Pascal 2017真题

1. The value of is

(A) 4 (B) 7 (C) 3 (D) 6 (E) 5

2. In the diagram, how many 1 × 1 squares are shaded in

the 6 × 6 grid?

(A) 29 (B) 30 (C) 31

(D) 32 (E) 33

3. In the diagram, the ratio of the number of shaded

triangles to the number of unshaded triangles is

(A) 5 : 2 (B) 5 : 3 (C) 8 : 5

(D) 5 : 8 (E) 2 : 5

4. Which of the following is closest in value to 7?

(A) (B) (C) (D) (E)

5. Kamal turned his computer on at 2 p.m. on Friday. He left his computer on for exactly 30 consecutive hours. At what time did he turn his computer off?

(A) 4 p.m. on Saturday (B) 6 p.m. on Saturday

(E) 8 p.m. on Saturday

6. At six different times on Canada Day in 2016, the

number of people at the Pascal Zoo were counted.

The graph to the right shows these results. During which of the following periods did the number of people at the zoo have the largest increase?

(A) 9:00 a.m. to 10:00 a.m.

(B) 10:00 a.m. to 11:00 a.m.

(D) 12:00 p.m. to 1:00 p.m.

(E) 1:00 p.m. to 2:00 p.m.8

7. If 2x - 3 = 10, what is the value of 4x?

(A) 23 (B) 24 (C) 28 (D) 26 (E) 20

8. Three integers from the list 1, 2, 4, 8, 16, 20 have a product of 80. What is the sum of these three integers?

(A) 21 (B) 22 (C) 25 (D) 29 (E) 26

9. Wally makes a whole pizza and shares it with three friends. Jovin takes of the pizza, Anna takes of the pizza, and Olivia takes of the pizza. What fraction of the pizza is left for Wally?

(A) (B) (C) (D) (E)

10. Which of the following expressions is equal to an odd integer for every integer n?

(D) 2017 + n2 (E) 2017 + 2n

11. Jeff and Ursula each run 30 km. Ursula runs at a constant speed of 10 km/h. Jeff also runs at a constant speed. If Jeff’s time to complete the 30 km is 1 hour less than Ursula’s time to complete the 30 km, at what speed does Jeff run?

(A) 6 km/h (B) 11 km/h (C) 12 km/h

(D) 15 km/h (E) 22.5 km/h

12. A small square is drawn inside a larger square as shown.

The area of the shaded region and the area of the unshaded region are each 18 cm2 . What is the side length of the larger square?

(A) 3 cm (B) 4 cm (C) 6 cm

(D) 9 cm (E) 12 cm

13. Janet picked a number, added 7 to the number, multiplied the sum by 2, and then subtracted 4. If the final result was 28, what number did Janet pick?

(A) 9 (B) 5 (C) 19 (D) 23 (E) 11

14. Tobias downloads m apps. Each app costs $2.00 plus 10% tax. He spends $52.80 in total on these m apps. What is the value of m?

(A) 20 (B) 22 (C) 18 (D) 24 (E) 26

15. In the diagram, the side lengths of four squares are shown.

The area of the fifth square is k. What is the value of k?

(A) 64 (B) 49 (C) 36

(D) 25 (E) 16

16. A circular spinner is divided into six regions, as shown.

Four regions each have a central angle of x◦ . The remaining regions have central angles of 20° and 140°. An arrow is attached to the centre of the circle. The arrow is spun once. What is the probability that the arrow stops on a shaded region?

(A) (B) (C)

(D) (E)

17. Igor is shorter than Jie. Faye is taller than Goa. Jie is taller than Faye. Han is shorter than Goa. Who is the tallest?

(A) Faye (B) Goa (C) Han (D) Igor (E) Jie

18. Given two different numbers on a number line, the

number to the right is greater than the number to the left.

The positions of x, x3 and x2 are marked on a number

line. Which of the following is a possible value of x?

(A) (B) (C)

(D) (E) 2

19. In the diagram, M is the midpoint of Y Z, ∠XMZ = 30°,

and ∠XYZ = 15° . The measure of ∠XZY is

(A) 75° (B) 65° (C) 60°

(D) 80° (E) 85°

20. A solid cube is made of white plastic and has dimensions n × n × n, where n is a positive integer larger than 1. The six faces of the cube are completely covered with gold paint. This cube is then cut into n3 cubes, each of which has dimensions 1×1×1. Each of these 1 × 1 × 1 cubes has 0, 1, 2, or 3 gold faces. The number of 1 × 1 × 1 cubes with 0 gold faces is strictly greater than the number of 1 × 1 × 1 cubes with

exactly 1 gold face. What is the smallest possible value of n?

(A) 7 (B) 8 (C) 9 (D) 10 (E) 4

21. Each of the numbers 1, 5, 6, 7, 13, 14, 17, 22, 26 is placed in a different circle below. The numbers 13 and 17 are placed as shown.

Jen calculates the average of the numbers in the first three circles, the average of the numbers in the middle three circles, and the average of the numbers in the last three circles. These three averages are equal. What number is placed in the shaded circle?

(A) 1 (B) 5 (C) 6 (D) 7 (E) 14U

22. In the diagram, UV W X is a rectangle that lies flat on a horizontal floor. A vertical semi-circular wall with diameter XW is constructed. Point Z is the highest point on this wall. If UV = 20 and VW = 30, the perimeter of △UVZ is closest to

(A) 95 (B) 86 (C) 102

(D) 83 (E) 92

23. An Anderson number is a positive integer k less than 10 000 with the property that k2 ends with the digit or digits of k. For example, 25 is an Anderson number because 625 ends with 25, but 75 is not an Anderson number because 5625 does not end with 75. If S is the sum of all even Anderson numbers, what is the sum of the digits of S?

(A) 17 (B) 18 (C) 11 (D) 33 (E) 24

24. A town has 2017 houses. Of these 2017 houses, 1820 have a dog, 1651 have a cat, and 1182 have a turtle. If x is the largest possible number of houses that have a dog, a cat, and a turtle, and y is the smallest possible number of houses that have a dog, a cat, and a turtle, then x - y is

(A) 1182 (B) 638 (C) 563 (D) 619 (E) 466

25. Sam thinks of a 5-digit number. Sam’s friend Sally tries to guess his number. Sam writes the number of matching digits beside each of Sally’s guesses. A digit is considered “matching” when it is the correct digit in the correct position.