Fractions

Algebra questions

Ratio & proportion

Miscellaneous

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

Find the simplified value of each expression:

a) 3 and a half divided by 5 over 4

b) 7/3x + 5/2x

a) 14/5, or 2 4/5

b) 29/6x

300

Rearrange the following equation into the form y = mx+c, and identify the gradient and y-intercept values.

y +2x -5 =0

y = -2x + 5. Gradient =-2, y-intercept = 5

300

The following numbers are in direct proportion. Fill in the missing ones and write an equation to show the relationship.

x =12 y=3

x= 8,y =

x = 16, y =

x = 20, y =5

x = 4,y =

y= 4x. OR x = y/4

300

Farmer Lulu is struggling with her maths homework. She needs to write an equation and an expression for the area of this shape. Can you help her?

Equation: Area = 6x squared + 10x + 4

Expression: 6x squared + 10x + 4

300

y =2x+3

Reasoning: So we could find the gradient and y-intercept/ so the graph can be drawn faster

400

Write the following as a simplified fraction and find x for b. Give any decimal answers to two decimal places.

a) 2x/2 + 3x/12

b) 3x squared/8 + x squared/6 = 96

a) 5x/4

b) 9x squared/24 + 4x squared/ 24 = 96. x = 13.31

400

(Non-calculator question). The double of three times my number add four, is less than 16. Write and solve an equality for this.

6x+8<16. x<1.3 recurring.

400

(Non-calculator question) If a varies directly as b and b = 46 when a = 80.5, find:

a) the formula for b in terms of a

b) the value of b given a = 241.5

c) the value of a given b = 20.125

Give any decimal answers to three decimal places.

a) b = 1.75a

b) b = 138

c) a = 35.219

400

Write the equation for the following line:

y= 3/2 (or 1.5)x - 1

400

Rearrange this equation into the form y = mx + c, and state the gradient and y-intercept of the line.

6y - 18 = 12x

y = 2x + 3

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) Determine the equation for a line with points (3,2) and (6,6) that hits the y axis at point (0,1).

b) Rearrange the following equation so that it matches the format for equations of a straight line graph: 4y - 12 = 24x

Would these two lines look the same on a graph?

a) y = 4/3 (or 1.33)x + 1

b) y = 6x + 3