1.
Which of the following calculations gives the largest answer?
Correct Answer
E. 2 + 1
Explanation
The calculation 2 + 1 gives the largest answer because addition results in a larger value compared to subtraction, division, and multiplication.
2.
Nadya is baking a cake. The recipe says that her cake should be baked in the oven for 1 hour and 35 minutes. She puts the cake in the oven at 11:40 am. At what time should she take the cake out of the oven?
Correct Answer
D. 1:15 pm
Explanation
Nadya puts the cake in the oven at 11:40 am and the recipe states that it should be baked for 1 hour and 35 minutes. To find out when she should take the cake out of the oven, we add 1 hour and 35 minutes to 11:40 am. This gives us a total of 1 hour and 35 minutes + 11:40 am = 1:15 pm. Therefore, Nadya should take the cake out of the oven at 1:15 pm.
3.
What is the value of x?
Correct Answer
D. 57
4.
A download is 95% complete. What fraction is yet to be downloaded?
Correct Answer
E.
Explanation
The fraction that is yet to be downloaded is 5%. This can be calculated by subtracting the completed fraction (95%) from the whole (100%).
5.
What is the value of 201 x 7 - 7 x 102?
Correct Answer
C. 693
Explanation
To find the value of 201 x 7 - 7 x 102, we first perform the multiplication: 201 x 7 = 1407. Then, we perform the second multiplication: 7 x 102 = 714. Finally, we subtract the second result from the first: 1407 - 714 = 693. Therefore, the value of the expression is 693.
6.
In a magic square, the numbers in each row, each column, and the two main diagonals have the same total. This magic square uses the integers 2 to 10. Which of the following are the missing cells?
Correct Answer
D. D
7.
If you work out the values of the following expressions and then place them in increasing numerical order, which comes in the middle?
Correct Answer
A.
8.
The diagram shows a rectangle PQRS and T is a point on PS such that QT is perpendicular to RT.
The length of QT is 4 cm. The length of RT is 2 cm.
What is the area of the rectangle PQRS?
Correct Answer
B. 8 cmÂ²
Explanation
In the given diagram, QT is perpendicular to RT. This means that QT and RT form a right angle. Since the length of QT is 4 cm and the length of RT is 2 cm, we can use the formula for the area of a rectangle, which is length multiplied by width. The length of the rectangle is PQ, which is equal to QT (4 cm), and the width of the rectangle is RS, which is equal to RT (2 cm). Therefore, the area of the rectangle PQRS is 4 cm multiplied by 2 cm, which equals 8 cmÂ².
9.
In William Shakespeare's play "As you like it". Rosalind speaks to Orlando about "He that will divide a minute into a thousand parts".
Which of the following is equal to the number of seconds in one-thousandth of one minute?
Correct Answer
D. 0.06
Explanation
In the play "As You Like It", Rosalind talks about dividing a minute into a thousand parts. To find the number of seconds in one-thousandth of one minute, we need to convert the fraction into seconds. There are 60 seconds in one minute, so dividing one minute by 1000 gives us 0.06 seconds. Therefore, the answer is 0.06.
10.
Which of the following integers is not a multiple of 45?
Correct Answer
E. 305
Explanation
To determine which integer is not a multiple of 45, we need to check if each integer is divisible by 45. Dividing 765 by 45 gives us a quotient of 17 with a remainder of 0, so it is a multiple of 45. Dividing 675 by 45 gives us a quotient of 15 with a remainder of 0, so it is also a multiple of 45. Dividing 585 by 45 gives us a quotient of 13 with a remainder of 0, so it is a multiple of 45. Dividing 495 by 45 gives us a quotient of 11 with a remainder of 0, so it is a multiple of 45. However, dividing 305 by 45 gives us a quotient of 6 with a remainder of 35, so it is not a multiple of 45. Therefore, the correct answer is 305.
11.
Seven squares are drawn on the sides of a heptagon so that they are outside the heptagon, as shown on the diagram.
What is the sum of the seven marked angles?
Correct Answer
B. 360°
Explanation
The sum of the angles in a heptagon is 900 degrees. Since the seven squares are drawn outside the heptagon, the sum of the angles in the squares is also 900 degrees. However, each square has four right angles, which add up to 360 degrees. Therefore, the sum of the seven marked angles is 360 degrees.
12.
Last year, at the school where Gill teaches Mathematics, 315 out of 360 pupils were girls.
This year, the number of pupils in the school increased to 640. The proportion of girls is the same as it was last year.
How many girls are there at the school this year?
Correct Answer
D. 336
Explanation
Last year, there were 315 girls out of 360 pupils, which means the proportion of girls was 315/360. This year, the total number of pupils increased to 640. Since the proportion of girls remains the same, we can set up a proportion: (number of girls this year) / 640 = (315/360). Solving for the number of girls this year, we get 336. Therefore, there are 336 girls at the school this year.
13.
Consider the following statements.
i) Doubling a positive number always makes it larger
ii) Squaring a positive number always makes it larger.
iii) Taking the positive square root of a positive number always makes it smaller.
Which statements are true?
Correct Answer
C. Only i)
Explanation
Statement i) is true because when a positive number is doubled, it will always result in a larger number. However, statement ii) is not true because squaring a positive number can result in a larger or smaller number, depending on the value of the original number. Statement iii) is also not true because taking the positive square root of a positive number will result in a smaller number only if the original number is greater than 1, but it will result in a larger number if the original number is between 0 and 1. Therefore, the correct answer is only i).
14.
Mathias is given a grid of twelve small squares. He is asked to shade grey exactly four of the small squares so that his grid has two lines of reflection symmetry.
How many different grids could he produce?
Correct Answer
B. 3
Explanation
Mathias can produce three different grids by shading exactly four small squares. In order to have two lines of reflection symmetry, Mathias needs to shade the squares in a way that the shaded squares can be reflected across two different lines and still produce the same pattern. There are three possible ways to achieve this: shading four squares in a straight line, shading four squares in a square shape, or shading four squares in an L shape. Therefore, Mathias can produce three different grids.
15.
What is the remainder when the square of 49 is divided by the square root of 49?
Correct Answer
A. 0
Explanation
The remainder when a number is divided by its square root is always 0. In this case, the square of 49 is 2401 and the square root of 49 is 7. When 2401 is divided by 7, the remainder is 0.
16.
In New Threeland there are three types of coins: the 2p, the 5p and one other. The smallest number of coins needed to make 13p is three. The smallest number of coins needed to make 19p is three. what is the value of the third coin?
Correct Answer
D. 9p
Explanation
The value of the third coin in New Threeland is 9p. This can be determined by subtracting the values of the two known coins (2p and 5p) from the total amount needed to make 13p and 19p, which leaves a remainder of 6p and 9p respectively. Since the smallest number of coins needed is three in both cases, the third coin must be 9p.
17.
I add up all even numbers between 1 and 101. Then from my total I subtract all odd numbers between 0 and 100.
What is the result?
Correct Answer
B. 50
Explanation
The sum of all even numbers between 1 and 101 is 2550. The sum of all odd numbers between 0 and 100 is 2500. Subtracting 2500 from 2550 gives us a result of 50.
18.
The diagram shows a regular hexagon, a square and an equilateral triangle.
What is the angle TVU?
Correct Answer
A. 45
Explanation
The angle TVU is 45 degrees because in a regular hexagon, each interior angle is equal to 120 degrees. Since the square and the equilateral triangle are congruent, each of their interior angles is equal to 90 degrees. Therefore, the remaining angle in the hexagon is 360 - (120 + 90 + 90) = 60 degrees. Since TVU is an exterior angle of the hexagon, it is equal to the sum of the two opposite interior angles, which is 60 + 45 = 105 degrees. However, since angles in a triangle add up to 180 degrees, the angle TVU is 180 - 105 = 75 degrees. Therefore, the given answer of 45 degrees is incorrect.
19.
The range of a list of integers is 20, and the median is 17.
What is the smallest possible number of integers in the list?
Correct Answer
B. 2
Explanation
If the range of a list of integers is 20, it means that the difference between the largest and smallest integers in the list is 20. Since the median is 17, it must be the middle value in the list. In order for the range to be 20 and the median to be 17, the smallest integer in the list must be 17 - 10 = 7 and the largest integer must be 17 + 10 = 27. Therefore, the smallest possible number of integers in the list is 2, with 7 and 27 being the only two integers.
20.
The small trapezium on the right has three equal sides and angles of 60 and 120. Nine copies of this trapezium can be placed together to make a larger version of it, as shown.
The larger trapezium has perimeter 18 cm
What is the perimeter of the smaller trapezium?
Correct Answer
C. 6 cm
Explanation
The larger trapezium is made up of 9 copies of the smaller trapezium. Since the larger trapezium has a perimeter of 18 cm, each copy of the smaller trapezium must have a perimeter of 18 cm divided by 9, which is 2 cm. However, since the smaller trapezium has three equal sides, two of the sides must be equal to 2 cm each, and the third side must be equal to 2 cm multiplied by 2, which is 4 cm. Therefore, the perimeter of the smaller trapezium is 2 cm + 2 cm + 4 cm, which equals 6 cm.