Fractions & percentages
Algebra questions
Miscellaneous
Miscellaneous 2.0
Equations
100
Solve the following and write your answer in its simplest form.
32/16 x 4/5
8/5.
100
What is the area of a circle with diameter 15.5m? Give your answer to two decimal places.
188.69m squared.
100
Write the following in the form 1:n (juice to water).
A cup with 750ml water and 250ml juice.
1:3
100
Calculate the gradient of the following line:
2
100
What is the gradient in the equation: y = 3x - 6?
3
200
What is 168/291 in its simplest form?
56/97
200
Calculate the area of this shape.
75m^2.
200
Write the ratio of the following shape's side length vs perimeter in the form 1:n.
A regular decagon with sides 12cm each.
1:12.
200
Farmer Lulu decides to become a postlady as a side hobby. On her first day, she delivers 120 letters in 46 minutes. How many letters does she deliver a minute? Give your answer to one decimal place.
2.6 letters per minute.
200
8x squared + 38x + 35
300
(Non-calculator) If Rainbow has £1000 and puts it in an account with 5% simple interest, how much will she have at the end of 5 years?
£1250.
300
(Non-calculator) Find the approximate area of a circle sector with central angle of 36 degrees and a diameter of 12cm. Take pi to be 3.1cm,
.
3.6 pi (or 11.16cm^2)
300
Someone has a triangular floor measuring 2m by 4m. If rainbow carpet costs £12.50 per square metre, calculate the cost it would be to carpet the entire floor.
£50.
300
Enlargement of -0.5
300
a) Write an expression for the perimeter and for the area of a rectangle with sides x+4 and x+6.
b) (Non-calculator) Taking the perimeter to be 168cm, find x.
a) Perimeter: 4x+20, Area: x^2+10x+24
b) x = 37cm
400
A regular, heptagonal die is thrown and comes to rest on one of its faces. What is the probability that it comes to rest on a number greater than 2?
5/7, or 71.43%
400
A train travels for 4x hours. It arrives at Manchester at 18:06pm, gets to Glasgow five hours later, and terminates at Edinburgh another 120 minutes later. Find the termination time, total travel time, and find x.
Termination time = 01:06am
Total travel time = 7 hours
x = 1.75
400
A wheelchair ramp has been designed to have the following dimensions: height 60cm, width 1.5m. The ramp can only be used if the gradient of the slope is less than 0.2.
(a) Calculate the gradient of the slope. (b) Can this ramp be used? Give a reason for your answer.
a) Gradient = 0.4.
b) This ramp cannot be used as the gradient is 0.4- double the >0.2 requirement- so does not meet the required specifications.
400
If a trapezium has horizontal sides of 8cm and 12cm, and an area of 2.6m^2, find the height. Give any decimal answers to two decimal places.
26cm.
400
A triangle has sides of x, 2x, and x+12. Taking x to be 32cm, is this triangle right-angled? State your reasoning for your answer.
It is not, as the Pythagoras' theorem substitution (of a^2 + b^2 = c^2) would be 1024 +1936 = 4096, which does not work. As Pythagoras' theorem only works for right-angled triangles, this triangle is not right=angled.
500
(Non-calculator) 67% of the area of a square is 536cm^2. What is 100% of the square's area?
800cm^2.
500
Rainbow paints a picture with a pattern. Here is how the pattern is built up:
1 donut: 6 rainbows, 2 donuts: 27 rainbows, 3 donuts: 121.5 rainbows
- Write down a formula for calculating the number of rainbows (R) needed for any number of donuts(D).
- Find the number of donuts (D) and number of rainbows (R) in patterns 4 and 6.
- xn+1 = 4.5xn
- 4D = 546.75 R, 6D = 2,460.375 R.
500
(3 mark question) Prove these triangles are congruent.
Sides AB and FE are the same, as well as sides AC and DE. As well as this, both triangles have an angle of 35 degrees, meaning that they are SAS (side angle side) congruent.
500
Ten adults were asked how many teddies they had. The number was recorded and the results are shown below:
14, 18, 100, 12, 16, 20, 3, 22, 17, 16
(a) Calculate the mean amount.
(b) Calculate the range.
a) Mean = 17 teddies
b) Range = 97 teddies
500
(Non-calculator) I have a large cylindrical container in my garden for collecting water. The area of the base of the container is 1.5 square metres. The height of the container is 1.2 metres. Calculate the volume of the container.
1.8m^3