Year 10 Exam Revision 2Year 10 Exam Revision 2

Groups of 4Groups of 4

Pupil A,B,C,DPupil A,B,C,D

1 point for each pupil1 point for each pupil

Expand and simplifyExpand and simplify

A 3(2x-1)+4(x+3)A 3(2x-1)+4(x+3) B B 5(2x+3)+3(x+2)5(2x+3)+3(x+2)

C 4(2x+1)-2(x+3)C 4(2x+1)-2(x+3) D 5(3X-1)-2(X-5)D 5(3X-1)-2(X-5)

Expand and simplify ANSWERSExpand and simplify ANSWERS

A 3(2x-1)+4(x+3)A 3(2x-1)+4(x+3)

6X-3+4X+126X-3+4X+12

10X+910X+9

B 5(2x+3)+3(x+2)B 5(2x+3)+3(x+2)

10x+15+3x+610x+15+3x+6

13x+2113x+21

C 4(2x+1)-2(x+3)C 4(2x+1)-2(x+3)

8x + 4 - 2x -68x + 4 - 2x -6

6x -26x -2

D 5(3X-1)-2(X-5)D 5(3X-1)-2(X-5)

15x – 5 -2x + 1015x – 5 -2x + 10

13x + 513x + 5

Nth term of a sequenceNth term of a sequenceWrite down the 1Write down the 1stst, 2, 2ndnd and 3 and 3rdrd termsterms• 4n+14n+1

• 5n-25n-2

• 2n+72n+7

• 3n-23n-2

Nth term of a sequence ANSWERS Nth term of a sequence ANSWERS Write down the 1Write down the 1st st and 2and 2ndnd terms terms• 4n+1 means x4 then +14n+1 means x4 then +1• N=1 1x4+1=5N=1 1x4+1=5• N=2 2x4+1=9N=2 2x4+1=9

• 5n-25n-2• N=1 1x5-2=3N=1 1x5-2=3• N=2 2x5-2=8N=2 2x5-2=8

• 2n+72n+7• N=1 1x2+7=9N=1 1x2+7=9• N=2 2x2+7=9N=2 2x2+7=9

• 3n-23n-2• N=1 1X3-2=1N=1 1X3-2=1• N=2 2X3-2=6N=2 2X3-2=6

Simplify by collecting like Simplify by collecting like termsterms• 4a + 2b + 3a + 3b4a + 2b + 3a + 3b

• 5x + 4y – 2x + 10y5x + 4y – 2x + 10y

• 3x + 10y + 2x + y – x3x + 10y + 2x + y – x

• 6a + 3b – a + b – 2a6a + 3b – a + b – 2a

Simplify by collecting like Simplify by collecting like terms ANSWERSterms ANSWERS• 4a4a + 2b + 2b + 3a+ 3a + 3b + 3b• 7a7a + 5b + 5b

• 5x5x + 4y + 4y – 2x– 2x + 10y + 10y• 3x3x + 14y + 14y

• 3x3x + 10y + 10y + 2x+ 2x + y + y – x– x• 4x4x + 11y + 11y

• 6a6a + 3b + 3b – a– a + b + b – 2a– 2a• 3a3a + 4b + 4b

Factorise by putting back into Factorise by putting back into bracketsbrackets• 2a + 102a + 10

• 5a + 305a + 30

• yy22 + 3y + 3y

• bb22 – 7b – 7b

Factorise by putting back into Factorise by putting back into brackets ANSWERSbrackets ANSWERS• 2a + 10 2a + 10 • 2(a + 5)2(a + 5)

• 5a + 305a + 30• 5(a + 6)5(a + 6)

• yy22 + 3y + 3y• y(y+3)y(y+3)

• bb22 – 7b – 7b• b(b – 7)b(b – 7)

Plot the following coordinates, join Plot the following coordinates, join them up then find the coordinates of them up then find the coordinates of the mid-pointthe 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)

Plot the following coordinates, join Plot the following coordinates, join them up then find the coordinates of them up then find the coordinates of the mid-pointthe mid-pointANSWERSANSWERS• (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)

Find the area of these Find the area of these shapesshapes• 6cm6cm

• 2cm2cm

• 4cm4cm

• 7cm7cm

• 6cm6cm

• 12cm12cm

Find the area of these shapesFind the area of these shapesANSWERSANSWERS• 6cm6cm

• 2cm 6x=12cm2cm 6x=12cm22

• 4cm 4x7=284cm 4x7=28

• 7cm 287cm 28÷2 = 14cm÷2 = 14cm22

• 6cm 6x12=726cm 6x12=72

• 12cm 7212cm 72÷2=36cm÷2=36cm22

Calculate the meanCalculate the meanAge(years)Age(years) FrequencyFrequency

33 55

44 77

55 1010

66 66

77 22

Calculate the mean Calculate the mean ANSWERSANSWERS

Age(years)Age(years) FrequencyFrequency Age x freqAge x freq

33 55 1515

44 77 2828

55 1010 5050

66 66 3636

77 22 1414

30 143

Mean = 143 ÷ 30 = 4.7

Calculate the meanCalculate the meanHeight (cm)Height (cm) FrequencyFrequency

10 10 ≤ h < 20≤ h < 20 33

20 20 ≤ h < 30≤ h < 30 77

30 30 ≤ h < 40≤ h < 40 88

40 40 ≤ h < 50≤ h < 50 22

Calculate the mean Calculate the mean ANSWERSANSWERSHeight (cm)Height (cm) FrequencyFrequency Midpoint x Midpoint x

freqfreq

10 10 ≤ h < 20≤ h < 20 33 15x3=4515x3=45

20 20 ≤ h < 30≤ h < 30 77 25x7=17525x7=175

30 30 ≤ h < 40≤ h < 40 88 35x8=28035x8=280

40 40 ≤ h < 50≤ h < 50 22 45x2=9045x2=90

20 590

Mean = 590 ÷ 20 = 29.5 cm

Expanding double bracketsExpanding double brackets• (x + 2)(x + 7)(x + 2)(x + 7)

• (x + 6)(x – 3)(x + 6)(x – 3)

• (x + 5)(x + 5)22

• (x + 7)(x + 7)22

Expanding double brackets Expanding double brackets ANSWERSANSWERS

• (x + 2)(x + 7) X(x + 2)(x + 7) X22+9X+14+9X+14

• (x + 6)(x – 3) X(x + 6)(x – 3) X22 + 3X - 18 + 3X - 18

• (x + 5)(x + 5)2 2 = (X+5)(X+5) X= (X+5)(X+5) X22 + 10X + 25 + 10X + 25

• (x + 7)(x + 7)2 2 = (X+7)(X+7) X= (X+7)(X+7) X22 + 14X + 49 + 14X + 49

XX 22

XX XX22 2X2X

77 7X7X 1414

Calculate the circumference of a Calculate the circumference of a circle. circle. • REMEMBER C=REMEMBER C=πdπd

10cm 7cm

6cm

Calculate the circumference of a Calculate the circumference of a circle. ANSWERScircle. ANSWERS• REMEMBER C=REMEMBER C=πdπd

• C = 3.14 x 10=31.4 c=3.14 x 7 = C = 3.14 x 10=31.4 c=3.14 x 7 = 21.98 21.98

• D=12 so c=3.14 x 12 = 37.68D=12 so c=3.14 x 12 = 37.68

10cm 7cm

6cm

Calculate the area of a circle. Calculate the area of a circle.

• REMEMBER a=REMEMBER a=ππrr22

10cm7cm

6cm

Calculate the area of a circle. Calculate the area of a circle. ANSWERS ANSWERS • REMEMBER a=REMEMBER a=ππrr22

• A=3.14 x 10A=3.14 x 1022=314 A=3.14 x 7=314 A=3.14 x 722=153.86=153.86

• R=3 so A=3.14 x 3R=3 so A=3.14 x 322 = 28.26 = 28.26

10cm7cm

6cm

Write these numbers in Write these numbers in standard formstandard form• 56000005600000

• 3180031800

• 0.000740.00074

• 0.0350.035

Write these numbers in Write these numbers in standard form ANSWERSstandard form ANSWERS• 56000005600000• 5.6 X 105.6 X 1066

• 3180031800• 3.18 X 103.18 X 1044

• 0.000740.00074• 7.4 X 107.4 X 10-4-4

• 0.0350.035• 3.5 X 103.5 X 10-2-2

Compound interest. 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

Compound interest. ANSWERSCompound interest. ANSWERS• £3000 invested at 2% at 5 years£3000 invested at 2% at 5 years• 3000 X 1.023000 X 1.025 5 = £3312.24= £3312.24

• £2400 invested at 4% for 3 years£2400 invested at 4% for 3 years• 2400 X 1.042400 X 1.0433 = £2699.67 = £2699.67

• £600 invested at 6% for 2 years£600 invested at 6% for 2 years• 600 X 1.06600 X 1.0622 = £674.16 = £674.16

• £2500 invested at 4.1% for 3 years£2500 invested at 4.1% for 3 years• 2500 X 1.0412500 X 1.04133 = £2820.28 = £2820.28

Histograms .Histograms .• Work out the frequency density then draw Work out the frequency density then draw

the histogramthe histogram

Height (cm)Height (cm) FrequencyFrequency

0 < h 0 < h ≤ 10≤ 10 4040

10 < h 10 < h ≤ 15≤ 15 3030

15 < h 15 < h ≤ 30≤ 30 3030

30 < h 30 < h ≤ 50≤ 50 100100

Histograms . ANSWERSHistograms . ANSWERS• Work out the frequency density then draw Work out the frequency density then draw

the histogramthe histogram

Height (cm)Height (cm) FrequencyFrequency F F ÷ class width÷ class width

0 < h 0 < h ≤ 10≤ 10 4040 40 40 ÷ 10 = 4÷ 10 = 4

10 < h 10 < h ≤ 15≤ 15 3030 30 30 ÷ 5 = 6÷ 5 = 6

15 < h 15 < h ≤ 30≤ 30 3030 30 30 ÷ 15 = 2÷ 15 = 2

30 < h 30 < h ≤ 50≤ 50 100100 100 100 ÷ 20 = 5÷ 20 = 5

Height

Freq

Density