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Maths
GCSE

Grade 8/9 question: Point A (0,1) and Point B (10,6) lie on a straight line. Find the equation of the line perpendicular to AB which also intersects B.

Gradient of AB: Change in Y/ Change in X .... (6-1)/(10-0) = 0.5Gradient of line perpendicular to AB: NEGATIVE (flip the sign) RECIPROCAL (flip th...

KR
Answered by Kim R. Maths tutor
4092 Views

The numbers a,b,c and d satisfy the equations: a+2b+3c+4d=k and 4a=3b=2c=d. What is the smallest value of k for which a,b,c and d are positive integers?

The key thing to notice here is that d must have the factors 4,3 and 2. The number 12 is the smallest to contain all those factors. We can then deduce c=6, b=4 and a=3 to get k=77.

DY
Answered by Dean Y. Maths tutor
3318 Views

Find an expression for the nth term of this sequence: 3 - 11 - 19 - 27 - 35 . The nth term of a different sequence is 2n^3 + 3. Write down the first 3 terms of this sequence.

First, the sequence is 3 - 11 - 19 - 27 - 35. Looking at it, we can observe that each element of the sequence is created by adding 8 to the previous. The first term is 3. The second term is 3 + 8...

Answered by Maths tutor
11404 Views

The equation of a curve is y = x^2 + ax + b where a and b are integers. The points (0,-5) and (5,0) lie on the curve. Find the coordinates of the turning point of the curve.

In the equation for our line we have 2 unknowns: a and b. However, we know that the line passes through two known points with x and y coordinates. Therefore, we can begin by substituting in our known x an...

Answered by Maths tutor
22250 Views

Show that (2x^2 + x -15)/(2x^3 +6x^2) * 6x^3/(2x^2 - 11x + 15) simplifies to ax/(x + b) where a and b are integers

As you begin the question, it is important to note that immediately multiplying the two fractions, while would eventually get you to the correct answer would take far too long in an exam scenario. Instead...

JO
Answered by Joe O. Maths tutor
5843 Views

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