Fractions/ percentages/ ratios
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 radius of a circle with diameter 12.75? Give your answer to two decimal places.
6.38
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: 2y = 6x - 4?
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
Charlie 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
Write an expression to represent the area of a rectangle with sides 2x+4 and x-3.
(2x+4)(x-3) (2x^2-2x-12)
300
Charlie is answering some questions on fractions. Here is one of Charlie's answers:
3/5 + 4/7 = 7/12
Explain her mistake. (1/2 marks)
Charlie hasn't found a common denominator- she has just added together the top numbers and then added together the bottom numbers.
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
Rotate this triangle 90 degrees clockwise around point (0,0).
(-1, -1), (-1, -3), (-2, -1)
300
Enlargement of -0.5
300
a) Write an expression for the perimeter and for the area of a rectangle with sides 2x-5 and 3x+6.
b) (Non-calculator) Taking x to be 15cm, find the value of the perimeter and area of this rectangle.
a) Perimeter: 10x+2, Area: 6x^2 -3x - 30
b) P = 152cm, A = 1275cm^2
400
Rainbow buys a house for £230,000. She goes to a house valuer, who tells her that her house is worth 25% less than the initial price and has an annual depreciation rate of 12%. Find the value of the house after 4 years. Give your answer to three significant figures. [3]
£103,000.
400
A giant ice cream cone is 3 metres tall, with a radius of 12 metres. Calculate the volume. Give your answer to 1 decimal place. (3 marks)
452.4m^3
400
Factorise the following expressions fully:
(a) x^2 - 2
b) 3x^2 - 9x
a) (x+2)(x-2)
b) 3x(3x-3)
400
Calculate the sum of the total interior angles and the size of each interior angle in the shape below.
Total = 1440 degrees, each angle = 144 degrees
400
(Non-calculator) Solve the following equation for x:
4x(8 -2) = 64
x = 2.67
500
Tony makes a six-sided spinner. The spinner has only the numbers 7, 8 and 9 on it. The probability the spinner will land on 7 is greater than the probability that the spinner will land on 8. The probability that the spinner will land on 9 is ⅓ Write how many 7s, 8s and 9s are on the spinner.
3 7s, 1 8, 2 9s
500
Below is a sequence of numbers: 12, 19, 26, 33… Calculate:
(a) the nth term
b) the 8th term
c) the 100th term
a) 7n +5
b) 61
c) 705
500
a) Complete a table from 1-5 for y = 2x-1. [2]
(b) On a grid, plot this line and the line 3y = 3x + 6.
a) (1,1), (2,3), (3, 5), (4, 7), (5, 9).
b) The above for line a, other line should be y = x+6 and have points (1, 7), (2, 8), (3,9), (4,10), (5, 11)
500
Find the smallest possible value of 20a + 10b + c where a, b and c are different positive whole numbers
43.
500
The diagram shows a semicircle of radius 2 cm containing a smaller circle which touches the circumference and midpoint of the diameter of the semicircle as shown. Calculate the fraction of the semicircle that is shaded.
3/4.