Common Entrance revision Year 8

Transcription

1 To multiply/divide any number including decimals by 10, 100, 1000 A) 5800 B) 390 C) D) A) 7.35 B) Harder questions: A) 230 B) 230 To multiply/divide/add/subtract using decimal numbers A) 5.56 B) C) 5.79 D) cm cm A) B) C) D) To order decimal numbers according to size order 4.06, 4.066, 4.6, 4.606, P a g e

2 To round numbers to the nearest whole, ten, hundred or thousand A) 760 B) 250 C) 2870 D) 1840 E) 30 F) 1000 G) 0 H) 3000 I) 2000 J) 0 To round numbers to a given number of decimals places A) 2.68 B) 5.93 C) 6.0 D) 8.1 To round numbers to a given number of significant figures A) 7.5 B) 0.06 C) D) 6000 E) 4000 F) x 6 = = Exact answer: A) (3dp) B) 2.04 (3sf) 2 P a g e

3 To round numbers to a given number of significant figures (Continued) 200 = 2 50 x 2 Exact answer: A) (3dp) B) 1.85 (3sf) To use all four operations with negative numbers To be able to find equivalent fractions or cancel down a fraction into its simplest terms A) -8 B) -4 C) 12 D) C 12 A) -15 B) 18 C) -35 D) 12 A) 25 B) x = 6 and x = = = = To use equivalent fractions to size order fractions 64 = Order these fractions from smallest to largest: P a g e

4 To add/subtract fractions = 1 7 / / 45 To find a fraction of an amount 2/5 of 45 = 18 3/7 of 406 = 174 3/8 of 768 = 288 5/6 of 426 = cm 16 boys 14 children play an instrument To multiply and divide using fractions 2/3 x 4/5 = 8/15 3/4 x 7/5 = 1 1 / 20 2/9 x 5/3 = 10/27 4/3 3/8 = 3 5 / 9 2/3 6/7 = 7/9 2/9 1/3 = 2/3 Find the area of the following rectangles: 4/21 cm / 24 cm 2 4 P a g e

5 To multiply and divide using fractions (continued) 9 times 9 days To find a percentage of an amount A) 30% of 710 = 213 B) 25% of 640 = 160 C) 38% of 540 = D) 33⅓% of 963 = 321 E) 5% of 340 = 17 F) 66⅔% of 1462 = 974 ⅔ Work out 15% of 12 = 1.80 Calculate 90% of 15 = The fee was m To express one number as a percentage of another 30% 80% To find percentage increase and decrease 20% discount 8% increase 45% 5 P a g e

6 To find percentage increase and decrease (Continued) (i) 1.78 profit (ii) 47.8% To know fraction/decimal/percentage equivalents (Pupils should memorise these: ½=0.5=50% ¼ = 0.25 = 25% 1/10 = 0.1 = 10% 1/5 = 0.2 = 20% 1/100 = 0.01 = 1% 6%, 3 / 20, 0.16, , 33%, 0.303, 3 / 10 ⅓ = = 33 1/3 % ⅔ = = 66 2/3 %) 15% % 4/25 To understand the order of operations (BIDMAS) Calculate: i) 34 ii) 7 iii) 36 To know what a prime number, square number and cube number is iv) 25 square number 49 cube number 8 or 27 prime number - 13 Why is 126 not a prime number? Because it is divisible by numbers other than itself and 1 (i.e. it has more than 2 factors) What is the first prime number? 2 6 P a g e

7 Answers To know what a prime number, square 64 and 36 number and cube number is (Continued) To write a number as the product of its primes 2 2 x 3 x x 3 x x 3 2 x LCM = 2 2 x 3 4 x 5 3 x 7 2 To collect like terms in an expression a) 8x +7y b) 18p 9q c) 13x + 3y d) 11x x e) -12m y + 7 To simplify algebraic expressions, including using laws of index notation Simplify: -6ab 6a 5 3c 2 12d 7 10a 3 3a 12a 2 7 P a g e

8 To multiply out brackets and simplify NB: REMEMBER NEGATIVE RULES!!! 12e e p x 15 To factorise an expression 6(2p + 3r) 4(2g + 5) 8(3-y) To solve linear equations b = 11 a = 48 c = - ½ d= -2 f= 6 ½ y = -2 To form an algebraic expression and solve a related equation. i) C = 2a ii) D = a 2 iii) a + a a = 22 4a = 24 a = 6 iv) 28 8 P a g e

9 To substitute into an expression i) 17 ii) 8 iii) -12 iv) -3 i) 12 ii) -8 iii) 36 iv) 2 V = -6 To use ratio and proportion to answer problems (i) 750ml (ii) 3 (i) 64 (ii) 2:3 9 P a g e

10 To use ratio and proportion to answer problems (continued) 3:2 To know the sum of angles in a triangle is 180⁰ 60 a = 120 b= 30 c = 90 To know the properties of a right angled, isosceles and equilateral triangle. To know what vertically opposite angle are and that they are equal. To know what corresponding angles are and that they are equal. To know what alternate angles are and that they are equal To know that interior angles (supplementary angles) add up to 180 To know the sum of angles on a straight line is 180⁰ and around a point is 360⁰ 10 P a g e

11 To use all of the above angle facts to calculate missing angles r = 70⁰ s = 55⁰ t = 35⁰ d = 55⁰ e = 45⁰ a = 50⁰ b = 40⁰ c = 65⁰ d = 65⁰ 11 P a g e

12 To use angle facts to calculate missing angles w = 120⁰ x = 40⁰ y = 120⁰ z = 70⁰ a = 50⁰ b = 65⁰ c = 65⁰ d = 15⁰ To be able to calculate the interior and exterior angles of a regular polygon. To know the relationship between the number of sides of a polygon and the exterior angle. To know that the exterior and interior angles of a polygon total 180 w = 36⁰ x = 144⁰ y = 18⁰ z = 144⁰ Which type of polygon has 10 sides? Decagon 12 P a g e

13 Regular polygon angle facts (continued) v = 30⁰ Sides = 12 w = 30⁰ x = 75⁰ y = 105⁰ w = 40⁰ x = 140⁰ y = 20⁰ z = 50⁰ nonagon 13 P a g e

14 To be able to draw and measure bearings To use bearings and map scales to construct scale drawings Total length of course = 1.1km Bearing from barn back to starting point = 140⁰ 14 P a g e

15 To be able to draw and measure bearings To use bearings and map scales to construct scale drawings Bearing of R from P = 046⁰ Bearing of P from R = 226⁰ Total distance travelled by ship = 28.5 km 15 P a g e

16 To find the probability of an event occurring (and not occurring) (a) 1/6 (b) 1/3 (c) 5/6 To complete a possibility space and find related probabilities You would expect him to score a 4 10 times Missing values read (left to right) 1,9 3,5 3,7 3,9 5,1 5,3 5,9 7,1 7,3 7,5 7,9 9,3 9,5 9,7 What is the probability that (a) ½ (b) 1/10 ¼ To find the mean, mode, median and range of a set of data. A) 3 B) 0 C) 5 and 6 D) No mode A) 21 B) 10 C) 21 D) P a g e

17 To find the mean, mode, median and range of a set of data (Continued) a) 6 b) 6.5 c) 8 a) 5 b) 3 c) 1 (i) 5.3 (ii) 17.6 (iii) 17.8 (iv) 0.6 To find the mean, mode, median and range from a frequency table i) 0 ii) 1 iii) a) 27 b) P a g e

18 To display data in graphical form e.g. pie chart Each cake is worth 4⁰ Chocolate : 120⁰ Lemon: 140⁰ Ginger: 36⁰ Coffee: 64⁰ Chocolate Ginger Coffee Lemon 2 4 To continue a given sequence a) 11, 13, 15, 17, b) 22, 27, 32, 37 c) -56, -73, -90, P a g e

19 To continue a given sequence (i) 60, 97 (ii) 5, 23, 37, 97 so there are 4 prime numbers less than 100 in this sequence (i) 32, 17 (ii) Any number less than 2. To find any term of a sequence given its nth term a) 34 b) -34 c) 119 To find the nth term of a linear sequence a) 7n - 5 b) 3n - 7 c) -8n + 28 d) -5n - 8 9n P a g e

20 To draw a straight line graph given an equation To find the coordinates of the point of intersection of two lines X = -5 Y= -1 Y= -x 20 P a g e

21 To draw a straight line graph given an equation To find the coordinates of the point of intersection of two lines (i) When x=3, y=3 When x=6, y=-3 (ii) See graph (iii) When x=2, y=0 When x=6, y=2 (iv) See graph (v) (4, 1) (vi) See graph (purple line) (vii) (0, 1.5) 21 P a g e

22 Y = ½ x -1 Y = 9 2x 22 P a g e

23 To enlarge a shape by a given scale factor (i) Trapezium (ii) See above (iii) Area of enlarged shape = SF 2 x original area = 9 x 10.5 = 94.5 cm 2 23 P a g e

24 To enlarge a shape by a given scale factor (b) Area of original shape = Area of enlarged shape SF 2 = 36 9 = 4cm 2 24 P a g e

25 To reflect a shape in a given mirror line Y = P a g e

26 To reflect a shape in a given mirror line A B C To translate a shape by a given vector On the above grid, translate quadrilateral A 5 units to the left and 8 units down. Label the image C. D C 26 P a g e

27 To rotate a shape around a given centre of rotation and by a given angle. D A 27 P a g e