OCR J560/01 MATHEMATICS FOUNDATION
PAPER 1 FULL REVISION NOTES WITH CORE
TOPICS AND FORMULAS
◉ How do you convert complex recurring decimals into fractions?
Answer: -Let your decimal be x
-Multiply x to move the non-repeating part past the decimal point, z
-Multiply x to move the recurring part past the decimal point, y
-Minus z from y
-Divide by y - z
◉ What are the two ways of converting fractions into recurring
decimals?
Answer: -Find an equivalent fraction with all nines on the bottom.
The numerator is the recurring part
-Divide it
◉ How can you estimate a square root?
Answer: -Find two square numbers either side of the number your
given
-Decide which number it's closest to
-Estimate the digit after the decimal point
,◉ How do you multiply or divide standard form?
Answer: -Rearrange to put the front numbers and powers of ten
together
-Multiply or divide the front numbers
-Multiply or divide the powers of 10
-Keep the answer in standard form
◉ How do you add or subtract standard form?
Answer: -Make the powers of ten the same, there is now only one of
them
-Add or subtract front numbers
-Keep the answer in standard form
◉ What does a negative power do?
Answer: -Negative reciprocal
-Denominator to the power of the indices
◉ What does a fractional power do?
Answer: -Base rooted by the denominator of the fraction (1/2 is
square root)
-Answer to the power of the numerator (3/2 would be square root,
then cubed)
,◉ How do you rationalise the denominator of a surd with
denominator a + √b?
Answer: -Multiply top and bottom by a - √b
-Essentially, change the sign in front of the surd
◉ If the discriminant in the quadratic formula is greater than 0, how
many roots are there?
Answer: 2
◉ If the discriminant in the quadratic formula is 0, how many roots
are there?
Answer: 1
◉ If the discriminant in the quadratic formula is less than 0, how
many roots are there?
Answer: 0
◉ If you get (x + m)² + n when completing the square, what is the
turning point?
Answer: (-m, n)
◉ How do you complete the square when a > 1?
, Answer: -Divide by a factor of a
-Write out a(x + m)²
-Multiply out to figure out what n should be
-Add n
-a(x + m)² + n
◉ How do you find the nth term of a quadratic sequence?
Answer: -Find the difference between each term
-Find the difference between the differences
-Divide this value by 2 to get the coefficient of n², giving you an²
-Subtract an² from each term to get a linear sequence
-Add the nth term of this linear sequence to an²
◉ What can you do if you know the interval that contains a solution
to an equation?
Answer: An iterative method like the decimal search method
◉ How do you solve a quadratic simultaneous equation?
Answer: -Rearrange the quadratic to get the non-quadratic unknown
on its own
-Substitute the quadratic into the other equation
-Rearrange to get a quadratic equation and solve
PAPER 1 FULL REVISION NOTES WITH CORE
TOPICS AND FORMULAS
◉ How do you convert complex recurring decimals into fractions?
Answer: -Let your decimal be x
-Multiply x to move the non-repeating part past the decimal point, z
-Multiply x to move the recurring part past the decimal point, y
-Minus z from y
-Divide by y - z
◉ What are the two ways of converting fractions into recurring
decimals?
Answer: -Find an equivalent fraction with all nines on the bottom.
The numerator is the recurring part
-Divide it
◉ How can you estimate a square root?
Answer: -Find two square numbers either side of the number your
given
-Decide which number it's closest to
-Estimate the digit after the decimal point
,◉ How do you multiply or divide standard form?
Answer: -Rearrange to put the front numbers and powers of ten
together
-Multiply or divide the front numbers
-Multiply or divide the powers of 10
-Keep the answer in standard form
◉ How do you add or subtract standard form?
Answer: -Make the powers of ten the same, there is now only one of
them
-Add or subtract front numbers
-Keep the answer in standard form
◉ What does a negative power do?
Answer: -Negative reciprocal
-Denominator to the power of the indices
◉ What does a fractional power do?
Answer: -Base rooted by the denominator of the fraction (1/2 is
square root)
-Answer to the power of the numerator (3/2 would be square root,
then cubed)
,◉ How do you rationalise the denominator of a surd with
denominator a + √b?
Answer: -Multiply top and bottom by a - √b
-Essentially, change the sign in front of the surd
◉ If the discriminant in the quadratic formula is greater than 0, how
many roots are there?
Answer: 2
◉ If the discriminant in the quadratic formula is 0, how many roots
are there?
Answer: 1
◉ If the discriminant in the quadratic formula is less than 0, how
many roots are there?
Answer: 0
◉ If you get (x + m)² + n when completing the square, what is the
turning point?
Answer: (-m, n)
◉ How do you complete the square when a > 1?
, Answer: -Divide by a factor of a
-Write out a(x + m)²
-Multiply out to figure out what n should be
-Add n
-a(x + m)² + n
◉ How do you find the nth term of a quadratic sequence?
Answer: -Find the difference between each term
-Find the difference between the differences
-Divide this value by 2 to get the coefficient of n², giving you an²
-Subtract an² from each term to get a linear sequence
-Add the nth term of this linear sequence to an²
◉ What can you do if you know the interval that contains a solution
to an equation?
Answer: An iterative method like the decimal search method
◉ How do you solve a quadratic simultaneous equation?
Answer: -Rearrange the quadratic to get the non-quadratic unknown
on its own
-Substitute the quadratic into the other equation
-Rearrange to get a quadratic equation and solve
