# HiSET Math Practice Quiz 3

#### What is the probability that if you randomly picked two students who sat for the examination you would find they both got a mark of 70 or better?

There were 466 students who sat for the examination. The number who got a mark of 70 or more was 28. The probability of the first student getting a mark of 70 or better is 28/466 . The probability of the second student getting a mark of 70 or better is 27/465 . The probability of both getting a mark of 70 or better is 28/466 x 27/465 .

#### Which of the following is the same as (√3 + √2)2 ?

(√3 + √2)2 = (√3 + √2)( √3 + √2) (√3 + √2)( (√3 + √2) = √3×√3 + √3×√2 + √2×√3 + √3×√3 √3×√3 + √3×√2 + √2×√3 + √3×√3 = 3 + √6 + √6 + 2 3 + √6 + √6 + 2 = 5 + 2√6

#### Which of the following mark intervals contains the highest percentage of students who sat this examination?

The largest number in a mark interval shown is 128. The interval associated with this number is 50-59. The number of students in the mark interval 10-29 is 32 + 45 = 77. 128 is greater than 77. Of the mark intervals shown the highest percentage of students who sat this examination was in the 50-59 interval.

#### The number of students who sat the examination was 466. What is true about the median mark obtained by students who sat this examination?

As there are 466 students the median will be found by averaging the 233rd and 234th marks, after the marks have been placed in order. Both the 233rd and 234th marks will lie somewhere from 40 to 49. The average of these two marks will lie somewhere from 40 to 49.

#### Results that senior students from a large high school received in an international mathematics examination. A pass in this examination is regarded as a mark of 40 or more. How many students in this high school failed to pass this mathematics examination?

The mark categories indicating failure are 0-9, 10-19, 20-29 and 30-39. The number of marks in those categories was 23, 32, 45 and 67. 23 + 32 + 45 + 67 = 167. The number of students who failed the examination was 167.

#### Which is the best simplification of (24 x 32) / (2 x 3)?

(24 x 32) / (2 x 3)= 24-1 × 32-1. 24-1 × 32-1 = 23 × 31 23 × 31 = 23 × 3

#### What percentage of students who got a mark below 30 got a mark below 20?

The number of students who got a mark less than 30 was 23 + 32 + 45 = 100. The number of students who got a mark less than 20 was 23 + 32 = 55. The percentage of students who got a mark less than 30 who got a mark less than 20 was 55÷100 = 55%.

#### How many ways can 6 people sit on a bench if 3 of them have to sit side by side?

Treat the 3 people who wish to sit side by side as a single unit. There are 4 units consisting of three people in the group. The 4 units can be arranged in 4! ways on the bench. The three people in the group can be arranged in 3! ways. The complete number of arrangements is 4! × 3! = 144.

#### What is the value of (x2 + x + 3) / (x + 2) when x = -1?

(x2 + x + 3) / (x + 2) = ( (-1)2 + (-1) + 3) / ((-1) + 2) when x=-1 ( (-1)2 + (-1) + 3) / ((-1) + 2) = (1 - 1 + 3)/ (-1 + 2) (1 - 1 + 3)/ (-1 + 2) = 3 / 1 = 3

#### Which of the following is the same as 10x2 - 11x + 3?

10x2 - 11x + 3 = 10x2 - 5x - 6x + 3 10x2 - 5x - 6x + 3 = 5x(2x - 1) - 3(2x - 1) 5x(2x - 1) - 3(2x - 1) = (5x - 3)(2x -1)

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