Mathletics Diagnostic Test Year 8 - National Curriculum 8803

Transcription

1 Mathletis iagnosti Test Year 8 - National Curriulum 8803 Number and lgebra Suggested Time: 60 minutes 50 marks Name: Teaher: ate: ll questions are worth one mark. Sub-strand and ontent elaborations are based on Version 1.2 CR ustralian National Mathematis Curriulum Year 8 Marh 2011

2 CMN182 Setion 1 - Number and Plae Value a What is the value of 6? 0 6 B undefined b 2² x 2³ = 2ª Find a. 0 5 B 6 C 10 4 Calulate 2² x 2³. 16 B d 4² 4³ = 4ª Find a. 3 B e 5² 5² is equivalent to: 5¹ 0 5 C 5 2 5² Spae for working CMN182

3 CMN183 Setion 2 - Number and Plae Value a x 9-4 = 42 b = (9-4) + 1 = 27 d (9-4 (1 + 8) + 1) = -129 e ( (1-8 ( 1 + 5) + 5) - 3) = -899 CMN183

4 CMN184/186 Setion 3 - Real Numbers a What is the differene between a 'terminating' and a 'reurring' deimal? terminating deimal is one that does not repeat, it ends eg: 0.5 reurring deimal repeats infinitely eg: 2/3 = (repeats) b Whih fration would result in a reurring deimal? 1/4 C 3/4 B 1/2 0 2/3 esribe the differene between a 'rational' and an 'irrational' number. rational number an be written as a ratio and as a fration. ny number that is not rational is irrational. Irrational numbers an not be written as frations. d Whih of the following is a rational number? 0 9 C 2 B π 3 e Can the square root of a perfet square ever be irrational? No, all square roots of perfet squares are rational. CMN184/186

5 CMN187 Setion 4 - Real Numbers a Calulate the disount if the original prie was $50 and the disount is 6%. $ $ 3.00 C $ 6.00 $ 8.33 b What is the perentage markup on an item that ost $98 and sells at $104? % B 12.24% C 8.12% 4.12% If GST in ustralia is 10%, how muh GST would be added to a produt that ost the retailer $46? 0 $ 4.60 B $ C $ $ 0.46 d produt osts $42 to manufature and the wholesaler sells it for $53, what is the profit made by the wholesaler? $11.00 e GST in ustralia is 10%. n item osts $56 inluding GST, what is the value of the GST? $5.09 CMN187

6 CMN188 Setion 5 - Real Numbers Use the information below to answer questions a and b. a ustralia is in the Oeania region. Comparing ustralia to sia, why do you think the growth rates are so different? sia is a developing region with high fertility rates and improving aess to medial failities. b gain, omparing ustralia to sia, why do you think sia's growth rate is delining and ustralia's is very slowly inreasing? sia's growth rate may deline as it self-regulates to a more sustainable level. ustralia is fairly stable at low inrease rates. grazier has 388 sheep and 2328 attle. What is the ratio of sheep to attle on the farm? 582: :582 C 291: :388 d 0 On this same farm, the attle drink 3 times more water than the sheep. If all the sheep drink 9312L of water per day, how many litres does eah ow drink per day? 7L 0 72 L C 8L an't tell e When the attle are latating, their water onsumption doubles. What is the new ratio of water onsumption for latating attle to sheep? 0 6:1 B 24:2 0 6:1 an't tell CMN188

7 CMN189 Setion 6 - Money and Finanial Mathematis a book shop sells a textbook for $70 and makes a loss of 2.1%. Calulate the ost prie of the book. $67.90 B $74.20 C $ $71.50 b new mobile phone is oming out on the market and promises to be sold 'at ost' for the first two weeks. If the prie then inreases to $288, and the ompany needs to make a 20% profit, what was the ost prie to the nearest $? $238 B $480 0 $240 $242 One method that retail stores use to offer disounted produts is the 'buy one get one free' model. This represents an effetive disount of 100% off both items 0 50% off both produts when ombined together B 50% off the first item, the seond for free 75% off the ombined prie d Selet the offer with the greatest disount on a $47 meal. GST free C 15% off 0 $10 ashbak $5 rebate e Whih offer represents the greatest dollar value disount? 20% disount on $300 C 10% disount on $ % disount on $250 30% disount on $200 CMN189

8 CMN190 Setion 7 - Patterns and lgebra a Whih expression best represents the area of the retangle below? a b a x b x 0 a(b+) B a + b+ b + (a) b For the retangle above, alulate the area in m² if a = 4, b = 5 and = C Whih of the equations below are orret when the values below are used? a = 5 b = 4 = = x b + a = ( + b)a B 122 = ( x a) + b 117= ( x b) + a d Whih of the equations below are orret when the values below are used? x = 5 y = 3 z = = (z+y)x C 42= (z/y) + x B 21 = (z+y)x 47 = (z/y) + x e Expand the following equation: 5a(a + 20) = 5a² + 20a CMN190

9 CMN191 Setion 8 - Patterns and lgebra a Fatorise 28a - 32 a(28-32) C 7(4a - 8) b Fatorise 4x + 4. B a = 4 0 4(7a - 8) 4(x + 1) Fatorise 15x +5 5(3x + 1) d Fatorise 20x -5 5(4x - 1) e Fatorise 6x² - 2x 2x(3x - 1) CMN191

10 CMN192 Setion 9 - Patterns and lgebra a Simplify 5h + 2k k + 9h 33hk - 7 C 22h + 11k h + 19k h -15k + 8 b Simplify 114wzy 6wz 20wzy C 19wz 0 19y 20y Simplify, a a a 2a 0 15 B 15 6a 2a C 15 8 d Simplify -5(2a - 8) 10a a + 40 B 10a a - 40 e Fatorise 18a (5-2a) C -9(2a + 5) B -9(2a - 5) 0 9(2a - 5) CMN192 CMN193/194 Setion 10 - Linear and Non-Linear Relationships

11 Use the following information to answer the questions below. In the linear equation y = mx + b b is the y-interept on the Cartesian plane m is the gradient (slope) of the line plotted on the Cartesian plane x and y are the o-ordinates of a point on the line a Label the x and y axes. (1 mark) b Plot the x and y o-ordinates shown in the table on the graph below. Use this graph to answer question. 10y-axis x y x-axis If b = 4, alulate the value of the gradient (m) of the line you have plotted. 0 1 C 4 B 5-1 Setion 10 Continued Use the graph below to answer the following questions

12 d The slope of this line is negative, whih means that the value of 'm' will be negative in the linear equation y = mx + b. Whih equation mathes the line graphed above? y = 4x + 1 C m = -4 0 y = -4x + 1 y = -4x +21 e Where does the line ut the y-axis on the graph above? ie: what is the y-interept? -4 C -3 B CMN193/194