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
Farmer Lulu gets in a fight with some technology and it shrinks her down very small and she has to build a new house. Given that all sides are measured in centimetres, what is the area of her new house?
576cm squared.
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
a) Charlie feeds her cat 2/5 of a can of cat food each day. Work out how many cans are eaten each fortnight. Give your answer as a mixed number and show your working.
b) Non-calculator: If one can of cat food costs £2.75, state how much Charlie spends on cat food each fortnight.
a) 5 and 3/5
b) £16.50
300
A circle has an area of 376cm squared. Write and solve a formula to calculate its radius. Give your answer to two decimal places.
square root (area/pi) = r. Radius = 10.94cm.
300
Rotate RST 275 degrees counter-clockwise around the origin.
R=(15, -5), S=(15, -15), T=(5, -10)
300
300
A circle has a radius of 76cm to the nearest centimetre. State its greatest possible area and circumference. Give your answer to three significant figures.
Area: 104,810,367cm squared.
Circumference: 152.98cm.
400
(Non-calculator) Solve the following:
a) 27% of 46 and 46% of 27.
b) 88% of 130 and 130% of 88.
c) 93% of 72 and 72% of 93.
a) 12.42
b) 114.4
c) 66.96
400
Solve (2x − 3)³ − (x − 4)³
7x³ - 24x^2 +6x +37
400
Shape A has been rotated 180 degrees around the point (0,0), giving it the new coordinates of (0,-3), (3,55), and (3,-3).
400
(Non-calculator) Rainbow and Charlie both travel 90 miles to get to Santa's lab, without any breaks. Rainbow drives and it takes her 1 hour 30 minutes. Charlie cycles and it takes her 7.25 hours. Work out the difference between their average speeds.
Rainbow= 60mph, Charlie = 12.41mph. Difference = 47.59
400
A triangle has angles of x, x and 2x - 20. Find the size of the angles and state the type of triangle it is.
50, 50, 80. Isosceles
500
Solve 1, 2 and 3 on this sheet:
1) x squared / 3x
2) 2am / 20b
3) y^5/ y^2+y-6
500
Farmer Lulu wants to build a new house. Calculate the area of her house according to its description:
A circle sector with diameter 3.16m and central angle 18 degrees, on top of an equilateral triangle with sides 16m each. Give your answer in cm squared and to one decimal place.
1,003,891.2 cm squared.
500
Farmer Lulu goes to see a new movie about aliens. It has a 12 hour running time split up in a 6:8:2 ratio, with breaks between each section. How long does each section last in minutes?
270:360:90.
500
Solve the following:
(x +2)(x+3) + (14/4 + 8/32)
x squared + 5x + 9.75
500
A cone has a radius of 6cm and a height of 46cm. Find its volume and give your answer to three decimal places.
V = 1/3 pi r^2 h. V = 1716.818 cm.