maths higher tier

How do you write a number as a product of primes? e.g. 20

Use a prime factor tree.

How do you find the LCM of two numbers? e.g. LCM of 20 and 70

1. Write as a product of primes.

2. Use a venn diagram.

3. Multiply ALL the numbers in the venn diagram.

How do you find the HCF of two numbers?

e.g. HCF of 20 and 70

1. Write as a product of primes.

2. Use a venn diagram.

3. Multiply the numbers in the middle.

What formula can you use for compound interest questions?

How do you cube a number? e.g. 5³

Multiply the number by itself and by itself again.

5 x 5 x 5 = 125

How do you work out 3⁴?

3 x 3 x 3 x 3 = 81

How do you cube root a number? e.g. ³√27

Find what number would be cubed to get the number you are cube rooting. ³√27 = 3

What is y³ x y⁵

y⁸ (add the powers)

What is y⁸ ÷ y²

y⁶ (subtract the powers)

What is (y²)⁴

y⁸ (multiply the powers)

How do you estimate a calculation? e.g. 198.7 x 0.203

Round all numbers to 1 significant figure and then calculate.

e.g. 198.7 x 0.203 ≈ 200 x 0.2 = 40

What are the first 10 prime numbers?

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

What are the first 10 square numbers?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

What are the first 5 cube numbers?

1, 8, 27, 64, 125

Positive X Positive

Positive.

e.g. 8 x 3 = 24

Positive X Negative

Negative.

e.g. 5 x -3 = -15

Negative X Positive

Negative.

-10 x 2 = -20

Negative X Negative

Positive.

-4 x -7 = 28

Positive ÷ Positive

Positive.

1000 ÷ 2 = 500

Positive ÷ Negative

Negative.

40 ÷ -4 = -10

Negative ÷ Positive

Negative.

-8 ÷ 4 = -2

Negative ÷ Negative

Positive.

-40 ÷ -8 = 5

How do you find the volume of a triangular prism?

Find the area of the triangle and then multiply by the length.

How do you find the volume of a cylinder?

Find the area of the circle and multiply by the length. V = π x r² x h

How do you find the nth term? e.g. 8, 11, 14, 17 ...

1. Find out what the size is increasing/decreasing by. (in this case 3)

2. Write the times tables for that number below the sequence and also 3n

3. See what you would have to do to 3 times tables to get to the sequence... +5

4. Then the nth term is 3n + 5

What is Pythagoras' Theorem?

a² + b² = c²

where c is the longest side (hypotenuse) and a&b are the shorter sides.

When asked to rotate a shape on a grid, what are the steps?

1. Ask for tracing paper.

2. Place the tracing paper on the grid and trace over the shape AND the centre of rotation.

3. Rotate the shape, the degrees and direction you are asked to - Make sure the centre of rotation stays in the correct place.

4. Draw the shape on the grid.

If the nth term is 4n + 1, what is the 100th term?

401.

4 x 100 + 1 = 401

When solving using trial and improvement to 1 decimal place, if 4.5 is too low and 4.6 is too high, what would you do next?

Try 4.55.

If it is too low, 4.6 is the answer.

If it is too high, 4.5 is the answer.

How do you share £40 in the ratio 2:3

1) Add 2 + 3 = 5

2) £40 ÷ 5 = £8 in one part

3) 2 x £8 = £16

4) 3 x £8 = £24

How do you calculate 'percentage change?'

Change ÷ original x 100

When asked to 'criticise' a question, what are the typical mistakes?

1. No timescale in the question.

2. The question is leading.

3. The catagories overlap.

4. No 'other' or 'more than' option.

Two shapes are similar. What does that mean?

One is an enlargement of the other. The same shape, but different size.

Two shapes are congruent. What does that mean?

They are the same shape and size.

How do you find how many times an outcome is "expected"?

Multiply the probability by the number of trials.

e.g. A dice is rolled 30 times. How many 2's are expected? ¹/₆ x 30 = 5 times.

Bearings should usually have how many figures?

3.

If a bearing is less than 100°, it has a zero in front. e.g. 050°

If a polygon is "regular," what does that mean?

All angles are the same size and all sides are the same length.

What is the sum of the angles in a triangle?

180⁰

What is the sum of the angles in a quadrilateral?

360⁰

What is the sum of the angles in a pentagon?

540⁰

What is the sum of the angles in a hexagon?

720⁰

What does each interior and exterior angle add up to?

180 degrees

What do all exterior angles of a polygon add up to?

360 degrees

What is the size of each interior angle for a regular pentagon?

108 degrees

Show x ≤ 3 on a number line

Show x ≥ 1 on a number line

Show x > 2 on a number line

Show x < 4 on a number line

Solve -x > -5

x < 5

When you multiply/divide an inequality by a negative, the sign will 'switch around.'

Solve the equation 6w + 1 = 4w + 13

How do you find the area of a triangle?

½base times height

How do you find the area of a trapezium?

½(a+b)h

How do you find the area of a parallelogram?

Base times height

What does factorise mean?

Putting the brackets back in.

How do you expand two brackets?

Use FOIL

How do you expand brackets?

Multiply the terms inside, by the term outside.

How do you construct an 'angle bisector?'

1. Put the point of the compass where the lines meet and draw an arc on each line.

2. Put the point of the compass on where the arc meets the line and draw an arc towards the middle of the angle.

3. Repeat

4. Join where the arcs cross to where the lines meet.

How do you construct a 'perpendicular bisector?'

1. Set your compass to OVER half the length of the line.

2. Place the compass point on one end of the line and draw an arc.

3. Repeat for the other end of the line.

4. Draw a line joining where the arcs cross.

How is the bearing of A from B found?

1. Join A and B with a straight line.

2. Draw a North line at B.

3. Measure the clockwise angle from the North line to the line that joins A and B.

What are co-interior angles?

These will always add to 180 degrees.

What are alternate angles?

What are corresponding angles?

What are vertically opposite angles?

When two lines cross, the opposite angles are equal. They are called vertically opposite angles.

How is the gradient of a line worked out?

Method 1 - Use rise ÷ run like in the picture.

Method 2 - go across 1 square and see how many the line goes up.

What does the graph y=2 look like?

What does the graph x=2 look like?

How do you draw the graph y=2x + 1?

1) Draw a xy table, with values of x, 0, 1 and 2.

2) Multiply the values of x by 2 and then add 1.

3) Plot the coordinates on the graph

4) Draw a straight line that passes through the points .... and continues.

What does no correlation look like?

What does negative correlation look like?

What does positive correlation look like?

How do you find the angles when drawing a pie chart?

1. Add up the frequencies.

2. Divide 360 by the total frequency

3. Multiply each frequency by that number.

What is a reciprocal?

You find a reciprocal by "flipping" over a fraction.

A number multiplied by it's reciprocal is 1.

How do you add fractions?

Make both fractions have a common denominator, then add.

How do you divide by a fraction?

Multiply by the reciprocal of the second fraction.

How do you multiply fractions?

Multiply numerators and multiply denominators. Simplify if you can.

How do you calculate the mean?

Add up all the values and divide by how many values there are.

How do you calculate the range?

Highest value subtract smallest value.

How do you find the mode?

It is the most common value (or item)

How do you find the median?

Arrange all the numbers in order, then find the middle value.

How do you find the estimated mean from a frequency table?

1) Find midpoints

2) Find 'fx column' by multiplying midpoints by frequency.

3) Add up the 'fx column' and divide by total frequency

How do you find the circumference of a circle?

π x diameter (or 2πr)

How do you find the area of a circle?

π x r² (πr²)

What is a segment?

The region between a chord and an arc.

What is an arc?

An arc is part of the circumference.

What is a diameter?

A line from one side of the circle to the other, passing through the centre.

What is a radius?

A line from the centre of the circle to the circumference

What is a sector?

The region bound between two radii and the arc.

Some people call it a 'pizza slice.'

What is a chord?

A line joining two points on the circle, but not passing through the centre (that is the diameter).

What is a tangent?

A straight line that touches a circle.

How do you find the area of a sector?

Where θ is the angle and r is the radius.

How do you find the length of an arc?

Where θ is the angle and r is the radius.

What does tessellate mean?

Identical shapes fit together with no gaps.

What does the speed, distance, time triangle look like?

How do you solve reverse percentages questions? e.g. David gets a 5% pay rise and now earns £315 a week. What was his pay before the increase?

105% = £315

1% = £3

100% = £300

How do you write recurring decimals as fractions? e.g. 0.717171...

1. Write x = 0.71717171...

2. Multiply by 10/100/1000 etc to find another number with the recurring section after the decimal point.

3. Subtract and divide.

What is the multiplier to increase by 6%

1.06

What is the multiplier to increase by 20%

1.2 (or 1.20)

What is the multiplier to decrease by 5%

0.95

A car travels 60 miles in 2 hours 30 minutes. What is it's speed?

60 ÷ 2.5 = 24mph

A van travels at 60mph for 3 hours 45 minutes. How far does it travel?

60 x 3.75 = 225 miles