[PDF] 2019 Reach and ICAS Practice Questions Mathematics Paper H.pdf | Plain Text

Mathematics PA PE R H Read the instructions on the ANSWER SHEET and fill in your NAME , SCHOOL and OTHER INFORMATION . Use a pencil. Do NOT use a coloured pencil or a pen. Rub out any mistakes completely. You MUST record your answers on the ANSWER SHEET . Mark only ONE answer for each question. Your score will be the number of correct answers. Marks are NOT deducted for incorrect answers. There are 5 MULTIPLE-CHOICE QUESTIONS (1 –5). Use the information provided to choose the BEST answer from the four possible options. On your ANSWER SHEET fill in the oval that matches your answer. You may use a ruler and spare paper. You are NOT allowed to use a calculator . DO NOT OPEN THIS BOOKLET UNTIL INSTRUCTED. Note : Some UNSW Global assessments are only available online. PRACTICE QUESTIONS

1. In which picture does the slice match the missing part of the cake? cake slice slice slice slice (A) (B) (C)(D) cake cake cake 2. This is a diagram of a triangle. NOT TO SCALE x y (A) 70 120 (B) 50 120 (C) 70 100 (D) 50 100 Which of these cannot be values for x and y ? NOT T O SCALE x y (A) 70 120 (B) 50 120 (C) 70 100 (D) 50 100 3. This is a sector graph (pie graph). cars Key trucks motorbikes bicycles Vehicles Passing the School 90 21 15 9 What is the angle at the centre for the number of cars passing this school? (A) 296° (B) 284° (C) 257° (D) 240° 4. In the toy car shown, the diameters of the back wheels are one-and-a-half times the diameters of the front wheels. When the car travels one metre, the back wheels go around 6 times. How many times do the front wheels go around when the car travels one metre? (A) 4 (B) 6 (C) 9 (D) 12 © UNSW Global Pty Limited 2

5.* Katya has a set of Russian dolls. The heights of her dolls are shown. They increase by a fixed ratio. 128 mm 96 mm 72 mm 54 mm 40.5 mm 1.1603 10 x mm The sm allest doll fits in the next larger doll. They both fit inside the next doll. The largest doll shown fits all four of the other dolls inside it. Katya calculates the height of the doll that can fit exactly 700 dolls inside it, including the dolls shown. She writes the answer as: 128 mm 96 mm 72 mm 54 mm 40.5 mm 1.1603 10 x mm What is the value of x? END OF PAPER END OF PAPER QUESTION 5 IS FREE RESPONSE. Write your answer in the boxes provided on the ANSWER SHEET and fill in the ovals that match your answer. 3 © UNSW Global Pty Limited * Free response questions are only applicable to some assessments.

5.* Katya has a set of Russian dolls. The heights of her dolls are shown. They increase by a fixed ratio. 128 mm 96 mm 72 mm 54 mm 40.5 mm 1.1603 10 x mm The sm allest doll fits in the next larger doll. They both fit inside the next doll. The largest doll shown fits all four of the other dolls inside it. Katya calculates the height of the doll that can fit exactly 700 dolls inside it, including the dolls shown. She writes the answer as: 128 mm 96 mm 72 mm 54 mm 40.5 mm 1.1603 10 x mm What is the value of x? END OF PAPER © UNSW Global Pty Limited 4 THIS PAGE MAY BE USED FOR WORKING.

Print your details clearly in the boxes provided. Make sure you fill in only one oval in each column. Rub out all mistakes completely. Do not use a coloured pencil or pen. HOW TO FILL OUT THIS SHEET: USE A PENCIL A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C a a a a a a a a a a a a a a a a a a a E E E E E E E E E E E E E E E E E E E c c c c c c c c c c c c c c c c c c c d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e I I I I I I I I I I I I I I I I I I I J J J J J J J J J J J J J J J J J J J h h h h h h h h h h h h h h h h h h h i i i i i i i i i i i i i i i i i i i M M M M M M M M M M M M M M M M M M M k k k k k k k k k k k k k k k k k k k l l l l l l l l l l l l l l l l l l l P P P P P P P P P P P P P P P P P P P Q n n n n n n n n n n n n n n n n n n R o o o o o o o o o o o o o o o o o o S S S S S S S S S S S S S S S S S S S T T T T T T T T T T T T T T T T T T T r r r r r r r r r r r r r r r r r r r s s s s s s s s s s s s s s s s s s s t t t t t t t t t t t t t t t t t t t u u u u u u u u u u u u u u u u u u u v v v v v v v v v v v v v v v v v v v Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ – – – – – – – – – – – – – – – – – – – / / / / / / / / / / / / / / / / / / / DATE OF BIRTH STUDENT ID CLASS Day Month Year (optional) (optional) 0 M M M M M M M M M M M M M M A h 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 B i 2 2 2 2 2 2 2 2 2 2 2 2 2 2 C M 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a k 4 4 4 4 4 4 4 4 4 4 4 4 4 E l 5 5 5 5 5 5 5 5 5 5 5 5 5 c P 6 6 6 6 6 6 6 6 6 6 6 6 6 d n 7 7 7 7 7 7 7 7 7 7 7 7 7 e o 8 8 8 8 8 8 8 8 8 8 8 8 8 I S 9 9 9 9 9 9 9 9 9 9 9 9 9 J T A A A A A A A A A A A A A A A A A A A A A A A A B B B B B B B B B B B B B B B B B B B B B B B B C C C C C C C C C C C C C C C C C C C C C C C C a a a a a a a a a a a a a a a a a a a a a a a a E E E E E E E E E E E E E E E E E E E E E E E E c c c c c c c c c c c c c c c c c c c c c c c c d d d d d d d d d d d d d d d d d d d d d d d d e e e e e e e e e e e e e e e e e e e e e e e e I I I I I I I I I I I I I I I I I I I I I I I I J J J J J J J J J J J J J J J J J J J J J J J J h h h h h h h h h h h h h h h h h h h h h h h h i i i i i i i i i i i i i i i i i i i i i i i i M M M M M M M M M M M M M M M M M M M M M M M M k k k k k k k k k k k k k k k k k k k k k k k k l l l l l l l l l l l l l l l l l l l l l l l l P P P P P P P P P P P P P P P P P P P P P P P P Q n n n n n n n n n n n n n n n n n n n n n n n R o o o o o o o o o o o o o o o o o o o o o o o S S S S S S S S S S S S S S S S S S S S S S S S T T T T T T T T T T T T T T T T T T T T T T T T r r r r r r r r r r r r r r r r r r r r r r r r s s s s s s s s s s s s s s s s s s s s s s s s t t t t t t t t t t t t t t t t t t t t t t t t u u u u u u u u u u u u u u u u u u u u u u u u v v v v v v v v v v v v v v v v v v v v v v v v Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ – – – – – – – – – – – – – – – – – – – – – – – – / / / / / / / / / / / / / / / / / / / / / / / / Are you male or female? Male Female Does anyone in your home usually speak a language other than English? Ye s No School name: Town / suburb: Today’s date: / / Postcode: PA PE R H *202510* EXAMPLE 1: Debbie Bach FIRST NAME LAST NAME ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD EXAMPLE 2: Chan Ai Beng FIRST NAME LAST NAME ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD EXAMPLE 3: Jamal bin Abas FIRST NAME LAST NAME ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD ABCD EEEE EEE EE EEE EE EEE EEEEE EEE EEEEEE EEE EEEE FIRST NAME to aSSear on certificate LAST NAME to aSSear on certificate PAPER M SAMPLE

MULTIPLE CHOICE Questions 1 to 35 Example: 4 + 6 = (A) 2 (B) 9 (C) 10 (D) 24 The answer is 10 , so fill in the oval C , as shown. a C B A 1 A B C a 11 A B C a 21 A B C a 31 A B C a 2 A B C a 12 A B C a 22 A B C a 32 A B C a 3 A B C a 13 A B C a 23 A B C a 33 A B C a 4 A B C a 14 A B C a 24 A B C a 34 A B C a 5 0 M M 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 PA PE R H TO ANSWER THE QUESTIONS START USE A PENCIL DO NOT USE A COLOURED PENCIL OR PEN M PA PE R A For details on how we handle your personal information, please see our Privacy Policy on our website at unswglobal.unsw.edu.au SAMPLE

7 © UNSW Global Pty Limited ICAS Mathematics Practice Questions Paper H © EAA QUESTIONKEYSOLUTION STRANDLEVEL OF DIFFICUL TY 1 CThe missing part in C is one thir d which matches the slice (one thir d); altogether they complete one whole. Space and Geometry Easy 2 AThe sum of x and y adds to 190° which is mor e than the angle sum of a triangle (180°). Space and Geometry Easy 3 DThe total number of vehicles = 135 The angle at the centr e for cars = 90 135 × 360° = 240° Chance and Data Medium 4 CLet D be the diameter of the big wheel (back wheel). Let d be the diameter of the small wheel (fr ont wheel). Accor ding to the question information, D = 3/2 × d. When the car travels 1 m, the big wheel mak es 6 turns. Ther efore, 6 × the cir cumference of the big wheel = 1 Cir cumfer ence of the big wheel is Ï€D, ther efore the equation can be pr esented as: 6 × Ï€D = 1….(Equation 1) . Let x be the number of turns the small wheel mak es when the car travels 1m. Using the same logic, we can form the equation x × Ï€d = 1…. (Equation 2) Dividing Equation 1 by Equation 2: 6D xd = 1 6D d x = 6 × 3 2 x = = 9 , make x the subject of the equation: 6D xd = 1 6D d x = 6 × 3 2 x = = 9 Substitute D= 3/2 d D xd = 1 6D d x = 6 × 3 2 x = = 9 . Measur ement Medium

ICAS Mathematics Practice Questions Paper H © EAA Level of difficulty refers to the e xpected level of difficulty for the question. Easy more than 70% of candidates will choose the cor rect option Medium about 50–70% of candidates will choose the cor rect option Medium/Har d about 30–50% of candidates will choose the cor rect option Har d less than 30% of candidates will choose the cor rect option 5 89Height of smallest doll is 40.5mm. Rate of incr ease in height of successive dolls is 128 96 12896 700 . Height of doll with 700 dolls inside = 40.5 × 128 96 12896 700 = 1.1603 × 10 89 mm Ther efore, the value of x is 89. Number and Arithmetic Har d © UNSW Global Pty Limited 8



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