Unit 2 RevisionNumber

1. 851 ÷ 372. 777 ÷ 373. 27.6 x 234. 36.2 ÷ 0.25. -2 + -46. 365 x 547. 753 ÷ 36 8. 3 x -59. -3 x -510. 10 ÷ -511. -10 ÷ -512. 5.36 + 7.813. 13.76 – 5.2114. 356 x 10015. 356 ÷ 10016. 3 x 0.417. 0.7 ÷ 100018. 8.8 x 1019. pens cost £0.45, how many can you buy

for £1820. 5 + -721. 13 x -522. write a fraction between ¼ and ½ 23. why is ¾ the same as 6/8?24. write in order: 3/8, 1/4 , 3/1025. order: 0.39, 0.4, 0.049, 0.49, 0.40926. write the first 10 primes27. write 30 in prime factor form28. write 18 as a product of its primes29. write 252 as a product of its primes30. list all the common factors of 24 & 3631. find the HCF of 24 & 3632. find the LCM of 15 & 2033. write 12 up to 152

34. write 13, 23, 33, 43 & 53

35. 103 = 36. work out root 10037. Find the length of a square with area

81cm2

38. Why is 2 cubed not 6?39. Why does root 9 have two answers?40. work out 70

41. 106 = 42. which is larger: 23 or 32?43. 57 ÷ 53 = 44. 33 x 34 = 45. (42)3 = 46. simplify 16/24 & 28/3547. write 27/10 as a mixed number48. 1½ + 2¾ = 49. 2/3 – ¼ 50. 21/3 + 1¾ 51. give the value of 6 in 3.47652. write 0.30 as a fraction53. write 0.3 as a fraction54. write 0.37 as a fraction55. write 0.65 as a fraction56. convert to decimals: ½, ¼, 1/5, 1/10, 1/100, 1/857. write 3/8 as a decimal58. write 1.25 as a mixed number59. write 1/3 as a decimal60. show 0.33333 = 1/361. find ¾ of 48

62. find ¾ of 663. find 3/5 of £3.5064. find 10% of £6065. find 5% of £6066. find 2.5% of £6067. find 17.5% of £6068. increase 60 by 20%69. decrease 60 by 20%70. multiply 60 by 1.0571. increase 60 by 5%72. compare answers to Q70 and Q7173. simplify the ratio 20:12

BODMAS74. insert brackets: 20 – 3 x 2 = 3475. insert brackets: 14.5 – 2.6 × 4.5 – 3.6 =

49.9576. 5 x 2 + 3 = 77. 5 x (2 + 3) = 78. 3(2 + 5)2 = 79. estimate √90 =80. Work out the value of 2 + 100

Ratio81. share £15 in the ratio 3:282. share 20m in the ratio 11:6:383. Bill & Mary share £P in the ratio 3:5, Bill

gets £12, how much does Mary get?84. Adapt a recipe for 6 people to serve 8

people85. round 54327 to the nearest ten, hundred

and thousand86. round 37451 to 1sf, 2sf, 3sf87. round 1.257 to 1.d.p, 2.d.p and 3.d.p88. round 0.0007269 to 1sf89. estimate

3.103.58.7

90. estimate 25.1

9.32.6 2

91. using: 17 × 19 = 323, work out: 0.17 × 1.9 and 323 ÷ 0.019

92. find the cost of 1 litre if 50 litres cost £45

Algebra93. if n is even, what is 2n?94. if n is even, what is n – 1?95. 2a = a x a, true/false?96. find the area of a square of length b97. find the area of a rectangle length 4 and

width (b + 2)98. simplify: 3a + 2c – a – 3c + 299. simplify: x + 5 – 2x – 1 + 4 – x100. simplify: a x b x 2101. 2(x + 4)102. 2a(a + 5)103. 3p(2q – 7)104. 3(2x – 1) -2(2x – 3)105. factorise: 10x = 5106. factorise: 9x – 3107. x2 + 3x108. 6x2 – 9x109. 2ab2 – 4ab110. Bhavna uses this formula to work

out her Electricity bill:

Cost = Number of units used × Cost for each unit + Meter hireBhavna uses 350 units. The cost for each unit is 7.5p. The Meter hire is £15.50.Work out the cost of her bill

Sequences111. find the next term: 2, 7, 12, 17, …112. find the nth term: 2, 7, 12, 17, …113. find the nth term: 4, 10, 16, 22, …114. find the 10th term if rule is 3n115. find the 10th and 20th terms if the rule is 3n – 4116. find the next term: 1, 2, 4, 8, …117. find the next term: 1,3,6,10, …118. find the next term: 1,4,5,8,…119. plot the points: (3,4), (3,-4), (0,6),

(-2,4)120. find the 4th coordinate of a

parallelogram with vertices: (2,1),(-7,3) & (5,6)

121. find the midpoint of A(1,7) & B(5,3)122. draw graphs of: y = 4, x = 3, y =

2x + 3, x + y = 7, y = ½x -1123. plot x + y = 6 without a table

Geometry124.

x º 4 3 º

1 0 8 º

y º

125.

x 6 2 °

A

B C D

D iagram accu ra te ly d raw n

N O T

126.

D iag ram acc u ra te ly dr aw n

N O T

6 2 ° y °

6 4 °

D E

F G

127.

D iag ra m a cc ura te ly d raw n

N O T

10 0 °

47 ° x °

2 °x

A

B C

D

128.

D iag ra m accu rate ly d raw n

N O T

find the exterior angle

129. find the exterior angle

130.D ia g ram ac cu ra te ly d ra w n

N O Tx

find x if this is a regular Octagon

131.

8 1 º 3 7 º

y º

x º

132.

A

D

G

F

CB

5 6 º

x

y

E

133. Name these shapes.

134. Which shapes have rotational symmetry?

135. Write down the order of rotational symmetry for:i rectangle ii parallelogram iii. Rhombus

136. Find the area of:

Metric & Imperial Unitsa. 3metres = ____cmb. 4 litres = _____ mlc. 2 gallons = ___ litresd. 5½ km = ____ me. 1 kg = _______ poundsf. 1 litre = ______ pintsg. 1 gallon = ____ pintsh. 5miles = _____ kmi. 1 foot = ______ inchesj. 1 foot = ______ cmk. 22 pounds = ___ kilogramsl. 28 miles = ___ kilometres

m. Fred went on holiday to France.He changed £475 to Euros.£1 = 1.57 Euros. Change £475 to Euros.n. How many miles has a car travelled in 3hours at 40mph?o. How long does it take to travel 200km at 60km/h?p. change 45km/h to m/s

HIGHER TIER ONLY

Fractional indices:1. 31/3 x 22/52. 15/8 ÷ ¾ 3. ¾ x 36 4. 106 = 5. 100 = 6. 9-1= 7. Evaluate:

a Write down the value ofi 50

ii 4-2

b Simplify: i

ii

iii

iv 80

v 5–2

vi 31

27

vii 21

25

Recurring decimals to fractions:Change 0.4444444444 to a fractionChange 0.3777777777 to a fractionChange 0.4545454545 to a fractionChange 0.3453453453 to a fractionChange 1.2323232323 to a fraction

Surds:√5 x √5 = √3 x √12 = √50 ÷ √2 = √50 = k√2 find k √8 = 2√m find m(√5 + 4)(√5 – 4)(3 – √3)2 = a + b√3

Expanding brackets:(x+2)(x+5) = (x+2)(x-5) = (x+3)(x-3)=(n+m)(n-m)=(x+7)2 =(p + q)2 =(a – b)2 = (3x+2)(2x-5) =

Factorising expressionsX2 + 5x + 6 X2 + 2x – 15X2 – 8x + 126x2 + x – 26x2 – 11x – 106(x+y)2 – 4(x+y)X2 – 49X2 – 81X2 – 1694x2 – 9y2

81p2 – 25q2

(xy)2 – (ab)2

Simplify these expressions:

884 2

kk

2–2

11–2

nnn

169376

2

2

xxxx

9–46–4

2

2

xxx

12x

+ 1–

3x

Substitutiona. Tayub said, “When x = 3, then 4x2 is 144”. Bryani said, “When x = 3, then 4x2 is 36”. Who was right? Explain why.b. Work out the value of 4(x + 1)2 when x = –3.

Straight lines & y=mx+ca. Write down the equation of a line parallel

to y = 21 x + 1

b. Draw the lines: x = 3 , y =5, x = -4 and y = -6, y = x and y = -x

c. The diagram shows 4 lines, P, Q, R and S.

P

O

Q

R S

x

y

The equations of the straight lines are:A: y = 2xB: y = 3 - 2xC: y = 2x + 3D: y = 3Match each straight line, P, Q, R and S to its equation.

d. The diagram shows three points A 5) ,1( , B 1) ,2( and C 5) ,0( .

A line L is parallel to AB and passes through C.Find the equation of the line L.

e. Find the equation of the straight line which passes through the point (0, 3) and is perpendicular to the straight line with equation y = 2x.

Upper & Lower Boundsx = 40, correct to the nearest 10.y = 60, correct to the nearest 10.a i Write down the lower bound of x & y.

ii Write down the upper bound of x & y.b Calculate the greatest possible value of xy.c Calculate the least possible value of xy.d Calculate the greatest possible value of x/y.

Standard Form

a.pq

qpx

If p = 4 × 105 & q = 1.25 × 104

Calculate the value of x.Give your answer in standard form

b. Write 0.000 000 03 in standard form.c. Express 0.327 105 in standard form.d. Write 2.5 105 as an ordinary number.

e. The mass of 5 m3 of copper is 44 800 kg.i. Work out the density of copper.

The density of zinc is 7130 kg/m3.ii. work out the mass of 5 m3 of zinc

f.

5 cm

8 cm

The volume this solid cuboid is 140 cm3.(a) Work out the height of the cuboid.The cuboid is made from wood.The wood has a density of 1.2 grams per cm3.(b) Work out the mass of the cuboid.

g. This triangular prism is made of wood with density 0.85 g/cm3. Work out its mass.

Other

1. Work out the size of angle SOB.

2. Work out the size of angle BAO.

3. What are the coordinates of the midpoint of the line segment PQ

4. There are 960 litres of water in a tank. A workman empties the tank. The water flows out of the tank at a constant rate of 0.4 litres per second. How long, in minutes does it tale the workman to empty the tank completely?

END OF QUESTIONS

UNIT 2_ June 2011

1.

Work out the area of this triangle.

(Total for Question 1 is 3 marks)

2. (a) Simplify 3y + 2x – 4 + 5x + 7

(1)(b) Factorise 2x2 – 4x

(2)

(c) Expand and simplify 11 – 3(x + 2) (2)

(d) Expand and simplify (x – 6)(3x + 7) (2)

3. (a) Express 48 as a product of its prime factors. (2)

Buses to Exeter leave a bus station every 20 minutes.Buses to Plymouth leave the bus station every 16 minutes.A bus to Exeter and a bus to Plymouth both leave the bus station at 8 a.m.

(b) When will buses to Exeter and Plymouth next leave the bus station at the same time?

(Total for Question 3 is 5 marks)

4. Lydia is buying a ring. The ring costs £60 She pays a deposit of 40%.

Work out how much she pays as the deposit. (Total for Question 4 is 2 marks)

5. (a) On the grid, draw the graph of y = 4x + 2 from x = –1 to x = 3

(b) (i) Write down the equation of a straight line that is parallel to y = 4x + 2

(ii) Write down the gradient of a straight line that is perpendicular to y = 4x + 2

(2)

6. The diagram shows the plan of the floor of Mrs Phillips’ living room.

Mrs Phillips is going to cover the floor with floor boards.One pack of floor boards will cover 2.5 m2.

How many packs of floor boards does she need?You must show your working.

(Total for Question 6 is 4 marks)

7. The point A has coordinates (3, 8).The point B has coordinates (7, 5).M is the midpoint of the line segment AB.Find the coordinates of M.

(Total for Question 7 is 2 marks)

8. (a) Simplify p3 × p5

(1)

(b) Simplify

(1)(c) Simplify (x2)3

(1)

9. Mr Smith drives 24 miles to work.On Monday his journey to work takes 30 minutes. On Tuesday the average speed of his journey to work is 56 km/h. Did Mr Smith drive more quickly to work on Monday or Tuesday?You must show all your working.

(Total for Question 9 is 4 marks)

10. Here are the first 5 terms of an arithmetic sequence.

6 10 14 18 22

(a) Write down an expression, in terms of n, for the nth term of this sequence. (2)

The nth term of a different sequence is 2n2 – 4

(b) Find the 3rd term of this sequence. (2)

11.

The diagram shows a regular decagon.

Work out the size of angle x. (Total for Question 11 is 4 marks)

12. Prove that (n – 1)2 + n2 + (n + 1)2 = 3n2 + 2(Total for Question 12 is 2 marks)

*13.

S and U are points on the circumference of a circle, centre O.ST and UT are tangents to the circle.Angle STU = 42°

Work out the size of angle SOU.Give reasons for your answer.

(Total for Question 13 is 3 marks)

14. (a)Express in the form , where n is a positive integer. (2)

(b) Rationalise the denominator of (2)

15. (a) Write down the value of

(1)(b) Find the value of

(2)

16. (a) Simplify

(3)

(b) Write as a single fraction –

(2)

TOTAL FOR PAPER IS 60 MARKS