(x + 7) X 2 +9X+14 (x + 2)(x + 7) X 2 +9X+14 (x + 6)(x – 3) X 2 + 3X - 18 (x + 6)(x – 3) X 2 + 3X - 18 (x + 5) 2 = (X+5)(X+5) X 2 + 10X + 25 (x + 5) 2 = (X+5)(X+5) X 2 + 10X + 25 (x + 7) 2 = (X+7)(X+7) X 2 + 14X + 49 (x + 7) 2 = (X+7)(X+7) X 2 + 14X + 49 X2 X X2X2X2X22X 77X14

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Calculate the circumference of a circle. REMEMBER C= πd REMEMBER C= πd 10cm 7cm 6cm

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Calculate the circumference of a circle. ANSWERS REMEMBER C= πd REMEMBER C= πd C = 3.14 x 10=31.4 c=3.14 x 7 = 21.98 C = 3.14 x 10=31.4 c=3.14 x 7 = 21.98 D=12 so c=3.14 x 12 = 37.68 D=12 so c=3.14 x 12 = 37.68 10cm 7cm 6cm

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Calculate the area of a circle. REMEMBER a= πr 2 REMEMBER a= πr 2 10cm 7cm 6cm

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Calculate the area of a circle. ANSWERS REMEMBER a= πr 2 REMEMBER a= πr 2 A=3.14 x 10 2 =314 A=3.14 x 7 2 =153.86 A=3.14 x 10 2 =314 A=3.14 x 7 2 =153.86 R=3 so A=3.14 x 3 2 = 28.26 R=3 so A=3.14 x 3 2 = 28.26 10cm 7cm 6cm

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Write these numbers in standard form 5600000 5600000 31800 31800 0.00074 0.00074 0.035 0.035

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Write these numbers in standard form ANSWERS 5600000 5600000 5.6 X 10 6 5.6 X 10 6 31800 31800 3.18 X 10 4 3.18 X 10 4 0.00074 0.00074 7.4 X 10 -4 7.4 X 10 -4 0.035 0.035 3.5 X 10 -2 3.5 X 10 -2

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Compound interest. £3000 invested at 2% at 5 years £3000 invested at 2% at 5 years £2400 invested at 4% for 3 years £2400 invested at 4% for 3 years £600 invested at 6% for 2 years £600 invested at 6% for 2 years £2500 invested at 4.1% for 3 years £2500 invested at 4.1% for 3 years

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Compound interest. ANSWERS £3000 invested at 2% at 5 years £3000 invested at 2% at 5 years 3000 X 1.02 5 = £3312.24 3000 X 1.02 5 = £3312.24 £2400 invested at 4% for 3 years £2400 invested at 4% for 3 years 2400 X 1.04 3 = £2699.67 2400 X 1.04 3 = £2699.67 £600 invested at 6% for 2 years £600 invested at 6% for 2 years 600 X 1.06 2 = £674.16 600 X 1.06 2 = £674.16 £2500 invested at 4.1% for 3 years £2500 invested at 4.1% for 3 years 2500 X 1.041 3 = £2820.28 2500 X 1.041 3 = £2820.28

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Histograms. Work out the frequency density then draw the histogram Work out the frequency density then draw the histogram Height (cm) Frequency 0 < h 10 40 10 < h 15 30 15 < h 30 30 30 < h 50 100

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Histograms. ANSWERS Work out the frequency density then draw the histogram Work out the frequency density then draw the histogram Height (cm) Frequency F ÷ class width 0 < h 10 40 40 ÷ 10 = 4 10 < h 15 30 30 ÷ 5 = 6 15 < h 30 30 30 ÷ 15 = 2 30 < h 50 100 100 ÷ 20 = 5 Height Freq Density

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