1.
write all the factors of 50 ( put the numbers in order from small to big and between them , with no spaces )
Explanation
The factors of 50 are all the numbers that can divide evenly into 50 without leaving a remainder. The factors of 50 are 1, 2, 5, 10, 25, and 50.
2.
Find the LCM 28 and 35
Explanation
The LCM (Least Common Multiple) of two numbers is the smallest number that is divisible by both numbers without leaving a remainder. In this case, the LCM of 28 and 35 is 140 because it is the smallest number that both 28 and 35 can divide into evenly.
3.
Simplify : _{(x}^{2}_{)}^{5}
Correct Answer
C. X^{10}
Explanation
The given expression is (x^2)^5. When we raise a power to another power, we multiply the exponents. So, in this case, we have x^(2*5) which simplifies to x^10. Therefore, the correct answer is x^10.
4.
Factorise completely : 6de - 9e^{2}
Correct Answer
3e(2d-3e)
Explanation
The expression 6de - 9e2 can be factorized completely as 3e(2d-3e). This is because both terms in the expression have a common factor of 3e. By factoring out this common factor, we are left with 2d-3e inside the parentheses. Therefore, the completely factorized form of the expression is 3e(2d-3e).
5.
Dave makes 600 cakes.
18% of the 600 cakes go to a hotel and 2/3 of the 600 cakes go to a supermarket.
Calculate how many cakes he has left.
Correct Answer
92
Explanation
After calculating the number of cakes that go to the hotel (18% of 600 = 108) and the number of cakes that go to the supermarket (2/3 of 600 = 400), we can subtract these amounts from the total number of cakes made (600 - 108 - 400 = 92). Therefore, Dave has 92 cakes left.
6.
Give your answer to 2 decimal places
Correct Answer
5384.45
7.
Find angle a and angle b ( write the size of angle a first then , size angle b ) (numbers only don't write degrees or letter )
Correct Answer
63,59
8.
Write seventeen thousand and seventeen in figures.
Correct Answer
17017
Explanation
The question asks for the number "seventeen thousand and seventeen" to be written in figures. The figure representation of this number is 17017.
9.
Find the number of minutes from 17 58 to 7.13 pm.
Correct Answer
75
Explanation
To find the number of minutes from 17:58 to 7:13 pm, we can subtract the starting time from the ending time. The starting time is 17:58 and the ending time is 7:13 pm. Since the ending time is in the afternoon (pm), we need to convert it to 24-hour format. 7:13 pm becomes 19:13. Subtracting 17:58 from 19:13 gives us a difference of 1 hour and 15 minutes, which is equal to 75 minutes. Therefore, the number of minutes from 17:58 to 7:13 pm is 75.
10.
Write 6789 correct to the nearest 100.
Correct Answer
6800
Explanation
The number 6789 is rounded to the nearest hundred, which means we need to look at the tens digit (8). Since the tens digit is 5 or greater, we round up the hundreds digit (6) to the next higher number, resulting in 6800.
11.
Write 6789 correct to 3 significant figures
Correct Answer
6790
Explanation
The number 6789 rounded to 3 significant figures is 6790. When rounding to 3 significant figures, we look at the first 4 digits after the decimal point. Since the digit after the third significant figure (8) is 9, we round up the third significant figure (7) to the next highest value, which is 8. Therefore, the correct answer is 6790.
12.
Dan either walks or cycles to school.The probability that he cycles to school is 1/5.
Write down the probability that Dan walks to school.(write your answer in the same way the fraction is written in the question )
Correct Answer
4/5
Explanation
The probability that Dan walks to school can be calculated by subtracting the probability that he cycles to school (1/5) from 1. Since there are only two options (either walking or cycling), the probability of walking is 1 minus the probability of cycling, which is 4/5.
13.
Write 2020 in standard form
Correct Answer
C. 2.02 x 10^{3}
Explanation
The correct answer is 2.02 x 103. This is the standard form of the number 2020. In standard form, a number is written as a decimal number multiplied by a power of 10. In this case, 2.02 is the decimal number and 103 is the power of 10.
14.
The mass, m kilograms, of a horse is 429 kg, correct to the nearest kilogram. find the lower bound of 429
Correct Answer
428.5
Explanation
The lower bound of 429 kg is 428.5 kg because when rounding to the nearest kilogram, any value greater than or equal to 428.5 kg would be rounded up to 429 kg. Therefore, the lower bound is the value just below 429 kg, which is 428.5 kg.
15.
Rearrange the formula 5w – 3y + 7 = 0 to make w the subject.
Correct Answer
D. (3y-7)/5
Explanation
To rearrange the formula 5w - 3y + 7 = 0 to make w the subject, we need to isolate w on one side of the equation.
First, we can start by subtracting 7 from both sides of the equation to get 5w - 3y = -7.
Next, we can move the -3y term to the other side of the equation by adding 3y to both sides, which gives us 5w = 3y - 7.
Finally, to make w the subject, we divide both sides of the equation by 5, resulting in w = (3y - 7)/5.
16.
Give your answer to one decimal place
Correct Answer
9.1
17.
Here is a sequence of numbers.
6, 9, 12, 15, …
Find an expression for the nth term of this sequence.
(don’t write space between your letters and numbers and the letters should be small )
Correct Answer
3n+3
Explanation
The given sequence starts with the number 6 and each subsequent number is obtained by adding 3 to the previous number. Therefore, the expression for the nth term of this sequence is 3n+3.
18.
The first number is for the mode and the second number is for the mean
Correct Answer
C. 4 , 4.3
Explanation
The given answer is 4 , 4.3, which means that the mode of the numbers is 4 and the mean is 4.3. The mode is the number that appears most frequently in the set of numbers, and in this case, 4 appears the most. The mean is the average of all the numbers, and in this case, when we add up all the numbers and divide by the total count, we get 4.3.
19.
X + 7 = 15 ( Just write the value as a number don't write x= )
Correct Answer
8
Explanation
The given equation x + 7 = 15 can be solved by subtracting 7 from both sides of the equation. This will give us x = 8. Therefore, the value of x is 8.
20.
5(3x + 8) = 10 ( just write the value of the answer don't write x= )
Correct Answer
-2
Explanation
The given equation is 5(3x + 8) = 10. To solve this equation, we can start by distributing the 5 to both terms inside the parentheses: 15x + 40 = 10. Then, we can subtract 40 from both sides of the equation to isolate the variable: 15x = -30. Finally, dividing both sides of the equation by 15 gives us the value of x, which is -2.
21.
Write your answer in the form y=mx+c with no spaces and no capital letters for example y=3x+9
Correct Answer
-5x+6
Explanation
The given expression is in the form of y = mx + c, where y represents the dependent variable, x represents the independent variable, m represents the slope, and c represents the y-intercept. In this case, the expression is -5x + 6, which means that the slope is -5 and the y-intercept is 6. Therefore, the equation represents a straight line with a slope of -5 and a y-intercept of 6.
22.
Find the value of angle y ( just write the number with no spaces and no degree sign )
Correct Answer
74
23.
Give your answer to one decimal place ( just write the number with no spaces and no degree sign )
Correct Answer
32.2
24.
Find the distance AB
Correct Answer
375
Explanation
The distance AB is 375.
25.
The radius of a sphere is 5.2 cm.Work out the surface area of this sphere.
[The surface area, A, of a sphere with radius r is A = 4πr^{2 }] ( give your answer to 3 significant figures )
Correct Answer
340
Explanation
The formula for the surface area of a sphere is A = 4πr^2, where r is the radius of the sphere. In this case, the radius is given as 5.2 cm. Plugging this value into the formula, we get A = 4π(5.2)^2. Simplifying this expression gives us A = 4π(27.04), which is approximately equal to 340. Therefore, the surface area of the sphere is 340 square units.