ACER Maths Test Set 01 Answers PDF

ACER MATHS TEST SET 01 ANSWERS Question 1. Factorise 2x+10+dx+5d A. (x+5)(2+d) B. (x+2)(5+d) C. (x+d)(2+5) D. (x+10)(d+5) E. None of these To factorise you need to identify the common factor. First, group the expression into two: (2x+10) + (dx+5d) The common factor of 2x+10...

ACER MATHS TEST SET 01 ANSWERS Question 1. Factorise 2x+10+dx+5d A. (x+5)(2+d) B. (x+2)(5+d) C. (x+d)(2+5) D. (x+10)(d+5) E. None of these To factorise you need to identify the common factor. First, group the expression into two: (2x+10) + (dx+5d) The common factor of 2x+10 is 2 -> 2(x+5) The common factor of dx +5d is d -> d(x+5) = 2(x+5) + d(x+5) Then, we can identify that the common factor of two groups is (x+5) -> (x+5) (2+d) Study the triangle shown below to answer questions 2-3. Question 2. Identify the correct expression of x using trigonometry A. 15 Sin 72° B. 15 Cos 72° C. 6 tan 72° D. 6 Cos 72° E. None of these Remember SOH CAH TOA Identify: Cos 72° = A/H = x/15 Therefore, x= 15 Cos 72° Question 3. Find the value of x A. 9 B.18 C. 3 29 D.3 21 E. None of these Using Pythagoras’ theorem: a^2 +b^2= c^2, we can find the value of x 15× 15= 225= 6 × 6 +x × x 225-36 =x × x x= 189 =3 21 Question 4. Expand and simplify 3x(x + 1) + x(x −4) A. −𝑥 ' + 4𝑥 B. 6𝑥^2 − 4𝑥 C.3𝑥 ' + 3𝑥 + 𝑥 ' − 4𝑥 D. 4𝑥 ' -x E. None of these C is the expanded form. To simplify, collect the like terms: (3𝑥 ' +𝑥 ' ) + (3x−4x) = 4𝑥 ' −x Question 5.Identify the coordinates of the turning point of the graph below: A. (-1,3) B. (1,3) C. (1,-3)  D. (-1,-3) E. None of these The turning point is in the first quadrant, and hence the x and y coordinates should be positive numbers. -. Question 6. Rationalise and Simplify : ' - - - ' A. B. C. 3 6 D. 6 6 E. None of these '. To rationalise, multiply both the numerator and denominator by 2 -.×' - - - - = = = =3 6 '×' 2. '. 6 Question 7. If 𝑥 = , 𝑦 = , 𝑧 = , calculate: 𝑥 ÷ 𝑧 − 𝑦. 2 - 8 6. '. 9 A. B. C. D. E. None of these 9 2.- 68 Remember BODMAS Firstly, you divide x by z : 2/3 ÷ 1/6 To divide fractions, you change the division sign to multiplication sign and convert the second fraction into its reciprocal. 2/3 x 6/1 = 4 Then, subtract ¾ from 4 by making the denominators to be the same first. 4-3/4=16/4-3/4=13/4 Question 8. Note that 280 ÷ 1.4 = 200. So, 28 ÷ 0.14 = A. 2 B.20 C.200 D.0.2 E. None of these 280/10=28 1.4/10=0.14 Both numbers had been divided by 10 so the answer would be the same, 200. Question 9. An American picture book has a picture of a kitten in it, which is 25 inches. How tall is the kitten in centimetres? A. 37.5 B. 50.5 C. 50.0 D. 63.5 E. None of these Note that 1 inch = 2.54 cm. Therefore, kitten is 2.54 x 25 =63.5 cm. Question 10. Study the first triangle to identify the value of Z in the second triangle.  5 10 3 4 8 Z A. 6 B. 7 C.4 D. 2 E. None of these From the first triangle, we can identify the pattern that the sum of squares of two numbers in the bottom sections equals to the square of the number at the top. i.e. 3' + 4' = 5' Therefore, to find the value of Z: 10' − 8' = 𝑍 ' Therefore, Z is 100 − 64 = 36 = 6 Use the Venn diagram below to answer the questions 11,12 and 13. There was a survey asking a class of students about what sports they play. T= Tennis B B= Badminton T 8 17 13 2 Question 11. How many students were surveyed? A. 48 B. 46 C. 37 D. 40 E. None of these There are 40 students altogether: 13 + 8 + 17 + 2. Question 12. How many students played tennis only? A. 13 B. 21 C. 17 D.25 E. None of these There are 13 students who played tennis only. Do not include 8 in the intersection. Question 13. How many students neither played tennis nor badminton? A. 8 B. 4 C. 2 D. 12 E. None of these Those who neither played tennis nor badminton are indicated by 2, outside of the circles. Question 14. The swimming pool is about 1.5 metres deep. If the diagram below shows the swimming pool, how much water (in litres) would be required to fill the pool to the very top? 1.8 m 1.1 m A. 1.98L B. 1,980L C. 2.97L D.2,970L E. None of these To find the volume: 𝑙 × 𝑤 × ℎ = 1.8 ×1.1×1.5 = 2.97 1 cubic metres= 1000L Therefore, 2.97 x 1000= 2970 L. Question 15. Simplify: (4 3 − 5)' A. 53 − 4 15 B. 16 − 4 15 C. 12 − 4 5 D. 53 − 8 15 E. None of these First, expand the brackets: (4 3 − 5)' = 4 3 − 5 × 4 3 − 5 = 16×3 − 4 15 − 4 15 + 5 = 48 + 5 − 8 15 = 53 − 8 15 Question 16. A tin of paint costs $3.2 and it can paint 450 square meter. If a room has a rectangular wall with dimensions of 43.2m x 29.1m, calculate the cost of paint a painter would need to buy altogether. 2..'×'D.6 2..'×'D.6×..' 2EF 2EF×..' A. B. C. D. E. None of these 2EF×..' 2EF 2..'×'D.6×..' 2..'×'D.6 Firstly, calculate the area of the rectangular wall: 43.2×29.1 Secondly, using the ratio that 1 tin of paint covers 450 square meter, calculate 2..'×'D.6 the number of tins needed: 2EF 2..'×'D.6×..' Then, calculate the cost: 2EF Question 17. Last Sunday, there was a medical conference and the audience consisted of doctors and researchers. 240 of the audience were researchers. This was 60% of the total number of audience. How many audience were there altogether? A. 384 B. 400 C. 300 D. 336 E. None of these 240 represents 60% of the total number. '2F To find 100% of the total number, = 400 F.- Question 18. Continued from question 17: How many doctors were there? A. 144 B. 400 C. 160 D. 60 E. None of these 400 = doctors + researchers doctors= 400 – 240 =160 Question 19. A number z is squared and is subtracted from three times its cube. If the result is 33, select the appropriate equation to identify the value of number z. A. 𝑧 ' − 3𝑧. = 33 B. 3𝑧. − 𝑧 ' = 33 C. 3𝑧 ' − 𝑧. = 33 D. 3 𝑧. − 𝑧 ' = 33 E. None of these Use the linear graph drawn below to answer the questions 20,21,22 and 23. The linear graph passes through the points: (0,10), (1,3) and (2,-4) Question 20. Identify the set of coordinates of the point that lie inside the shaded area. A. (3,6) B. (1, 6) C. (-1, -3) D. (2,4) E. None of these Question 21. Identify the set of coordinates of the point that lie outside the shaded area. A. (-1,3) B. (0,5) C. (-1,-2) D.(3-,4) E. None of these Question 22. Identify the gradient of the linear graph. A. 2 B. -2 C. 7 D. -7 E. None of these HIJK N9 Gradient= 𝑚 = = = −7 HLM 6 Question 23. Identify the equation of the linear graph. A.𝑦 = −7𝑥 + 10 B. 𝑦 = 7𝑥 + 10 C. 𝑦 = −2𝑥 + 4 D. 𝑦 = 2𝑥 − 4 E. None of these 𝑦 = 𝑚𝑥 + 𝑐, 𝑤ℎ𝑒𝑟𝑒 𝑐 𝑖𝑠 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 0,10 𝑦 = −7𝑥 + 10 Question 24. Tim was paid $313 after working 20 hours. What is the hourly pay? A. 15.35 B. 15.55 C.15.65 D.15.85 E. None of these.6. To calculate the hourly pay, = 15.65 'F Question 25. What is the intersection point of the two graphs of 𝑦 = 3 − 2𝑥 and 𝑦 = 𝑥 '. A. (1,1) B. (2,3) C. (3,-1) D. (-1,3) E. None of these To find the intersection point, let 𝑦 = 3 − 2𝑥 = 𝑥 '. 0 = 𝑥 ' + 2𝑥 − 3 0 = 𝑥 − 1 (𝑥 + 3) ∴ 𝑥 = 1, −3 In the options given, there is no 𝑥 = −3. Substitute 𝑥 = 1 into 𝑦 = 𝑥 ' = 1  6 Question 26. Laura started reading a book at 2:55pm. If she read a book for 2 ' hours, what time did she finish reading a book? A. 4:15pm B. 4:25pm C. 5:15pm D.5:25pm E. None of these 2 hours after 2:55pm is 4:55pm. 30 minutes after 55 is 85. There are 60 minutes in 1 hour, so 85 minutes indicate 1 hour and 25 minutes. 4+1:25pm = 5:25pm Use the grid drawn below to answer the questions 27, 28 and 29. Question 27. If each individual square has an area of 1.44𝑐𝑚 ' , what is the size of the length of this square? A. 1.44cm B.1.2cm C.1.4cm D.0.72cm E. None of these area of the square= l x l = 1.44𝑐𝑚 ' length= 1.44 = 1.2𝑐𝑚 Question 28. What is the area of the triangle? A. 5.76𝑐𝑚 ' B.12.96𝑐𝑚 ' C. 5.04𝑐𝑚 ' D. 6.48𝑐𝑚 ' E. None of these There are 4.5 squares in the triangle. Therefore, the triangle has an area of : 4.5×1.44 = 6.48𝑐𝑚 ' Question 29. What is the area of the circle? (use 𝜋 = 3.14) A. 11.31𝑐𝑚 ' B. 4.52𝑐𝑚 ' C.7.54𝑐𝑚 ' D.10.17𝑐𝑚 ' E. None of these The radius of the circle is 1.5 length of the individual square = 1.5 × 1.2 = 1.8𝑐𝑚 The area of the circle is 𝜋𝑟 ' = 3.14×1.8' = 10.17 Question 30. Simplify (2𝑤 + 4)(2𝑤 − 4) A. 4𝑤 ' + 8𝑤 − 16 B. 4𝑤 ' − 8𝑤 − 16 C. 4𝑤 ' + 16𝑤 − 16  D. 4𝑤 ' − 16𝑤 − 16 E. 4𝑤 ' − 16 Firstly, expand the brackets: 4𝑤 ' + 8𝑤 − 8𝑤 − 16 Then, collect the like terms: =4𝑤 ' − 16 Question 31. – (−4). = A. -12 B.12 C. -64 D. 64 E. None of these −4. = −4×−4×−4 = −64 − −4. = −64×−1 = 64 [(\N2) Question 32. If 𝐴 = , what is C? '] ^[_2 '^] '^] ^[ A. B. C. +4 D. A. +4 E. None of these '] [_2 [ '] 2𝐴𝐷 = 𝐵 𝐶 − 4 2𝐴𝐷 = 𝐶−4 𝐵 2𝐴𝐷 +4=𝐶 𝐵 Refer to the diagram below to answer questions 33, 34,35 and 36. 7cm 2cm Question 33. What is the volume of the rectangular prism? A.70𝑐𝑚. B. 118𝑐𝑚. C.59𝑐𝑚. D.90𝑐𝑚. E. None of these Volume= 𝑙 × 𝑤 × ℎ = 2𝑐𝑚 × 5𝑐𝑚 × 7𝑐𝑚 = 70𝑐𝑚. Question 34.What is the mass of the rectangular prism, given that Density= Mass ÷ Volume? Note that density = 1.4gm /𝑐𝑚. A.165.2gm B.82.6gm C.98gm D.126gm E. None of these 𝑚𝑎𝑠𝑠 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 = 𝑣𝑜𝑙𝑢𝑚𝑒 𝑑𝑒𝑛𝑠𝑖𝑡𝑦×𝑣𝑜𝑙𝑢𝑚𝑒 = 𝑚𝑎𝑠𝑠  𝑚𝑎𝑠𝑠 = 1.4 × 70 = 98𝑔𝑚 Question 35. What is the surface area of the rectangular prism? A.70𝑐𝑚 ' B. 118𝑐𝑚 ' C.59𝑐𝑚 ' D.90𝑐𝑚 ' E. None of these Surface area = sum of area of 6 faces = 2×2×5 + 2×5×7 + (2×2×7) =20 + 70 + 28 = 118𝑐𝑚 ' Question 36. Jo wants to giftwrap a present that has the same dimension as the rectangular prism in the above diagram. If the giftwrapping paper costs $0.42 per 20𝑐𝑚 ' , how much will it cost her to buy the required area of giftwrapping paper? A.$2.40 B.$9.12 C.$1.89 D.$1.47 E. None of these 118 𝑝𝑟𝑖𝑐𝑒 = ×0.42 = $2.48 20 Question 37. What is the probability that a total of 7 is thrown, if two six sided dice are thrown together? 6 6 6 6 A. B. C. D. E. None of these - 6' D 68 Total of 7 can be achieved: 1. 1,6 2. 6,1 3. 2,5 4. 5,2 5. 3,4 6. 4,3 The total events are 36. - 6 Hence, the probability is =.- - Question 38. Which equation is most likely to be the equation of the graph below? A. 𝑦 = 4𝑥 + 2 B. 𝑦 = −7𝑥 − 3 C. 𝑦 = −3𝑥 − 2 D. 𝑦 = −2𝑥 + 3 E. None of these The gradient is positive, so options B, C, D are wrong. The y-intercept is negative so A is also wrong.  Question 39. Given that the x-intercept is (2,0) and y-intercept is (0,-5) for the linear graph of question 38, identify the gradient. A. 10 B. -10 C. 2.5 D. -2.5 E. None of these HIJK FNNE E Gradient= 𝑚 = = = HLM 'NF ' Question 40. 2𝑥 F ×(3𝑥. )F A. 6𝑥. B.2𝑥. C.2x D.2 E. None of these F. F 2𝑥 ×(3𝑥 ) = 2 1 × 1 = 2 j Question 41. 21k can be also written as '6j j k A. B. 21. C.( 21)' D. ( 21)E E. None of these '6k.l k -m n Question 42. × = 2m ml n Dml k Dm ' Dm Dl ' A. B. C. D. E. None of these ' l 'l 'm 18𝑥. 𝑦 ' 9𝑥 = '. = 4𝑥 𝑦 2𝑦 Question 43. The refrigerator my mum wanted to buy is $2400 at Harvey Norman. My friend who works at Good Guys, can give her a 15% discount. What is the discounted price of the refrigerator at Good Guys? A. $360 B. $1800 C. $2040 D.$2280 E. None of these 15% of $2400= $360 Therefore, the discounted price = $2400-360 = $2040 Refer to the table below to answer questions 44 and 45. I II III IV A 3 5 7 9 B 13 15 17 … 23 … … Question 44. If the pattern continues down the table, the number in column IV and row E would be: A. 41 B. 51 C. 59 D. 49 E. None of these I II III IV A 3 5 7 9 B 13 15 17 19 C23 25 27 29 C D 33 35 37 39 E 43 47 37 49 Question 45. The number 77 would be in A. Column VII, Row G B. Column III, Row G C. Column III, Row H D. Column VII, Row H E. None of these I II III IV A 3 5 7 9 B 13 15 17 19 C23 25 27 29 C D 33 35 37 39 E 43 45 47 49 F 53 55 57 59 G 63 65 67 6 9 H 73 75 77 79 Question 46. Last Saturday was 17th September. What is the date of tomorrow if today is Thursday? A. 22nd September B. 23rd September C. 24th September D. 25th September E. None of these There are 7 days in a week. This Saturday therefore would be 17+7= 24th September. Today is Thursday so tomorrow would be Friday. Hence, tomorrow would be 23rd September. Question 47. Erin turned 15 in 2001. Her brother is 3 years older. In what year was her brother born? A. 2004 B. 1986 C. 1990 D. 1983 E. None of these Erin’s brother would have turned 18 in 2001, as he is 3 years older than her. 2001-18= 1983. Question 48. Simplify 2 40 A. 20 B. 4 20 C. 2 10 D. 4 10 E. None of these 2 40 = 2 4×10 = 2× 4× 10 = 2×2× 10 = 4 10 Question 49. Peter’s smart phone was worth $1200 last year. However, due to release of newer version of the smart phone, the value of his phone had decreased by 25%. What is the new value of his phone this year? A. $300 B. $600 C. $900 D. $800 E. None of these As the price had dropped by 25%, its current value would be 75% of the original value. 9E 75% of $1200 = ×1200 = 75×12 = 900 6FF Question 50. What is this shape called?. A. Triangular prism B. Triangular based pyramid C. Square based pyramid D. Cube E. None of these END OF ANSWERS