January 2015 SAT Math Facts
Week of January 5
January 5 – The equation of a horizontal line is always of the form y = #. This is because the y-values of all the
points in a horizontal line are all the same.
January 6 – The equation of a vertical line is always of the form x = #. This is because the x-values of all the
points in a vertical line are all the same.
January 7 – In any triangle, the length of a side is smaller than the sum of the other two sides and greater than
the difference of the other two sides. (This is known as the Triangle Inequality Theorem.)
January 8 – A good formula to know is:
January 9 – 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 =
distance = rate × time
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
Week of January 12
January 12 – If you’re given two points (𝑥1 , 𝑦1 ) (𝑥2 , 𝑦2 ) and you need to find the slope (m) of the line that
connects them, use the formula:
𝑚=
𝑦2 − 𝑦1
𝑥2 − 𝑥1
January 13 – If you’re given the graph of a line and you need to find the slope (m) of the line, choose two
points on the line and use either of these formulas:
𝑚=
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
or 𝑚 =
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦−𝑣𝑎𝑙𝑢𝑒𝑠
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥−𝑣𝑎𝑙𝑢𝑒𝑠
or
𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑦−𝑣𝑎𝑙𝑢𝑒𝑠
𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑥−𝑣𝑎𝑙𝑢𝑒𝑠
January 14 – To find an equation of the line if you’re given the y-intercept (b) and the slope (m), use the slopeintercept formula:
𝑦 = 𝑚𝑥 + 𝑏
January 15 – To find an equation of the line if you’re given a point on the line (𝑥1 , 𝑦1 ) and the slope of the line
(m), use the point-slope formula:
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
January 16 – To find an equation of the line if you’re given two points on the line ((𝑥1 , 𝑦1 ) 𝑎𝑛𝑑 (𝑥2 , 𝑦2 )), first
𝑦2 −𝑦1
use the slope formula to find the slope (
𝑥2 −𝑥1
point in the point-slope formula:
) of the line and then use the slope and either
Week of January 19
January 19 – NO SCHOOL
January 20 – To find percent change, use this formula:
𝑝𝑒𝑟𝑐𝑒𝑛𝑡 𝑐ℎ𝑎𝑛𝑔𝑒 =
𝑛𝑒𝑤 𝑣𝑎𝑙𝑢𝑒 − 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒
× 100
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒
January 21 – If you’re given an average and you need to find the sum of the numbers, multiply the average by
the number of items.
Example: “The average of 5 numbers is 8. What is the sum of the numbers?” ANSWER: 40
January 22 – The total number of degrees in the interior angles of an n-sided polygon is: (n – 2) x 180
January 23 – The number of degrees in any one interior angle of a regular n-sided polygon is:
(n – 2) x 180
𝑛
Week of January 26
January 26 – Other ways to refer to solutions: x-intercepts, zeros, roots.
January 27 – FINAL EXAMS
January 28 – FINAL EXAMS
January 29 – FINAL EXAM MAKE-UP DAY
January 30 – The graph of a quadratic equation is a parabola. If the coefficient of the 𝑥 2 term is positive, the
parabola opens upward. If the coefficient is negative, the parabola opens downward. The most
important aspect is that the parabola has a line of symmetry through the vertex.