MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 ĐỖ ĐỨC THÀNH MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 MỤC LỤC A MOCK TEST MOCK TEST MOCK TEST MOCK TEST MOCK TEST MOCK TEST MOCK TEST MOCK TEST7 MOCK TEST MOCK TEST 10 MOCK TEST 10 B ANSWER KEYS MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 CAMBRIDGE PRIMARY MATHEMATICS EXAM May, 2020 Time allowed: 60 minutes Full name: _ MARK Date of birth: Gender: _ School name: INSTRUCTIONS AND INFORMATION Read carefully and ansure your name, date of birth, gender and your school name are filled in Calculators are NOT allowed You have 60 minutes to complete the exam Marks will NOT be deducted for incorrect answers Each correct answer in Section A is worth 0.2 marks Each correct answer in Section B is worth 1.2 marks MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 MOCK TEST 01 SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Q1 Which is the value of A+B if 𝐴 = × (3 + + + + 7) and 𝐵 = (2 + + + + 6) × 7? A 180 B 190 C 200 D 210 Q2 Daniella places some small cubes in the big cube as shown How many cubes are there missing to fill up the big cube? A B C 17 D 19 Q3 Write the missing number: 21036 - ……… = 10897 E 13901 F 11039 G 10139 H 10193 Q4 What is the average of 1, 3, 5, 7, 9, 11, 13, 15, 17? A B C D Q5 If 435526, 245928 and n have a total of 999999 then the value of n is … A 318545 B 318544 C 381445 D 318554 Q6 Find the value of k if 𝐾 + 985 =1 1995 × 101 − 1010 A 199050 B 199500 C 198500 D 189500 Q7 What is the greatest number n such that 293 + n < 1000 and 293 + n is divisible by 9? A 700 B 670 C 706 D 760 Q8.Three years ago, Nora was half as old as Mary is now If Mary is four years older than Nora, how old is Mary now? A 12 B 13 C 14 D 15 Q9 Several pairs of positive integers (natural numbers) (m, n) satisfy the condition 19m + 90 + 8n = 1998 Of these, (100, 1) is the pair with the smallest value for n Find the pair with the smallest value for m A B C D Q10 A teacher gives a star for every correct answers and a smiley face for every 10 correct answers Emily has 50 correct answers How many times has she had a star and a smiley face at the same time? A B C D Q11 What is the product of the factors 𝟏 𝟏 ? 𝟏 𝟏 C D A 𝟏𝟎 B 𝟗 C 𝟐 D 𝟓 Q12 On a digital clock displaying hours, minutes and seconds, how many times in each 24-hour period all the six digits change siultaneously? A B MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 Q13 In the following sequence of block, if the pattern continues, how many blocks will you need to make a model that is blocks high? A 10 B 15 C 20 D 25 Q14 Erin’s dog just had three puppies The total weight of the dog and puppies is 32 pounds The mother dog’s weight equals the weight of all the three puppies combined What is the weight of the mother dog? A B C 12 D 16 Q15 Which of the following can be expressed as the product of two consecutive even integers? A 22 B 36 1 Q16 Find the fraction halfway between and 𝟏 𝟐 C 48 𝟒 D 60 𝟖 A 𝟒 B 𝟏𝟓 C 𝟏𝟓 D 𝟏𝟓 Q17 Using 5c, 10c, 20c and 50 c coins, in how many different ways can you make 50c? A 12 B 13 C 14 D 15 Q18 Calculate the perimeter of a square (cm) if the length of its side is 9cm The perimeter of a square is…(cm) A 12 B 18 C 24 D 36 Q19 What is the largest total can be made by adding two of these numbers: 223853, 310093, 209109, 100984 The largest total can be made is… A 533496 B 533946 C 539346 D 353946 Q20 Find the value of x if x-(45+56)=21 The value of x is… A 121 B 211 C 112 D 122 Q21 John’s father is times older than John and John is twice as old as his sister Alice In two years time, the sum of their ages will be 58 How old is John now? A 10 B 12 C 15 D Q22 A "stair-step" figure is made of alternating black and white squares in each row Rows through are shown All rows begin and end with a white square The number of black squares in the 37th row is A 34 B 35 C 36 D 37 Q23 In Town A, five students are standing at different intersections on the same east-west street, as shown The differences between adjacent intersections are given in kilometers The students agree to meet somewhere on the street such that the total distance travelled by all five students is as small as possible Where should they meet? A Bo’s B Carla’s C Denise’s D Ernie MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 Q24 A piece of paper containing six joined squares labeled as shown in the diagram is folded along the edges of the squares to form a cube The label of the face opposite the face labeled X is A Z B U C V D Y Q25 Joan originally had twice as many books as Emily After she gave Emily books, Joan still had 10 more than Emily Then Joan orginally has (had)…books A 4000 B 400 C 40 D Q26 The perimeter of a rectangle is 96cm If you add 3cm to the width and subtract 3cm from the length of that rectangle, it’ll be a square.Then the area of that rectangle is…(cm2) A 657 B 567 C 756 D 765 Q27 Find the odd number k if there are exactly 35 odd numbers between k and 100 The result is… A 27 B 28 C 29 D 30 Q28 In the following sequence of card numbers, If the pattern of numbers continues, what number will you put on the next card? A 91 B 93 C 95 D 97 Q29 In the figure below, what fractions (fraction) of this square is shaded? A 𝟒 𝟖 B 𝟓 𝟖 C 𝟔 𝟖 D 𝟕 𝟖 Q30 The area of polygon ABCDEF, in square units, is A 24 B 30 C 46 D 74 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 Q31 A ream of paper containing 500 sheets is cm thick Approximately how many sheets of this type of paper would there be in a stack 7.5 cm high? A 250 B 550 C 667 D 750 Q32 The bar graph shows the grades in a mathematics class for the last grading period If A, B, C, and D are satisfactory grades, what fraction of the grades shown in the graph are satisfactory? A 𝟏 𝟐 B 𝟐 𝟑 C 𝟑 𝟒 Q33 Calculate: A 150 B 199 C 200 Q34.Which of the following numbers is the largest? A .99 B .9099 C .9 401 Q35 Estimate to determine which of the following numbers is closest to 0.205 A B 20 C 200 Q36 If the markings on the number line are equally spaced, what is the number ? A Q37 Calculate: 𝟏 A 𝟑 Q38.The product 𝟏 A 𝟖 B 10 B B 𝟐 𝟑 𝟐 𝟖 C 12 C C 𝟑 𝟒 𝟐 𝟒 D 𝟒 𝟓 D 250 D .09 D 2000 D 15 D D 𝟒 𝟑 𝟒 𝟑 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 Mr Zack buys 11 pencils Each pencil costs $2, and 23 pens, each pen costs $3 He gets a discount of $1 for every pencils he buys and a discount of $2 for every pens he buys How much in total does he pay? SOLUTION: Q40 Four circles of radius are arranged as shown Their centers are the vertices of a 22 square Find the area of the shaded region (Take 𝜋 = ) SOLUTION: MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 MOCK TEST 02 SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Q1 In the last test, Nam has 42 correct answers If each correct answer is equivalent to points, then Nam has … points in this test A 74 B 84 C 94 D 104 Q2 The difference of two numbers is 12 If one number is times greater than the other, then the sum of these two numbers is … A B 14 C 24 D 34 Q3 If the sum of two numbers is 18 and the ratio of these two numbers is 5, then the value of the greater number is … A 15 B 25 C 35 D 45 Q4 The sum of two consecutive numbers is 149 The greater number is … A 55 B 65 C 75 D 85 Q5 It costs $15 to buy books at the store If Nam wants to buy books, he must pay $… A 15 B 25 C 35 D 45 Q6 A teacher gives a star for every correct answers and a smiley face for every 10 correct answers Emily has 50 correct answers How many times has she had a star and a smiley face at the same time? A B C D Q7 It costs $216 to stay for days at Daewoo hotel How many days would Mr Minh stay if Mr Minh pays $540? A B.10 C 15 D 20 Q8 Three years ago, Kien was years older than Minh In the next two years from now, the sum of Kien’s age and Minh’s age is 20 Now Minh is … years old A B C D Q9 Find the smallest – digit number made from five digits 0, 3, 5, 6, if all digits of this number are distinct A 10365 B 10356 C 13056 D 13065 Q10 Find the greatest – digit number if it is the product of two consecutive numbers A 70 B 80 C 90 D 100 Q11 It took boys hours to clean a house How many more boys are needed to clean the house in hours? A B C D Q12 How many cubes have been taken out if the original cube is made up of 125 small cubes? A 64 B 84 C 81 D 100 Q13 If and are nonzero digits, then the number of digits (not necessarily different) in the sum of the three whole numbers is A B C D MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 Q34 Each of the three large squares shown below is the same size Segments that intersect the sides of the squares intersect at the midpoints of the sides Which shapes have the same area? A and B and Q35 The number halfway between A 𝟏 𝟑 B 𝟏 𝟓 C and D All of them and is C 𝟓 𝟐𝟒 D 𝟕 𝟐𝟒 Q36 The perimeter of one square is times the perimeter of another square The area of the larger square is how many times the area of the smaller square? A B C D Q37 An airplane flies for 120 minutes with a constant speed of 600 km/h and then for another 180 minutes with a constant speed of 1000 km/h What distance did it go? A 3200 km B 3400 km C 4200 km D 2400 km Q38 The difference between two numbers is 705 The sum is five times as much as the smaller number What is the greater number A 235 B 940 C 325 D 904 SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 The average age of 50 members of a summer camp is 19 years including 19 girls, 22 boys and teachers The average age of the teachers is 35, the average age of the girls is 16 What is the average age of the boys? SOLUTION: MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 53 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 Q40 It is given that AC=10 cm Find the area of the shaded part 22   Use    SOLUTION: MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 54 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 MOCK TEST 01 ANSWER KEYS SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Answer Question Answer Question Answer Question Answer Q1 B Q11 A Q21 D Q31 C Q2 C Q12 C Q22 C Q32 D Q3 C Q13 B Q23 B Q33 D Q4 D Q14 D Q24 D Q34 A Q5 A Q15 C Q25 C Q35 D Q6 B Q16 C Q26 B Q36 C Q7 C Q17 B Q27 C Q37 D Q8 C Q18 D Q28 C Q38 C Q9 B Q19 B Q29 C Q10 D Q20 D Q30 C SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 Mr Zack buys 11 pencils Each pencil costs $2, and 23 pens, each pen costs $3 He gets a discount of $1 for pencils he buys and a discount of $2 for pens he buys How much in total does he pay? RESULT: $80 SOLUTION: The money he has to pay for the pencils is: $2 × 11 − × $1 = $19 The money he has to pay for the pens is: 23 × $3 − × $2 = $61 Thus, the total amount of money he has to pay is: $80 Q40 Four circles of radius cm are arranged as shown Their centers are the vertices of a 22 square Find the area of the shaded region (Take 𝜋 = ) RESULT: 𝟓𝟒 𝟕 𝒄𝒎𝟐 SOLUTION: The side of the square of made up of two radii, and the area of the square is (3 + 32 = 36 𝑐𝑚2 The unshaded region of the square is composed of four quarter circles, and has the area of one circle, which is × 𝜋 As a result, the area of the shaded region is 36 − × 𝜋 = 54 𝑐𝑚2 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 55 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 MOCK TEST 02 ANSWER KEYS SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Answer B C A C B D A B B C Question Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Answer D A B D C D D C D A Question Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30 Answer B B B B C C D C B D Question Q31 Q32 Q33 Q34 Q35 Q36 Q37 Q38 Answer D A D C A C A B SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 Katherine had 80 potatoes to peel She started peeling at the rate of 12 potatoes in minutes minutes later, her sister joined and peeled at the rate of potatoes per minute How many more potatoes does Katherine peel than her sister? RESULT: 40 SOLUTION: The rate at which Katherine peels the potatoes is: 12 ÷ = 𝑝𝑜𝑡𝑎𝑡𝑜𝑒𝑠 𝑝𝑒𝑟 𝑚𝑖𝑛𝑢𝑡𝑒 The number of potatoes Katherine peels in the first minutes is: × = 30 The remaining number of potatoes is: 80-30=50 The number of potatoes peeled in each minute is: 4+6=10 Thus, the time it takes both of them to peel the remaining potatoes is: 50:10= minutes So, the number of potatoes Katherine peels more than her sister in those minutes is: (6 − 4) × = 10 As a result, the total number of potatoes Katherine peels more than her sister is: 30+10=40 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 56 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 Q40 Around the outside of a 4- by-4 square, construct four semicircles (as shown in the figure) with the four sides of the square as their diameters Another square, ABCD, has its sides parallel to the corresponding sides of the original square, and each side of ABCD is tangent to one of the semicircles The area of the square ABCD is RESULT: 64 SOLUTION: The radius of each semicircle is 2, half the sidelength of the square The line straight down the middle of square ABCD is the sum of two radii and the length of the smaller square, which is equivalent to its sidelength The area of ABCD is (4 + + 2)2 = 64 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 57 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 MOCK TEST 03 ANSWER KEYS SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Answer Question Answer Question Answer Question Answer Q1 B Q11 D Q21 B Q31 C Q2 D Q12 C Q22 A Q32 C Q3 C Q13 A Q23 C Q33 D Q4 D Q14 C Q24 C Q34 B Q5 C Q15 D Q25 B Q35 B Q6 B Q16 A Q26 A Q36 A Q7 C Q17 C Q27 A Q37 C Q8 C Q18 C Q28 B Q38 D Q9 B Q19 B Q29 A Q10 C Q20 C Q30 B SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 Zack has pairs of blue shoes, x pairs of red shoes, and (x+1) pairs of white shoes He is so lazy that he always puts all of his shoes in a large box How many pairs of white shoes does he have if he has to take out 24 shoes to make sure that he has a pair of blue shoes? RESULT: SOLUTION: The number of shoes he has to take out to make sure that he will have a pair of blue shoe is: 5+2x+2(x+1)+1=24 Solve this equation for x, we have x=4 Thus, the number of pairs of white shoes is 4+1=5 Q40 Triangles ABC, ADE, and EFG are all equilateral Points D and G are midpoints of AC and AE, respectively If AB=4, what is the perimeter of figure ABCDEFG ? RESULT: 15 SOLUTION: The large triangle ABC has sides of length The medium triangle has sides of length The small triangle has sides of length There are segment sizes, and all segments depicted are one of these lengths Starting at A and going clockwise, the perimeter is: AB+BC+CD+DE+EF+FG+GA=4+4+2+2+1+1+1=15 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 58 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 MOCK TEST 04 ANSWER KEYS SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Answer Question Answer Question Answer Question Answer Q1 B Q11 B Q21 C Q31 D Q2 C Q12 C Q22 A Q32 A Q3 A Q13 B Q23 A Q33 A Q4 B Q14 C Q24 B Q34 A Q5 D Q15 C Q25 B Q35 B Q6 C Q16 C Q26 A Q36 D Q7 C Q17 B Q27 A Q37 B Q8 B Q18 B Q28 C Q38 C Q9 B Q19 D Q29 C Q10 D Q20 B Q30 D SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 Zack learns 20 new English words each day for days in a row and 25 new English words each day for the next days How many words does he have to learn on the twelfth day so that the word average is 28 words? RESULT: 86 SOLUTION: The total number of words learned in 11 days is: 5x20+25x6=250 The total number of words learned in 12 days is: 28x12=336 The number of words learned in the twelfth day is 336-250=86 Q40 The large circle has diameter The two small circles have their centers on and just touch at , the center of the large circle If each small circle has radius , what is the value of the ratio of the area of the shaded region to the area of one of the small circles? RESULT: SOLUTION: The small circle has radius 1, thus its area is The large circle has radius 2, thus its area is The area of the semicircle above AC is then MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 59 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 The part that is not shaded are two small semicircles Together, these form one small circle, hence their total area is This means that the area of the shaded part is This is equal to the area of a small circle MOCK TEST 05 ANSWER KEYS SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Answer Question Answer Question Answer Question Answer Q1 B Q11 D Q21 A Q31 B Q2 D Q12 C Q22 C Q32 A Q3 C Q13 A Q23 B Q33 B Q4 D Q14 A Q24 A Q34 A Q5 C Q15 B Q25 B Q35 B Q6 C Q16 D Q26 B Q36 C Q7 A Q17 A Q27 C Q37 D Q8 A Q18 D Q28 C Q38 C Q9 D Q19 C Q29 C Q10 C Q20 B Q30 B SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 A multiple choice examination consists of 20 questions The scoring is +5 for each correct answer, -2 for each incorrect answer, and for each unanswered question John's score on the examination is 48 What is the maximum number of questions he could have answered correctly? KEYS: 12 SOLUTION: If John answered 16 questions correctly, then he answered at most questions incorrectly, giving him at least points Therefore, John did not answer 16 questions correctly If he answered 12 questions correctly and questions incorrectly (leaving questions unanswered), then he scored points As all other options are less than 12, we conclude that 12 is the most questions MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 60 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 Q40 ABCD is a rectangle, D is the center of the circle, and B is on the circle If AD=4 22 cm and CD=3 cm, BD=5 cm then find the area of the shaded region (Take pi= ) KEYS: 𝟏𝟎𝟕 𝟏𝟒 SOLUTION: We have: The shaded region = One fourth of the circle area – the rectangle area 1 22 𝟏𝟎𝟕 = × 𝜋 × 52 -4 × = × × 25 − 12 = 𝟏𝟒 MOCK TEST 06 ANSWER KEYS SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Answer Question Answer Question Answer Question Answer Q1 C Q11 A Q21 D Q31 D Q2 D Q12 D Q22 B Q32 C Q3 B Q13 A Q23 C Q33 A Q4 B Q14 D Q24 C Q34 A Q5 B Q15 A Q25 D Q35 C Q6 D Q16 C Q26 D Q36 D Q7 C Q17 A Q27 B Q37 B Q8 B Q18 C Q28 A Q38 A Q9 B Q19 B Q29 B Q10 C Q20 D Q30 B SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 A shopkeeper bought 600 oranges and 400 bananas He found 15% of oranges and 8% of bananas were rotten Find the percentage of fruits in good condition RESULT: 87.8% SOLUTION: Total number of fruits shopkeeper bought = 600 + 400 = 1000 Number of rotten oranges = 15% of 600 = 15/100 × 600 = 9000/100 = 90 Number of rotten bananas = 8% of 400 = 8/100 × 400 = 3200/100 = 32 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 61 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 Therefore, total number of rotten fruits = 90 + 32 = 122 Therefore Number of fruits in good condition = 1000 - 122 = 878 Therefore Percentage of fruits in good condition = (878/1000 × 100)% = (87800/1000)% = 87.8% Q40 In the figure, two half-circles are inscribed in a square These two half-circles intersect at the center of the square If the side of the square has length of 14 cm, then 22 what is the area of the shaded region? (Take 𝜋 = ) RESULT: 𝟓𝟔 cm2 SOLUTION The area of the hemi-circle whose diameter is AB is: × 𝜋 × 72 = × 22 × 72 = 77 cm2 The area of triangle OAB is: × 14 × 14 = 49 cm2 The figure contains identical shaded parts, so, the area of each shaded part is given by: (The area of the hemi-circle - The area of triangle OAB):2=(77-49):2=14 cm2 Consequently, the total area of the shaded regions is: × 14 = 56 cm2 MOCK TEST 07 ANSWER KEYS SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Answer Question Answer Question Answer Question Answer Q1 A Q11 C Q21 D Q31 B Q2 A Q12 B Q22 C Q32 B Q3 D Q13 D Q23 B Q33 B Q4 C Q14 D Q24 A Q34 A Q5 B Q15 A Q25 C Q35 C Q6 A Q16 D Q26 B Q36 D Q7 B Q17 C Q27 B Q37 C Q8 B Q18 D Q28 A Q38 B Q9 D Q19 D Q29 D Q10 B Q20 B Q30 B MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 62 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 Zack has pairs of blue shoes, pairs of red shoes, and x pairs of white shoes He is so lazy that he always puts all of his shoes in a large box How many pairs of white shoes does he have if he has to take out 23 shoes to make sure that he has one pair of red shoes or one pair of white shoes? RESULT: pairs SOLUTION: The number of shoes he has to take out to make sure that he will have either a pair of red shoes or a pair of white shoes is 10+6+x+1=23 Solve this equation for x, we have x=5 Thus, the number of pairs of white shoes is 5+1=6 pairs Q40 Circles of radius cm and cm are externally tangent and are circumscribed by a third 22 circle, as shown in the figure Find the area of the shaded region (Take 𝜋 = ) 264 RESULT: SOLUTION: It is noticeable that the diameter of the largest circle is the sum of the diameters of the two smaller circles which is: 3+3+2+2=10 (cm) Thus, the area of the largest circle is:  52  25  sq cm  The areas of the second largest and the smallest circle are:  32  9  sq cm  ,  22  4  sq cm  respectively Finally, the area of the shaded region is: 25   9  4   12  sq cm  =12 × 22 = 264 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 63 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 MOCK TEST 08 SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Answer Question Answer Question Answer Question Answer Q1 A Q11 A Q21 C Q31 D Q2 B Q12 A Q22 B Q32 A Q3 C Q13 B Q23 C Q33 B Q4 B Q14 C Q24 A Q34 A Q5 B Q15 A Q25 A Q35 C Q6 C Q16 A Q26 B Q36 C Q7 A Q17 B Q27 B Q37 D Q8 B Q18 B Q28 D Q38 C Q9 D Q19 C Q29 D Q10 A Q20 B Q30 B SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 Joe gets on a 10-problem test, on a 30-problem test and on a 60-problem test If the three tests are combined into one 100-problem test, what is his score? RESULT: 75 SOLUTION: The number of right answers in the 10-problem test is: The number of right answers in the 30-problem test is: 21 The number of right answers in the 60-problem test is: 48 So, the total number of right answers in the 100-problem test is: 6+21+48=75 Thus, the score is 75/100 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 64 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 Q40 In the figure, the diameter of the largest circle is 28 cm Two circles of diameter 14 cm are inscribed in it Two circles of diameter cm are inscribed in each of the circles of diameter 14 cm What is the area, in cm2, of the shaded 22   region? Use    7  RESULT: 𝟏𝟓𝟒 cm2 SOLUTION: The radius of the largest circle is: 28:2=14 cm The radius of the second largest circle is 14:2=7 cm The radius of the smallest circle is: 7:2= cm It is noticeable that The area of the shaded region = The total area of the two second largest circle – The total area of the smallest circles 7 22 Thus, The area of the shaded region = × (𝜋 × × − × 𝜋 × × 2) = 49 × 𝜋 = 49 × = 154 cm2 MOCK TEST 09 SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Answer Question Answer Question Answer Question Answer Q1 B Q11 B Q21 C Q31 C Q2 C Q12 C Q22 B Q32 D Q3 D Q13 A Q23 B Q33 A Q4 A Q14 A Q24 D Q34 B Q5 C Q15 C Q25 C Q35 B Q6 C Q16 B Q26 C Q36 B Q7 B Q17 C Q27 A Q37 A Q8 B Q18 B Q28 D Q38 D Q9 B Q19 D Q29 B Q10 D Q20 C Q30 C MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 65 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 A shopper buys a 100 dollar coat on sale for 20% off An additional dollars are taken off the sale price by using a discount coupon A sales tax of 8%is paid on the final selling price Find the total amount the shopper pays for the coat KEY: 81 dollars SOLUTION After the 20% sale, the coat costs 100 × 0.8 = 80 dollars Then dollars are taken off for a cost of 80-5=75 Adding on the sales tax, the final amount is 75 × 1.08 = 81 𝑑𝑜𝑙𝑙𝑎𝑟𝑠 Q40 The radius of each smaller circle is cm Find the area of the shaded 22   area Use    7  KEY: 𝟑𝟓𝟐 𝟕 cm2 SOLUTION Because the radius of each smaller circle is cm, then the radius of the larger circle is cm It is noticeable that the area of the shaded parts = The area of the larger circle – the total area of the smaller circles = 𝜋 × × − × 𝜋 × × = 16 × 22 = 352 cm2 MOCK TEST 10 SECTION A Mark the letters A, B, C or D on your answer sheet to indicate the correct answer to each of the following questions Question Answer Question Answer Question Answer Question Answer Q1 D Q11 C Q21 C Q31 B Q2 B Q12 A Q22 B Q32 D Q3 A Q13 B Q23 B Q33 D Q4 C Q14 B Q24 C Q34 D Q5 B Q15 C Q25 B Q35 C Q6 B Q16 B Q26 A Q36 D Q7 C Q17 A Q27 B Q37 C Q8 B Q18 B Q28 A Q38 B Q9 A Q19 A Q29 A Q10 D Q20 C Q30 D MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 66 MATHIENCE CLUB-LEARNING MATHS AND SCIENCE WITH MR ZACK 2019-2020 SECTION B Write the full answer to each of the following questions in the space provided in the answer sheet Q39 The average age of 50 members of a summer camp is 19 years including 19 girls, 22 boys and teachers The average age of the teachers is 35, the average age of the girls is 16 What is the average age of the boys? RESULT: 15 SOLUTION: The sum of age of the 50 members is: 50 × 19 = 950 The sum of age of the teachers is: 35 × = 315 The sum of age of the 19 girls is: 16 × 19 = 304 Thus, the sum of age of the 22 boys is: 950-315-304=331 Consequently, the average age of the 22 boys is: 331:22=15.045 Q40 It is given that AC=10 cm Find the area of the shaded part 22   Use    RESULT: 𝟖𝟐𝟓 𝟏𝟒 cm2 SOLUTION: The radius of the larger circle is 10:2=5 cm The radius of the smaller circle is: 5:2= cm It is noticeable that the shaded area = The area of the larger circle – the area of the smaller circle 5 =𝜋×5×5−𝜋×2×2 = 75 ×𝜋 = 75 × 22 = 825 14 cm2 MATHS AND SCIENCE ARE THE LIFEBLOOD OF THE FUTURE 67 ... SCIENCE WITH MR ZACK 2019-2020 MỤC LỤC A MOCK TEST MOCK TEST MOCK TEST MOCK TEST MOCK TEST MOCK TEST MOCK TEST MOCK TEST7 MOCK TEST MOCK TEST 10 MOCK TEST 10 B ANSWER KEYS MATHS AND SCIENCE ARE... It takes him minutes to travel from point A to point D (taking the shortest route) How long does it take him to travel from point A to point E(taking the shortest route)? A minutes B hours C minutes... 248 C 244 D 484 Q10 Joe gets on a 10-problem test, on a 30-problem test and on a 60-problem test If the three tests are combined into one 100-problem test, what is his score? A 60/100 B 75/100