SHSAT 1.4 Math

1. Michelle scored 84, 77 and 91 on her chemistry exams. What is the lowest score she needs on her fourth and final exam to receive an average of 85 if all the exams are weighted equally?

Question 1 of 50

2. On a number line, what is the midpoint of a line segment beginning at -4 and ending at 2 $\frac{3}{4}$ ?

$-\frac{5}{8}$

$-\frac{3}{4}$

$\frac{3}{4}$

$\frac{5}{8}$

Question 2 of 50

3. Victor works 5.5 hours a day, 4 days a week. He is paid $9.25 per hour. How much is his weekly pay?

$50.88

$183.55

$203.50

$224.23

$241.10

Question 3 of 50

4. Express $4,231\times1,000$ in scientific notation.

$4.2\times10^{6}$

$4.231\times10^{6}$

$42.31\times10^{5}$

$4.231\times10^{5}$

$4231\times10^{3}$

Question 4 of 50

5. What is the value of x in the equation $5x- 7 = y$ , if $y = 8$ ?

-1

Question 5 of 50

6. What is the prime factorization of 459?

$3^3\times17$

$3^3\times13$

$3^3\times11$

$2^2\times3^2\times11$

$2^2\times3^2\times13$

Question 6 of 50

7. If $5x+12=17-4(\frac{x}{2}+1)$

, what is the value of x?

$\frac{1}{7}$

$\frac{1}{3}$

$\frac{6}{7}$

$1\frac{2}{7}$

$2$

Question 7 of 50

8. There are 837 students at Castleton Middle School. If there are 372 male students, what is the ratio of male students to female students?

4 : 5

5 : 4

3 : 4

4 : 3

5 : 6

Question 8 of 50

9. Jim must make a 5-digit password for his school account. The first digit must be a letter and the next four digits must be numbers (0-9). How many different codes are possible? (Thepassword is not case-sensitive.)

260

2,600

260,000

Question 9 of 50

10. For what value of x is $4(x-1)=2(x+2)$ ?

Question 10 of 50

11. What is the value of $|-7|+|3|+|-5|+|\frac{1}{5}|\times|-5|$

-16

Question 11 of 50

12. Circle A has a radius r. Circle B has radius r + 1. What is the difference between the circumference of circle B and the circumference of circle A?

$1$

$2\pi$

$2\pi+1$

$2r+2\pi$

$2r\pi+2\pi$

Question 12 of 50

13. 32% of high school students take an AP class. If a high school has 1250 students, how many students do not take an AP class?

250

400

625

750

850

Question 13 of 50

14. In the figure below, what is the value of n?

$30^o$

$45^o$

$50^o$

$60^o$

$90^o$

Question 14 of 50

15. If n is an integer, which of the following must be odd?

$n + 1$

$2n + 1$

$3n + 1$

$n^2$

$n^2 + 1$

Question 15 of 50

16. What is the value of $20-(3\times2^3-5)$ ?

-191

131

Question 16 of 50

17. What is the value of $4+(-1(-2-1))^2$ ?

-5

Question 17 of 50

18. If 3xy = 6, what is the value of x in terms of y?

$2$

$\frac{2}{y}$

$\frac{2}{y^2}$

$2y$

$2y^2$

Question 18 of 50

19. There are 845 students that are taking school buses on a trip. Each school bus seats 45 students. If the school busses are filled to maximum capacity before the next one starts, how many students will be in the last school bus?

Question 19 of 50

20. At a local farmer’s market, a 10 oz. bag of carrots sells for $2.25. At this rate, what would be the price of a 2-pound bag of carrots?

$4.50

$6.75

$7.05

$7.20

$7.75

Question 20 of 50

21. On a map, 1 inch represents 8 miles. If the distance between two cities is 60 miles, how many inches would they be apart on this map?

7.5

7.75

8.25

Question 21 of 50

22. When positive integer p is divided by 6, the remainder is 3. When p is divided by 4, the remainder is 3. What is the least possible value of p?

Question 22 of 50

23. What is the value of $10(x+3)+6(x-5)$ in terms of y if $x = 2y$ ?

$4y$

$8y$

$16y$

$32y$

$16y+30$

Question 23 of 50

24. Liverpool had 4 times as many losses as it had draws in a season. If Liverpool won none of its games, which could be the total number of games it played that season?

Question 24 of 50

25. On the number line below, $\overline{AB}=2\frac{1}{2}$

and $\overline{BC}=3\frac{3}{4}$

.What is the position of C?

$6\frac{1}{4}$

$6\frac{1}{2}$

$9\frac{1}{4}$

$9\frac{1}{2}$

$9\frac{3}{4}$

Question 25 of 50

26. If a is 25% of b, and b is 40% of c, what is the value of a when c = 150?

37.5

Question 26 of 50

27. If $x=2$ and $y=3$ , what is the value of $\frac{xy}{x^y}$

$\frac{3}{4}$

$1$

$\frac{3}{2}$

$2$

$3$

Question 27 of 50

28. All the line segments in the figure below are equal. What is the measure of angle ABC?

$60^o$

$90^o$

$120^o$

$135^o$

$150^o$

Question 28 of 50

29. Concert tickets will be given to two groups of people. Group A contains 225 people. One-fifth of the people in Group A will be selected to win concert tickets. Group B contains 500 people. One-tenth of the people in Group B will be selected to win concert tickets. What is the ratio of non-winners in Group A to non-winners in Group B?

9 : 10

10 : 9

2 : 5

5 : 2

4 : 5

Question 29 of 50

30. Hank is three times as old as Julian. The difference in their ages is 12 years. How old is Hank?

Question 30 of 50

31. If the perimeter of a square is 36 inches, then what is its area, in square inches?

324

Question 31 of 50

32. What is the value of $2 (5x - 7)$ in terms of y if $x = 3y$ ?

$15y - 7$

$30y$

$30y + 7$

$30y -7$

$30y - 14$

Question 32 of 50

33. A certain comet only passes by earth once every 23 years. This comet was first sighted in 1819. How many times did this comet pass by earth between 1840 and 2013 inclusive?

Question 33 of 50

34. Kate ran 7 miles on the first day and 10 miles on the second day. How many miles did Kate run on the third day if she ran an average of 11 miles over the three days?

17.5

Question 34 of 50

35. How many positive integers are between $\frac{33}{4}$ and $\frac{58}{5}$ ?

Question 35 of 50

36. John finished $\frac{2}{7}$ of his homework in 24 minutes. If he continues at the same rate, how many minutes will it take him to finish the remainder of his homework?

Question 36 of 50

37. Terry got a 15% discount when he bought his new pair of shoes. If the discount was $25, what was the original price?

$28.75

$150.00

$166.67

$180.00

$186.67

Question 37 of 50

38. What is the least integer greater than $\frac{13}{3}$ ?

4.3

4.4

Question 38 of 50

39. In the figure below, points N and P are on linesegment $\overline{MQ}$
$\overline{MQ}$ = 42 cm
$\overline{MN}$ : $\overline{NQ}$ = 4:3
$\overline{NP}$ : $\overline{PQ}$ = 2:1

3 cm

6 cm

8 cm

9 cm

12 cm

Question 39 of 50

40. Henry has n baseball autographs and Raymond has 3 times as many baseball autographs. If Raymond gives Henry 6 autographs, they would have an equal number of autographs. How many autographs does Henry have?

Question 40 of 50

41. The 5 numbers shown below are repeated indefinitely. What is the product of the first 20 numbers of this sequence?
$-1, 2, 3, 1, \frac{1}{2}$

-3

Question 41 of 50

42. There are 3 different positions available in student office. The positions are president, vice-president, and secretary. If 10 students are eligible for election, but a student can only occupy one position at a time, then how many different outcomes are possible in the election?

720

1,000

Question 42 of 50

43. There is a leak in Robert’s basement. The water is 3 inches deep and the basement is 20 feet by 14 feet. What is the volume of water in Robert’s basement?

70 cu ft

84 cu ft

96 cu ft

720 cu ft

840 cu ft

Question 43 of 50

44. If x is an odd integer and y is an even integer, which of the following must be odd?

$2x + y$

$xy + y$

$2(x + y)$

$2x + y^2$

$x^2 + y^2$

Question 44 of 50

45. If $\frac{9y}{x}$ , what is $\frac{x}{y}$ equal to?

$3$

$3x$

$3xy$

$27$

$27y$

Question 45 of 50

46. One side of a rectangle with a length of 8 units lies on the y-axis of a coordinate system. The coordinates of one corner of the rectangle is (-3, 5). Which of the following could be the coordinates of the opposite corner?

(0, 5)

(0,-3)

(8, 0)

(-3, 13)

(-3, -3)

Question 46 of 50